TSTP Solution File: SEU323+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 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 09:18:59 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 74 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 80 ( 33 ~; 26 |; 11 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t51_tops_1,conjecture,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t51_tops_1) ).
fof(d1_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tops_1) ).
fof(fc3_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& closed_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(subset_complement(the_carrier(X1),X2),X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc3_tops_1) ).
fof(fc2_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> closed_subset(topstr_closure(X1,X2),X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc2_tops_1) ).
fof(dt_k6_pre_topc,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k6_pre_topc) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k3_subset_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
inference(assume_negation,[status(cth)],[t51_tops_1]) ).
fof(c_0_7,negated_conjecture,
( topological_space(esk1_0)
& top_str(esk1_0)
& element(esk2_0,powerset(the_carrier(esk1_0)))
& ~ open_subset(interior(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_6])])])])]) ).
fof(c_0_8,plain,
! [X3,X4] :
( ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| interior(X3,X4) = subset_complement(the_carrier(X3),topstr_closure(X3,subset_complement(the_carrier(X3),X4))) ),
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)],[d1_tops_1])])])])]) ).
cnf(c_0_9,negated_conjecture,
~ open_subset(interior(esk1_0,esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X3,X4] :
( ~ topological_space(X3)
| ~ top_str(X3)
| ~ closed_subset(X4,X3)
| ~ element(X4,powerset(the_carrier(X3)))
| open_subset(subset_complement(the_carrier(X3),X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_tops_1])]) ).
cnf(c_0_14,negated_conjecture,
~ open_subset(subset_complement(the_carrier(esk1_0),topstr_closure(esk1_0,subset_complement(the_carrier(esk1_0),esk2_0))),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]) ).
cnf(c_0_15,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_17,plain,
! [X3,X4] :
( ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| closed_subset(topstr_closure(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_tops_1])]) ).
cnf(c_0_18,negated_conjecture,
( ~ element(topstr_closure(esk1_0,subset_complement(the_carrier(esk1_0),esk2_0)),powerset(the_carrier(esk1_0)))
| ~ closed_subset(topstr_closure(esk1_0,subset_complement(the_carrier(esk1_0),esk2_0)),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12]),c_0_16])]) ).
cnf(c_0_19,plain,
( closed_subset(topstr_closure(X1,X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X3,X4] :
( ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| element(topstr_closure(X3,X4),powerset(the_carrier(X3))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pre_topc])]) ).
cnf(c_0_21,negated_conjecture,
( ~ element(topstr_closure(esk1_0,subset_complement(the_carrier(esk1_0),esk2_0)),powerset(the_carrier(esk1_0)))
| ~ element(subset_complement(the_carrier(esk1_0),esk2_0),powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]),c_0_16])]) ).
cnf(c_0_22,plain,
( element(topstr_closure(X1,X2),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| element(subset_complement(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
cnf(c_0_24,negated_conjecture,
~ element(subset_complement(the_carrier(esk1_0),esk2_0),powerset(the_carrier(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_12])]) ).
cnf(c_0_25,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 12:06:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41 # Preprocessing time : 0.016 s
% 0.23/1.41
% 0.23/1.41 # Proof found!
% 0.23/1.41 # SZS status Theorem
% 0.23/1.41 # SZS output start CNFRefutation
% See solution above
% 0.23/1.41 # Proof object total steps : 27
% 0.23/1.41 # Proof object clause steps : 14
% 0.23/1.41 # Proof object formula steps : 13
% 0.23/1.41 # Proof object conjectures : 12
% 0.23/1.41 # Proof object clause conjectures : 9
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 9
% 0.23/1.41 # Proof object initial formulas used : 6
% 0.23/1.41 # Proof object generating inferences : 5
% 0.23/1.41 # Proof object simplifying inferences : 13
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 21
% 0.23/1.41 # Removed by relevancy pruning/SinE : 8
% 0.23/1.41 # Initial clauses : 18
% 0.23/1.41 # Removed in clause preprocessing : 0
% 0.23/1.41 # Initial clauses in saturation : 18
% 0.23/1.41 # Processed clauses : 25
% 0.23/1.41 # ...of these trivial : 0
% 0.23/1.41 # ...subsumed : 0
% 0.23/1.41 # ...remaining for further processing : 25
% 0.23/1.41 # Other redundant clauses eliminated : 0
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 0
% 0.23/1.41 # Backward-rewritten : 0
% 0.23/1.41 # Generated clauses : 11
% 0.23/1.41 # ...of the previous two non-trivial : 9
% 0.23/1.41 # Contextual simplify-reflections : 2
% 0.23/1.41 # Paramodulations : 11
% 0.23/1.41 # Factorizations : 0
% 0.23/1.41 # Equation resolutions : 0
% 0.23/1.41 # Current number of processed clauses : 25
% 0.23/1.41 # Positive orientable unit clauses : 5
% 0.23/1.41 # Positive unorientable unit clauses: 0
% 0.23/1.41 # Negative unit clauses : 3
% 0.23/1.41 # Non-unit-clauses : 17
% 0.23/1.41 # Current number of unprocessed clauses: 2
% 0.23/1.41 # ...number of literals in the above : 12
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 0
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 44
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 31
% 0.23/1.41 # Non-unit clause-clause subsumptions : 2
% 0.23/1.41 # Unit Clause-clause subsumption calls : 2
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 0
% 0.23/1.41 # BW rewrite match successes : 0
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 1668
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.016 s
% 0.23/1.41 # System time : 0.002 s
% 0.23/1.41 # Total time : 0.018 s
% 0.23/1.41 # Maximum resident set size: 2944 pages
%------------------------------------------------------------------------------