TSTP Solution File: SET877+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET877+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 00:55:09 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 : 18 ( 8 unt; 0 def)
% Number of atoms : 40 ( 29 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 36 ( 14 ~; 13 |; 4 &)
% ( 2 <=>; 3 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 3 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t18_zfmisc_1,conjecture,
! [X1,X2] :
( set_intersection2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t18_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k3_xboole_0) ).
fof(l30_zfmisc_1,axiom,
! [X1,X2] :
( set_intersection2(X1,singleton(X2)) = singleton(X2)
=> in(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l30_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( set_intersection2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t18_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
( set_intersection2(singleton(esk1_0),singleton(esk2_0)) = singleton(esk1_0)
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_7,plain,
! [X3,X4] :
( set_intersection2(X3,singleton(X4)) != singleton(X4)
| in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l30_zfmisc_1])]) ).
cnf(c_0_8,negated_conjecture,
set_intersection2(singleton(esk1_0),singleton(esk2_0)) = singleton(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,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])])])])])])]) ).
cnf(c_0_11,plain,
( in(X1,X2)
| set_intersection2(X2,singleton(X1)) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
set_intersection2(singleton(esk2_0),singleton(esk1_0)) = singleton(esk1_0),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
in(esk1_0,singleton(esk2_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( X1 = esk1_0
| singleton(esk2_0) != singleton(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n007.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 : Sun Jul 10 19:32:32 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 : 18
% 0.24/1.41 # Proof object clause steps : 9
% 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 : 5
% 0.24/1.41 # Proof object initial formulas used : 4
% 0.24/1.41 # Proof object generating inferences : 3
% 0.24/1.41 # Proof object simplifying inferences : 2
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 8
% 0.24/1.41 # Removed by relevancy pruning/SinE : 2
% 0.24/1.41 # Initial clauses : 10
% 0.24/1.41 # Removed in clause preprocessing : 0
% 0.24/1.41 # Initial clauses in saturation : 10
% 0.24/1.41 # Processed clauses : 19
% 0.24/1.41 # ...of these trivial : 0
% 0.24/1.41 # ...subsumed : 1
% 0.24/1.41 # ...remaining for further processing : 18
% 0.24/1.41 # Other redundant clauses eliminated : 1
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 0
% 0.24/1.41 # Backward-rewritten : 1
% 0.24/1.41 # Generated clauses : 24
% 0.24/1.41 # ...of the previous two non-trivial : 19
% 0.24/1.41 # Contextual simplify-reflections : 0
% 0.24/1.41 # Paramodulations : 21
% 0.24/1.41 # Factorizations : 0
% 0.24/1.41 # Equation resolutions : 3
% 0.24/1.41 # Current number of processed clauses : 16
% 0.24/1.41 # Positive orientable unit clauses : 4
% 0.24/1.41 # Positive unorientable unit clauses: 1
% 0.24/1.41 # Negative unit clauses : 2
% 0.24/1.41 # Non-unit-clauses : 9
% 0.24/1.41 # Current number of unprocessed clauses: 10
% 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 : 1
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 9
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 9
% 0.24/1.41 # Non-unit clause-clause subsumptions : 1
% 0.24/1.41 # Unit Clause-clause subsumption calls : 2
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 4
% 0.24/1.41 # BW rewrite match successes : 4
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 658
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.014 s
% 0.24/1.41 # System time : 0.002 s
% 0.24/1.41 # Total time : 0.016 s
% 0.24/1.41 # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------