TSTP Solution File: SET882+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n007.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 00:55:11 EDT 2022
% Result : Theorem 0.24s 1.41s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 61 ( 39 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 67 ( 28 ~; 26 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 6 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_zfmisc_1,conjecture,
! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t23_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).
fof(l39_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l39_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
inference(assume_negation,[status(cth)],[t23_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,negated_conjecture,
( esk1_0 != esk2_0
& set_difference(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)) != singleton(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( ~ in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( in(X5,X6)
| X4 = X5
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( ~ in(X5,X6)
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) )
& ( X4 != X5
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = 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)],[inference(fof_simplification,[status(thm)],[l39_zfmisc_1])])])])])]) ).
cnf(c_0_9,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
set_difference(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)) != singleton(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| in(X1,X3)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| X2 != singleton(X1) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
set_difference(unordered_pair(esk2_0,esk1_0),singleton(esk2_0)) != singleton(esk1_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X2)
| in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_16,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
in(esk1_0,singleton(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
( X1 = esk1_0
| singleton(esk2_0) != singleton(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 08:35:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41 # Preprocessing time : 0.015 s
% 0.24/1.41
% 0.24/1.41 # Proof found!
% 0.24/1.41 # SZS status Theorem
% 0.24/1.41 # SZS output start CNFRefutation
% See solution above
% 0.24/1.41 # Proof object total steps : 22
% 0.24/1.41 # Proof object clause steps : 13
% 0.24/1.41 # Proof object formula steps : 9
% 0.24/1.41 # Proof object conjectures : 9
% 0.24/1.41 # Proof object clause conjectures : 6
% 0.24/1.41 # Proof object formula conjectures : 3
% 0.24/1.41 # Proof object initial clauses used : 6
% 0.24/1.41 # Proof object initial formulas used : 4
% 0.24/1.41 # Proof object generating inferences : 5
% 0.24/1.41 # Proof object simplifying inferences : 5
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 7
% 0.24/1.41 # Removed by relevancy pruning/SinE : 2
% 0.24/1.41 # Initial clauses : 12
% 0.24/1.41 # Removed in clause preprocessing : 0
% 0.24/1.41 # Initial clauses in saturation : 12
% 0.24/1.41 # Processed clauses : 38
% 0.24/1.41 # ...of these trivial : 0
% 0.24/1.41 # ...subsumed : 11
% 0.24/1.41 # ...remaining for further processing : 27
% 0.24/1.41 # Other redundant clauses eliminated : 2
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 0
% 0.24/1.41 # Backward-rewritten : 2
% 0.24/1.41 # Generated clauses : 43
% 0.24/1.41 # ...of the previous two non-trivial : 34
% 0.24/1.41 # Contextual simplify-reflections : 3
% 0.24/1.41 # Paramodulations : 37
% 0.24/1.41 # Factorizations : 0
% 0.24/1.41 # Equation resolutions : 6
% 0.24/1.41 # Current number of processed clauses : 23
% 0.24/1.41 # Positive orientable unit clauses : 2
% 0.24/1.41 # Positive unorientable unit clauses: 1
% 0.24/1.41 # Negative unit clauses : 3
% 0.24/1.41 # Non-unit-clauses : 17
% 0.24/1.41 # Current number of unprocessed clauses: 8
% 0.24/1.41 # ...number of literals in the above : 23
% 0.24/1.41 # Current number of archived formulas : 0
% 0.24/1.41 # Current number of archived clauses : 2
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 89
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 82
% 0.24/1.41 # Non-unit clause-clause subsumptions : 14
% 0.24/1.41 # Unit Clause-clause subsumption calls : 5
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 5
% 0.24/1.41 # BW rewrite match successes : 5
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 1010
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.015 s
% 0.24/1.41 # System time : 0.002 s
% 0.24/1.41 # Total time : 0.017 s
% 0.24/1.41 # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------