TSTP Solution File: SEU341+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU341+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n025.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 09:19:09 EDT 2022
% Result : Theorem 0.26s 1.44s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 127 ( 11 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 149 ( 58 ~; 48 |; 20 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_connsp_2,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t5_connsp_2) ).
fof(d1_connsp_2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_connsp_2) ).
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(t52_pre_topc,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( ( closed_subset(X2,X1)
=> topstr_closure(X1,X2) = X2 )
& ( ( topological_space(X1)
& topstr_closure(X1,X2) = X2 )
=> closed_subset(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t52_pre_topc) ).
fof(t30_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t30_tops_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',involutiveness_k3_subset_1) ).
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_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t5_connsp_2]) ).
fof(c_0_8,negated_conjecture,
( ~ empty_carrier(esk1_0)
& topological_space(esk1_0)
& top_str(esk1_0)
& element(esk2_0,powerset(the_carrier(esk1_0)))
& element(esk3_0,the_carrier(esk1_0))
& open_subset(esk2_0,esk1_0)
& in(esk3_0,esk2_0)
& ~ point_neighbourhood(esk2_0,esk1_0,esk3_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)],[inference(fof_simplification,[status(thm)],[c_0_7])])])])])]) ).
fof(c_0_9,plain,
! [X4,X5,X6] :
( ( ~ point_neighbourhood(X6,X4,X5)
| in(X5,interior(X4,X6))
| ~ element(X6,powerset(the_carrier(X4)))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ topological_space(X4)
| ~ top_str(X4) )
& ( ~ in(X5,interior(X4,X6))
| point_neighbourhood(X6,X4,X5)
| ~ element(X6,powerset(the_carrier(X4)))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ topological_space(X4)
| ~ top_str(X4) ) ),
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)],[inference(fof_simplification,[status(thm)],[d1_connsp_2])])])])])])]) ).
cnf(c_0_10,negated_conjecture,
~ point_neighbourhood(esk2_0,esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( empty_carrier(X1)
| point_neighbourhood(X3,X1,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ in(X2,interior(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
element(esk3_0,the_carrier(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_17,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_18,negated_conjecture,
~ in(esk3_0,interior(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_19,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_17]) ).
fof(c_0_20,lemma,
! [X3,X4] :
( ( ~ closed_subset(X4,X3)
| topstr_closure(X3,X4) = X4
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) )
& ( ~ topological_space(X3)
| topstr_closure(X3,X4) != X4
| closed_subset(X4,X3)
| ~ element(X4,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)],[t52_pre_topc])])])])])]) ).
fof(c_0_21,lemma,
! [X3,X4] :
( ( ~ open_subset(X4,X3)
| closed_subset(subset_complement(the_carrier(X3),X4),X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) )
& ( ~ closed_subset(subset_complement(the_carrier(X3),X4),X3)
| open_subset(X4,X3)
| ~ element(X4,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)],[t30_tops_1])])])])])]) ).
cnf(c_0_22,negated_conjecture,
~ in(esk3_0,subset_complement(the_carrier(esk1_0),topstr_closure(esk1_0,subset_complement(the_carrier(esk1_0),esk2_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_13]),c_0_14])]) ).
cnf(c_0_23,lemma,
( topstr_closure(X1,X2) = X2
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,lemma,
( closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ open_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
open_subset(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,lemma,
( ~ closed_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0)
| ~ element(subset_complement(the_carrier(esk1_0),esk2_0),powerset(the_carrier(esk1_0)))
| ~ in(esk3_0,subset_complement(the_carrier(esk1_0),subset_complement(the_carrier(esk1_0),esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13])]) ).
cnf(c_0_27,negated_conjecture,
closed_subset(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_24,c_0_25]),c_0_13]),c_0_14])]) ).
fof(c_0_28,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,subset_complement(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
cnf(c_0_29,lemma,
( ~ element(subset_complement(the_carrier(esk1_0),esk2_0),powerset(the_carrier(esk1_0)))
| ~ in(esk3_0,subset_complement(the_carrier(esk1_0),subset_complement(the_carrier(esk1_0),esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_30,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_32,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_33,lemma,
~ 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_29,c_0_30]),c_0_31]),c_0_14])]) ).
cnf(c_0_34,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU341+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : run_ET %s %d
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 20 00:20:44 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.26/1.44 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.44 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.44 # Preprocessing time : 0.072 s
% 0.26/1.44
% 0.26/1.44 # Proof found!
