TSTP Solution File: SEU337+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU337+2 : TPTP v8.1.0. Released v3.3.0.
% 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 09:19:07 EDT 2022
% Result : Theorem 0.28s 1.47s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 61 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 65 ( 26 ~; 24 |; 4 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t17_tops_2,conjecture,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t17_tops_2) ).
fof(t16_tops_2,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( closed_subsets(X2,X1)
<=> open_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t16_tops_2) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',involutiveness_k7_setfam_1) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k7_setfam_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t17_tops_2]) ).
fof(c_0_5,lemma,
! [X3,X4] :
( ( ~ closed_subsets(X4,X3)
| open_subsets(complements_of_subsets(the_carrier(X3),X4),X3)
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ top_str(X3) )
& ( ~ open_subsets(complements_of_subsets(the_carrier(X3),X4),X3)
| closed_subsets(X4,X3)
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ top_str(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_tops_2])])])])])]) ).
fof(c_0_6,negated_conjecture,
( top_str(esk1_0)
& element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
& ( ~ open_subsets(esk2_0,esk1_0)
| ~ closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0) )
& ( open_subsets(esk2_0,esk1_0)
| closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
cnf(c_0_7,lemma,
( open_subsets(complements_of_subsets(the_carrier(X1),X2),X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ closed_subsets(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0)
| open_subsets(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| complements_of_subsets(X3,complements_of_subsets(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(c_0_11,negated_conjecture,
( open_subsets(complements_of_subsets(the_carrier(esk1_0),complements_of_subsets(the_carrier(esk1_0),esk2_0)),esk1_0)
| open_subsets(esk2_0,esk1_0)
| ~ element(complements_of_subsets(the_carrier(esk1_0),esk2_0),powerset(powerset(the_carrier(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
cnf(c_0_12,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
element(esk2_0,powerset(powerset(the_carrier(esk1_0)))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( ~ closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0)
| ~ open_subsets(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,lemma,
( closed_subsets(X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ open_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
( open_subsets(esk2_0,esk1_0)
| ~ element(complements_of_subsets(the_carrier(esk1_0),esk2_0),powerset(powerset(the_carrier(esk1_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
( ~ open_subsets(complements_of_subsets(the_carrier(esk1_0),complements_of_subsets(the_carrier(esk1_0),esk2_0)),esk1_0)
| ~ element(complements_of_subsets(the_carrier(esk1_0),esk2_0),powerset(powerset(the_carrier(esk1_0)))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_9])]),c_0_16]) ).
fof(c_0_18,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(complements_of_subsets(X3,X4),powerset(powerset(X3))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
cnf(c_0_19,negated_conjecture,
~ element(complements_of_subsets(the_carrier(esk1_0),esk2_0),powerset(powerset(the_carrier(esk1_0)))),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_12]),c_0_13])]),c_0_16]) ).
cnf(c_0_20,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU337+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 20 04:50:41 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.28/1.47 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.28/1.47 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.28/1.47 # Preprocessing time : 0.106 s
% 0.28/1.47
% 0.28/1.47 # Proof found!
% 0.28/1.47 # SZS status Theorem
% 0.28/1.47 # SZS output start CNFRefutation
% See solution above
% 0.28/1.47 # Proof object total steps : 22
% 0.28/1.47 # Proof object clause steps : 13
% 0.28/1.47 # Proof object formula steps : 9
% 0.28/1.47 # Proof object conjectures : 12
% 0.28/1.47 # Proof object clause conjectures : 9
% 0.28/1.47 # Proof object formula conjectures : 3
% 0.28/1.47 # Proof object initial clauses used : 8
% 0.28/1.47 # Proof object initial formulas used : 4
% 0.28/1.47 # Proof object generating inferences : 5
% 0.28/1.47 # Proof object simplifying inferences : 12
% 0.28/1.47 # Training examples: 0 positive, 0 negative
% 0.28/1.47 # Parsed axioms : 556
% 0.28/1.47 # Removed by relevancy pruning/SinE : 455
% 0.28/1.47 # Initial clauses : 1188
% 0.28/1.47 # Removed in clause preprocessing : 2
% 0.28/1.47 # Initial clauses in saturation : 1186
% 0.28/1.47 # Processed clauses : 1196
% 0.28/1.47 # ...of these trivial : 1
% 0.28/1.47 # ...subsumed : 43
% 0.28/1.47 # ...remaining for further processing : 1152
% 0.28/1.47 # Other redundant clauses eliminated : 261
% 0.28/1.47 # Clauses deleted for lack of memory : 0
% 0.28/1.47 # Backward-subsumed : 1
% 0.28/1.47 # Backward-rewritten : 23
% 0.28/1.47 # Generated clauses : 18242
% 0.28/1.47 # ...of the previous two non-trivial : 18187
% 0.28/1.47 # Contextual simplify-reflections : 12
% 0.28/1.47 # Paramodulations : 17861
% 0.28/1.47 # Factorizations : 2
% 0.28/1.47 # Equation resolutions : 416
% 0.28/1.47 # Current number of processed clauses : 939
% 0.28/1.47 # Positive orientable unit clauses : 17
% 0.28/1.47 # Positive unorientable unit clauses: 0
% 0.28/1.47 # Negative unit clauses : 2
% 0.28/1.47 # Non-unit-clauses : 920
% 0.28/1.47 # Current number of unprocessed clauses: 17301
% 0.28/1.47 # ...number of literals in the above : 133364
% 0.28/1.47 # Current number of archived formulas : 0
% 0.28/1.47 # Current number of archived clauses : 24
% 0.28/1.47 # Clause-clause subsumption calls (NU) : 331602
% 0.28/1.47 # Rec. Clause-clause subsumption calls : 11680
% 0.28/1.47 # Non-unit clause-clause subsumptions : 56
% 0.28/1.47 # Unit Clause-clause subsumption calls : 1252
% 0.28/1.47 # Rewrite failures with RHS unbound : 0
% 0.28/1.47 # BW rewrite match attempts : 1
% 0.28/1.47 # BW rewrite match successes : 1
% 0.28/1.47 # Condensation attempts : 0
% 0.28/1.47 # Condensation successes : 0
% 0.28/1.47 # Termbank termtop insertions : 555826
% 0.28/1.47
% 0.28/1.47 # -------------------------------------------------
% 0.28/1.47 # User time : 0.777 s
% 0.28/1.47 # System time : 0.020 s
% 0.28/1.47 # Total time : 0.797 s
% 0.28/1.47 # Maximum resident set size: 24964 pages
%------------------------------------------------------------------------------