TSTP Solution File: SEU326+2 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU326+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n032.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 09:19:01 EDT 2022
% Result : Theorem 0.20s 1.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 51 ( 32 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 56 ( 26 ~; 14 |; 11 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_tops_2,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t10_tops_2) ).
fof(t46_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t46_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',dt_k7_setfam_1) ).
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',involutiveness_k7_setfam_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
inference(assume_negation,[status(cth)],[t10_tops_2]) ).
fof(c_0_5,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| complements_of_subsets(X3,X4) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).
fof(c_0_6,negated_conjecture,
( element(esk2_0,powerset(powerset(esk1_0)))
& ( complements_of_subsets(esk1_0,esk2_0) != empty_set
| esk2_0 != empty_set )
& ( esk2_0 = empty_set
| esk2_0 != empty_set )
& ( complements_of_subsets(esk1_0,esk2_0) != empty_set
| complements_of_subsets(esk1_0,esk2_0) = empty_set )
& ( esk2_0 = empty_set
| complements_of_subsets(esk1_0,esk2_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_7,lemma,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( complements_of_subsets(esk1_0,esk2_0) = empty_set
| esk2_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,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_11,negated_conjecture,
esk2_0 = empty_set,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
fof(c_0_12,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_13,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
element(empty_set,powerset(powerset(esk1_0))),
inference(rw,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_15,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( esk2_0 != empty_set
| complements_of_subsets(esk1_0,esk2_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
element(complements_of_subsets(esk1_0,empty_set),powerset(powerset(esk1_0))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
complements_of_subsets(esk1_0,complements_of_subsets(esk1_0,empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
complements_of_subsets(esk1_0,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_11]),c_0_11])]) ).
cnf(c_0_20,lemma,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_17]),c_0_18])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU326+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : run_ET %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sun Jun 19 08:55:47 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.20/1.39 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.20/1.39 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.20/1.39 # Preprocessing time : 0.033 s
% 0.20/1.39
% 0.20/1.39 # Proof found!
% 0.20/1.39 # SZS status Theorem
% 0.20/1.39 # SZS output start CNFRefutation
% See solution above
% 0.20/1.39 # Proof object total steps : 21
% 0.20/1.39 # Proof object clause steps : 12
% 0.20/1.39 # Proof object formula steps : 9
% 0.20/1.39 # Proof object conjectures : 11
% 0.20/1.39 # Proof object clause conjectures : 8
% 0.20/1.39 # Proof object formula conjectures : 3
% 0.20/1.39 # Proof object initial clauses used : 6
% 0.20/1.39 # Proof object initial formulas used : 4
% 0.20/1.39 # Proof object generating inferences : 4
% 0.20/1.39 # Proof object simplifying inferences : 8
% 0.20/1.39 # Training examples: 0 positive, 0 negative
% 0.20/1.39 # Parsed axioms : 539
% 0.20/1.39 # Removed by relevancy pruning/SinE : 482
% 0.20/1.39 # Initial clauses : 226
% 0.20/1.39 # Removed in clause preprocessing : 4
% 0.20/1.39 # Initial clauses in saturation : 222
% 0.20/1.39 # Processed clauses : 234
% 0.20/1.39 # ...of these trivial : 1
% 0.20/1.39 # ...subsumed : 14
% 0.20/1.39 # ...remaining for further processing : 219
% 0.20/1.39 # Other redundant clauses eliminated : 38
% 0.20/1.39 # Clauses deleted for lack of memory : 0
% 0.20/1.39 # Backward-subsumed : 0
% 0.20/1.39 # Backward-rewritten : 6
% 0.20/1.39 # Generated clauses : 704
% 0.20/1.39 # ...of the previous two non-trivial : 677
% 0.20/1.39 # Contextual simplify-reflections : 44
% 0.20/1.39 # Paramodulations : 662
% 0.20/1.39 # Factorizations : 2
% 0.20/1.39 # Equation resolutions : 40
% 0.20/1.39 # Current number of processed clauses : 175
% 0.20/1.39 # Positive orientable unit clauses : 19
% 0.20/1.39 # Positive unorientable unit clauses: 0
% 0.20/1.39 # Negative unit clauses : 5
% 0.20/1.39 # Non-unit-clauses : 151
% 0.20/1.39 # Current number of unprocessed clauses: 631
% 0.20/1.39 # ...number of literals in the above : 2896
% 0.20/1.39 # Current number of archived formulas : 0
% 0.20/1.39 # Current number of archived clauses : 6
% 0.20/1.39 # Clause-clause subsumption calls (NU) : 16362
% 0.20/1.39 # Rec. Clause-clause subsumption calls : 1662
% 0.20/1.39 # Non-unit clause-clause subsumptions : 58
% 0.20/1.39 # Unit Clause-clause subsumption calls : 163
% 0.20/1.39 # Rewrite failures with RHS unbound : 0
% 0.20/1.39 # BW rewrite match attempts : 3
% 0.20/1.39 # BW rewrite match successes : 2
% 0.20/1.39 # Condensation attempts : 0
% 0.20/1.39 # Condensation successes : 0
% 0.20/1.39 # Termbank termtop insertions : 33488
% 0.20/1.39
% 0.20/1.39 # -------------------------------------------------
% 0.20/1.39 # User time : 0.052 s
% 0.20/1.39 # System time : 0.003 s
% 0.20/1.39 # Total time : 0.055 s
% 0.20/1.39 # Maximum resident set size: 5324 pages
%------------------------------------------------------------------------------