% 0.26/1.44 # SZS status Theorem
% 0.26/1.44 # SZS output start CNFRefutation
% See solution above
% 0.26/1.44 # Proof object total steps : 36
% 0.26/1.44 # Proof object clause steps : 21
% 0.26/1.44 # Proof object formula steps : 15
% 0.26/1.44 # Proof object conjectures : 14
% 0.26/1.44 # Proof object clause conjectures : 11
% 0.26/1.44 # Proof object formula conjectures : 3
% 0.26/1.44 # Proof object initial clauses used : 14
% 0.26/1.44 # Proof object initial formulas used : 7
% 0.26/1.44 # Proof object generating inferences : 6
% 0.26/1.44 # Proof object simplifying inferences : 21
% 0.26/1.44 # Training examples: 0 positive, 0 negative
% 0.26/1.44 # Parsed axioms : 573
% 0.26/1.44 # Removed by relevancy pruning/SinE : 472
% 0.26/1.44 # Initial clauses : 585
% 0.26/1.44 # Removed in clause preprocessing : 1
% 0.26/1.44 # Initial clauses in saturation : 584
% 0.26/1.44 # Processed clauses : 615
% 0.26/1.44 # ...of these trivial : 1
% 0.26/1.44 # ...subsumed : 37
% 0.26/1.44 # ...remaining for further processing : 577
% 0.26/1.44 # Other redundant clauses eliminated : 116
% 0.26/1.44 # Clauses deleted for lack of memory : 0
% 0.26/1.44 # Backward-subsumed : 0
% 0.26/1.44 # Backward-rewritten : 9
% 0.26/1.44 # Generated clauses : 3841
% 0.26/1.44 # ...of the previous two non-trivial : 3757
% 0.26/1.44 # Contextual simplify-reflections : 44
% 0.26/1.44 # Paramodulations : 3675
% 0.26/1.44 # Factorizations : 4
% 0.26/1.44 # Equation resolutions : 173
% 0.26/1.44 # Current number of processed clauses : 469
% 0.26/1.44 # Positive orientable unit clauses : 31
% 0.26/1.44 # Positive unorientable unit clauses: 0
% 0.26/1.44 # Negative unit clauses : 17
% 0.26/1.44 # Non-unit-clauses : 421
% 0.26/1.44 # Current number of unprocessed clauses: 3668
% 0.26/1.44 # ...number of literals in the above : 25258
% 0.26/1.44 # Current number of archived formulas : 0
% 0.26/1.44 # Current number of archived clauses : 10
% 0.26/1.44 # Clause-clause subsumption calls (NU) : 112609
% 0.26/1.44 # Rec. Clause-clause subsumption calls : 6633
% 0.26/1.44 # Non-unit clause-clause subsumptions : 75
% 0.26/1.44 # Unit Clause-clause subsumption calls : 2548
% 0.26/1.44 # Rewrite failures with RHS unbound : 0
% 0.26/1.44 # BW rewrite match attempts : 53
% 0.26/1.44 # BW rewrite match successes : 2
% 0.26/1.44 # Condensation attempts : 0
% 0.26/1.44 # Condensation successes : 0
% 0.26/1.44 # Termbank termtop insertions : 139568
% 0.26/1.44
% 0.26/1.44 # -------------------------------------------------
% 0.26/1.44 # User time : 0.244 s
% 0.26/1.44 # System time : 0.003 s
% 0.26/1.44 # Total time : 0.247 s
% 0.26/1.44 # Maximum resident set size: 9336 pages
% 0.26/23.45 eprover: CPU time limit exceeded, terminating
% 0.26/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.46 eprover: No such file or directory
% 0.26/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.47 eprover: No such file or directory
% 0.26/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.48 eprover: No such file or directory
% 0.26/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.48 eprover: No such file or directory
% 0.26/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.49 eprover: No such file or directory
% 0.26/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.49 eprover: No such file or directory
% 0.26/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.50 eprover: No such file or directory
% 0.26/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.50 eprover: No such file or directory
% 0.26/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.51 eprover: No such file or directory
% 0.26/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.52 eprover: No such file or directory
% 0.26/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.26/23.52 eprover: No such file or directory
%------------------------------------------------------------------------------