TSTP Solution File: SEU324+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n015.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 09:19:00 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 128 ( 27 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 143 ( 52 ~; 49 |; 18 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t55_tops_1,conjecture,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t55_tops_1) ).
fof(t52_pre_topc,axiom,
! [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(fc6_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(interior(X1,X2),X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc6_tops_1) ).
fof(t30_tops_1,axiom,
! [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(c_0_7,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])])])])]) ).
fof(c_0_8,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])]) ).
fof(c_0_9,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])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t55_tops_1]) ).
cnf(c_0_11,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_7]) ).
cnf(c_0_12,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [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_15,plain,
! [X3,X4] :
( ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| open_subset(interior(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_tops_1])]) ).
fof(c_0_16,negated_conjecture,
( topological_space(esk1_0)
& top_str(esk1_0)
& top_str(esk2_0)
& element(esk3_0,powerset(the_carrier(esk1_0)))
& element(esk4_0,powerset(the_carrier(esk2_0)))
& ( interior(esk1_0,esk3_0) = esk3_0
| open_subset(esk4_0,esk2_0) )
& ( ~ open_subset(esk3_0,esk1_0)
| open_subset(esk4_0,esk2_0) )
& ( interior(esk1_0,esk3_0) = esk3_0
| interior(esk2_0,esk4_0) != esk4_0 )
& ( ~ open_subset(esk3_0,esk1_0)
| interior(esk2_0,esk4_0) != esk4_0 ) ),
inference(distribute,[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)],[c_0_10])])])])])]) ).
cnf(c_0_17,plain,
( subset_complement(the_carrier(X1),topstr_closure(X1,X2)) = interior(X1,subset_complement(the_carrier(X1),X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_18,plain,
( 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_14]) ).
cnf(c_0_19,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( interior(esk1_0,esk3_0) = esk3_0
| interior(esk2_0,esk4_0) != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
element(esk3_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( interior(esk2_0,esk4_0) != esk4_0
| ~ open_subset(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( interior(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),X2)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
interior(esk2_0,esk4_0) != esk4_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_27,plain,
( interior(X1,X2) = X2
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_12]),c_0_13]) ).
cnf(c_0_28,negated_conjecture,
element(esk4_0,powerset(the_carrier(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
top_str(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_30,plain,
! [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_31,negated_conjecture,
( open_subset(esk4_0,esk2_0)
| interior(esk1_0,esk3_0) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,negated_conjecture,
( open_subset(esk4_0,esk2_0)
| ~ open_subset(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_33,negated_conjecture,
~ closed_subset(subset_complement(the_carrier(esk2_0),esk4_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_34,plain,
( 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_30]) ).
cnf(c_0_35,negated_conjecture,
open_subset(esk4_0,esk2_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_31]),c_0_21]),c_0_22]),c_0_23])]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 06:37:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.009 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.40 # Proof object total steps : 37
% 0.22/1.40 # Proof object clause steps : 22
% 0.22/1.40 # Proof object formula steps : 15
% 0.22/1.40 # Proof object conjectures : 16
% 0.22/1.40 # Proof object clause conjectures : 13
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 15
% 0.22/1.40 # Proof object initial formulas used : 7
% 0.22/1.40 # Proof object generating inferences : 7
% 0.22/1.40 # Proof object simplifying inferences : 19
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 25
% 0.22/1.40 # Removed by relevancy pruning/SinE : 8
% 0.22/1.40 # Initial clauses : 31
% 0.22/1.40 # Removed in clause preprocessing : 0
% 0.22/1.40 # Initial clauses in saturation : 31
% 0.22/1.40 # Processed clauses : 45
% 0.22/1.40 # ...of these trivial : 0
% 0.22/1.40 # ...subsumed : 3
% 0.22/1.40 # ...remaining for further processing : 42
% 0.22/1.40 # Other redundant clauses eliminated : 0
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 2
% 0.22/1.40 # Backward-rewritten : 1
% 0.22/1.40 # Generated clauses : 52
% 0.22/1.40 # ...of the previous two non-trivial : 39
% 0.22/1.40 # Contextual simplify-reflections : 12
% 0.22/1.40 # Paramodulations : 52
% 0.22/1.40 # Factorizations : 0
% 0.22/1.40 # Equation resolutions : 0
% 0.22/1.40 # Current number of processed clauses : 39
% 0.22/1.40 # Positive orientable unit clauses : 8
% 0.22/1.40 # Positive unorientable unit clauses: 0
% 0.22/1.40 # Negative unit clauses : 2
% 0.22/1.40 # Non-unit-clauses : 29
% 0.22/1.40 # Current number of unprocessed clauses: 22
% 0.22/1.40 # ...number of literals in the above : 96
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 3
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 130
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 74
% 0.22/1.40 # Non-unit clause-clause subsumptions : 16
% 0.22/1.40 # Unit Clause-clause subsumption calls : 10
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 1
% 0.22/1.40 # BW rewrite match successes : 1
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 3444
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.008 s
% 0.22/1.40 # System time : 0.003 s
% 0.22/1.40 # Total time : 0.011 s
% 0.22/1.40 # Maximum resident set size: 2980 pages
%------------------------------------------------------------------------------