TSTP Solution File: SET931+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 00:55:33 EDT 2022
% Result : Theorem 0.25s 1.43s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 6 unt; 0 def)
% Number of atoms : 90 ( 72 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 113 ( 50 ~; 41 |; 18 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 9 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t75_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t75_zfmisc_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t37_xboole_1) ).
fof(l46_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l46_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
inference(assume_negation,[status(cth)],[t75_zfmisc_1]) ).
fof(c_0_4,plain,
! [X3,X4,X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])])])]) ).
fof(c_0_5,negated_conjecture,
( ( esk1_0 != empty_set
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( esk1_0 != singleton(esk2_0)
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( esk1_0 != singleton(esk3_0)
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( esk1_0 != unordered_pair(esk2_0,esk3_0)
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set )
& ( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0)
| esk1_0 = singleton(esk3_0)
| esk1_0 = unordered_pair(esk2_0,esk3_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_6,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( ~ subset(X4,unordered_pair(X5,X6))
| X4 = empty_set
| X4 = singleton(X5)
| X4 = singleton(X6)
| X4 = unordered_pair(X5,X6) )
& ( X4 != empty_set
| subset(X4,unordered_pair(X5,X6)) )
& ( X4 != singleton(X5)
| subset(X4,unordered_pair(X5,X6)) )
& ( X4 != singleton(X6)
| subset(X4,unordered_pair(X5,X6)) )
& ( X4 != unordered_pair(X5,X6)
| subset(X4,unordered_pair(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l46_zfmisc_1])])])])]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( esk1_0 = unordered_pair(esk2_0,esk3_0)
| esk1_0 = singleton(esk3_0)
| esk1_0 = singleton(esk2_0)
| esk1_0 = empty_set
| set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( subset(X1,unordered_pair(X2,X3))
| X1 != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( X1 = unordered_pair(X2,X3)
| X1 = singleton(X3)
| X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
subset(esk1_0,unordered_pair(esk2_0,esk3_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10]),c_0_11]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( unordered_pair(esk2_0,esk3_0) = esk1_0
| singleton(esk3_0) = esk1_0
| singleton(esk2_0) = esk1_0
| esk1_0 = empty_set ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
esk1_0 != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14])]) ).
cnf(c_0_19,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != singleton(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != unordered_pair(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( set_difference(esk1_0,unordered_pair(esk2_0,esk3_0)) != empty_set
| esk1_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( unordered_pair(esk2_0,esk3_0) = esk1_0
| singleton(esk2_0) = esk1_0
| singleton(esk3_0) = esk1_0 ),
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
singleton(esk2_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_14])]) ).
cnf(c_0_24,negated_conjecture,
unordered_pair(esk2_0,esk3_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_14])]) ).
cnf(c_0_25,negated_conjecture,
singleton(esk3_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_14])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 21:59:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.25/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.43 # Preprocessing time : 0.015 s
% 0.25/1.43
% 0.25/1.43 # Proof found!
% 0.25/1.43 # SZS status Theorem
% 0.25/1.43 # SZS output start CNFRefutation
% See solution above
% 0.25/1.43 # Proof object total steps : 27
% 0.25/1.43 # Proof object clause steps : 20
% 0.25/1.43 # Proof object formula steps : 7
% 0.25/1.43 # Proof object conjectures : 16
% 0.25/1.43 # Proof object clause conjectures : 13
% 0.25/1.43 # Proof object formula conjectures : 3
% 0.25/1.43 # Proof object initial clauses used : 12
% 0.25/1.43 # Proof object initial formulas used : 3
% 0.25/1.43 # Proof object generating inferences : 6
% 0.25/1.43 # Proof object simplifying inferences : 16
% 0.25/1.43 # Training examples: 0 positive, 0 negative
% 0.25/1.43 # Parsed axioms : 8
% 0.25/1.43 # Removed by relevancy pruning/SinE : 0
% 0.25/1.43 # Initial clauses : 17
% 0.25/1.43 # Removed in clause preprocessing : 0
% 0.25/1.43 # Initial clauses in saturation : 17
% 0.25/1.43 # Processed clauses : 27
% 0.25/1.43 # ...of these trivial : 0
% 0.25/1.43 # ...subsumed : 2
% 0.25/1.43 # ...remaining for further processing : 24
% 0.25/1.43 # Other redundant clauses eliminated : 0
% 0.25/1.43 # Clauses deleted for lack of memory : 0
% 0.25/1.43 # Backward-subsumed : 1
% 0.25/1.43 # Backward-rewritten : 0
% 0.25/1.43 # Generated clauses : 27
% 0.25/1.43 # ...of the previous two non-trivial : 18
% 0.25/1.43 # Contextual simplify-reflections : 4
% 0.25/1.43 # Paramodulations : 25
% 0.25/1.43 # Factorizations : 0
% 0.25/1.43 # Equation resolutions : 0
% 0.25/1.43 # Current number of processed clauses : 21
% 0.25/1.43 # Positive orientable unit clauses : 4
% 0.25/1.43 # Positive unorientable unit clauses: 1
% 0.25/1.43 # Negative unit clauses : 5
% 0.25/1.43 # Non-unit-clauses : 11
% 0.25/1.43 # Current number of unprocessed clauses: 8
% 0.25/1.43 # ...number of literals in the above : 22
% 0.25/1.43 # Current number of archived formulas : 0
% 0.25/1.43 # Current number of archived clauses : 3
% 0.25/1.43 # Clause-clause subsumption calls (NU) : 19
% 0.25/1.43 # Rec. Clause-clause subsumption calls : 14
% 0.25/1.43 # Non-unit clause-clause subsumptions : 7
% 0.25/1.43 # Unit Clause-clause subsumption calls : 13
% 0.25/1.43 # Rewrite failures with RHS unbound : 0
% 0.25/1.43 # BW rewrite match attempts : 2
% 0.25/1.43 # BW rewrite match successes : 2
% 0.25/1.43 # Condensation attempts : 0
% 0.25/1.43 # Condensation successes : 0
% 0.25/1.43 # Termbank termtop insertions : 1003
% 0.25/1.43
% 0.25/1.43 # -------------------------------------------------
% 0.25/1.43 # User time : 0.013 s
% 0.25/1.43 # System time : 0.003 s
% 0.25/1.43 # Total time : 0.016 s
% 0.25/1.43 # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------