%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU328+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n019.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 09:19:02 EDT 2022
% Result : Theorem 0.27s 1.45s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 6 unt; 0 def)
% Number of atoms : 91 ( 44 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 40 ~; 31 |; 8 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 5 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_tops_2,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t12_tops_2) ).
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(t11_tops_2,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t11_tops_2) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k5_setfam_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).
fof(l71_subset_1,lemma,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l71_subset_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.mepo_128.in',involutiveness_k7_setfam_1) ).
fof(t10_tops_2,lemma,
! [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.mepo_128.in',t10_tops_2) ).
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_9,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[t12_tops_2]) ).
fof(c_0_10,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_11,lemma,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| meet_of_subsets(X3,complements_of_subsets(X3,X4)) = subset_complement(X3,union_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t11_tops_2])]) ).
fof(c_0_12,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(union_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
fof(c_0_13,negated_conjecture,
( element(esk2_0,powerset(powerset(esk1_0)))
& esk2_0 != empty_set
& union_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,meet_of_subsets(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_14,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,lemma,
( meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X3,X4,X3] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk6_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[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)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])]) ).
fof(c_0_18,lemma,
! [X4,X5] :
( ( in(esk10_2(X4,X5),X4)
| element(X4,powerset(X5)) )
& ( ~ in(esk10_2(X4,X5),X5)
| element(X4,powerset(X5)) ) ),
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)],[l71_subset_1])])])])])]) ).
cnf(c_0_19,negated_conjecture,
union_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,meet_of_subsets(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,lemma,
( union_of_subsets(X1,X2) = subset_complement(X1,meet_of_subsets(X1,complements_of_subsets(X1,X2)))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
fof(c_0_21,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])]) ).
fof(c_0_22,lemma,
! [X3,X4] :
( ( X4 = empty_set
| complements_of_subsets(X3,X4) != empty_set
| ~ element(X4,powerset(powerset(X3))) )
& ( complements_of_subsets(X3,X4) = empty_set
| X4 != empty_set
| ~ element(X4,powerset(powerset(X3))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_tops_2])])]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,lemma,
( element(X1,powerset(X2))
| in(esk10_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( complements_of_subsets(esk1_0,esk2_0) = empty_set
| subset_complement(esk1_0,meet_of_subsets(esk1_0,complements_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)))) != subset_complement(esk1_0,meet_of_subsets(esk1_0,esk2_0))
| ~ element(complements_of_subsets(esk1_0,esk2_0),powerset(powerset(esk1_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_28,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_29,lemma,
( complements_of_subsets(X2,X1) = empty_set
| ~ element(X1,powerset(powerset(X2)))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,lemma,
( element(X1,powerset(X2))
| X1 != empty_set ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( complements_of_subsets(esk1_0,esk2_0) = empty_set
| ~ element(complements_of_subsets(esk1_0,esk2_0),powerset(powerset(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,lemma,
( complements_of_subsets(X1,empty_set) = X2
| X2 != empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_29]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
complements_of_subsets(esk1_0,esk2_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27])]) ).
cnf(c_0_35,lemma,
complements_of_subsets(X1,empty_set) = empty_set,
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_34]),c_0_35]),c_0_27])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU328+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 21:15:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.27/1.45 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.27/1.45 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.27/1.45 # Preprocessing time : 0.046 s
% 0.27/1.45
% 0.27/1.45 # Proof found!
% 0.27/1.45 # SZS status Theorem
% 0.27/1.45 # SZS output start CNFRefutation
% See solution above
% 0.27/1.45 # Proof object total steps : 38
% 0.27/1.45 # Proof object clause steps : 19
% 0.27/1.45 # Proof object formula steps : 19
% 0.27/1.45 # Proof object conjectures : 10
% 0.27/1.45 # Proof object clause conjectures : 7
% 0.27/1.45 # Proof object formula conjectures : 3
% 0.27/1.45 # Proof object initial clauses used : 11
% 0.27/1.45 # Proof object initial formulas used : 9
% 0.27/1.45 # Proof object generating inferences : 8
% 0.27/1.45 # Proof object simplifying inferences : 10
% 0.27/1.45 # Training examples: 0 positive, 0 negative
% 0.27/1.45 # Parsed axioms : 541
% 0.27/1.45 # Removed by relevancy pruning/SinE : 440
% 0.27/1.45 # Initial clauses : 267
% 0.27/1.45 # Removed in clause preprocessing : 1
% 0.27/1.45 # Initial clauses in saturation : 266
% 0.27/1.45 # Processed clauses : 1809
% 0.27/1.45 # ...of these trivial : 15
% 0.27/1.45 # ...subsumed : 1021
% 0.27/1.45 # ...remaining for further processing : 773
% 0.27/1.45 # Other redundant clauses eliminated : 64
% 0.27/1.45 # Clauses deleted for lack of memory : 0
% 0.27/1.45 # Backward-subsumed : 58
% 0.27/1.45 # Backward-rewritten : 55
% 0.27/1.45 # Generated clauses : 7869
% 0.27/1.45 # ...of the previous two non-trivial : 6974
% 0.27/1.45 # Contextual simplify-reflections : 321
% 0.27/1.45 # Paramodulations : 7769
% 0.27/1.45 # Factorizations : 4
% 0.27/1.45 # Equation resolutions : 107
% 0.27/1.45 # Current number of processed clauses : 645
% 0.27/1.45 # Positive orientable unit clauses : 45
% 0.27/1.45 # Positive unorientable unit clauses: 0
% 0.27/1.45 # Negative unit clauses : 33
% 0.27/1.45 # Non-unit-clauses : 567
% 0.27/1.45 # Current number of unprocessed clauses: 5162
% 0.27/1.45 # ...number of literals in the above : 24434
% 0.27/1.45 # Current number of archived formulas : 0
% 0.27/1.45 # Current number of archived clauses : 114
% 0.27/1.45 # Clause-clause subsumption calls (NU) : 96550
% 0.27/1.45 # Rec. Clause-clause subsumption calls : 55181
% 0.27/1.45 # Non-unit clause-clause subsumptions : 846
% 0.27/1.45 # Unit Clause-clause subsumption calls : 2316
% 0.27/1.45 # Rewrite failures with RHS unbound : 0
% 0.27/1.45 # BW rewrite match attempts : 89
% 0.27/1.45 # BW rewrite match successes : 6
% 0.27/1.45 # Condensation attempts : 0
% 0.27/1.45 # Condensation successes : 0
% 0.27/1.45 # Termbank termtop insertions : 136209
% 0.27/1.45
% 0.27/1.45 # -------------------------------------------------
% 0.27/1.45 # User time : 0.249 s
% 0.27/1.45 # System time : 0.007 s
% 0.27/1.45 # Total time : 0.256 s
% 0.27/1.45 # Maximum resident set size: 9864 pages
% 0.27/23.45 eprover: CPU time limit exceeded, terminating
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52 eprover: No such file or directory
% 0.27/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.53 eprover: No such file or directory
%------------------------------------------------------------------------------