TSTP Solution File: SEU328+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU328+1 : 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 0.24s 1.43s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 59 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 23 ~; 17 |; 3 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 26 !; 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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t12_tops_2) ).
fof(t48_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t48_setfam_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d4_subset_1) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k2_subset_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k6_subset_1) ).
fof(dt_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k6_setfam_1) ).
fof(c_0_7,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_8,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| union_of_subsets(X3,complements_of_subsets(X3,X4)) = subset_difference(X3,cast_to_subset(X3),meet_of_subsets(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_setfam_1])]) ).
fof(c_0_9,plain,
! [X2] : cast_to_subset(X2) = X2,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
fof(c_0_10,plain,
! [X2] : element(cast_to_subset(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(c_0_11,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_7])])]) ).
fof(c_0_12,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
cnf(c_0_13,plain,
( union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
cnf(c_0_16,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(meet_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])]) ).
cnf(c_0_18,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_11]) ).
cnf(c_0_19,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( X2 = empty_set
| union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,X1,meet_of_subsets(X1,X2))
| ~ element(X2,powerset(powerset(X1))) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_23,plain,
( element(meet_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( set_difference(esk1_0,meet_of_subsets(esk1_0,esk2_0)) != union_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0))
| ~ element(meet_of_subsets(esk1_0,esk2_0),powerset(esk1_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( set_difference(X1,meet_of_subsets(X1,X2)) = union_of_subsets(X1,complements_of_subsets(X1,X2))
| X2 = empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_26,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
~ element(meet_of_subsets(esk1_0,esk2_0),powerset(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU328+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n019.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 : Sun Jun 19 17:24:09 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.24/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43 # Preprocessing time : 0.018 s
% 0.24/1.43
% 0.24/1.43 # Proof found!
% 0.24/1.43 # SZS status Theorem
% 0.24/1.43 # SZS output start CNFRefutation
% See solution above
% 0.24/1.43 # Proof object total steps : 30
% 0.24/1.43 # Proof object clause steps : 15
% 0.24/1.43 # Proof object formula steps : 15
% 0.24/1.43 # Proof object conjectures : 9
% 0.24/1.43 # Proof object clause conjectures : 6
% 0.24/1.43 # Proof object formula conjectures : 3
% 0.24/1.43 # Proof object initial clauses used : 9
% 0.24/1.43 # Proof object initial formulas used : 7
% 0.24/1.43 # Proof object generating inferences : 4
% 0.24/1.43 # Proof object simplifying inferences : 10
% 0.24/1.43 # Training examples: 0 positive, 0 negative
% 0.24/1.43 # Parsed axioms : 59
% 0.24/1.43 # Removed by relevancy pruning/SinE : 21
% 0.24/1.43 # Initial clauses : 76
% 0.24/1.43 # Removed in clause preprocessing : 1
% 0.24/1.43 # Initial clauses in saturation : 75
% 0.24/1.43 # Processed clauses : 606
% 0.24/1.43 # ...of these trivial : 12
% 0.24/1.43 # ...subsumed : 200
% 0.24/1.43 # ...remaining for further processing : 394
% 0.24/1.43 # Other redundant clauses eliminated : 0
% 0.24/1.43 # Clauses deleted for lack of memory : 0
% 0.24/1.43 # Backward-subsumed : 3
% 0.24/1.43 # Backward-rewritten : 5
% 0.24/1.43 # Generated clauses : 1865
% 0.24/1.43 # ...of the previous two non-trivial : 1413
% 0.24/1.43 # Contextual simplify-reflections : 31
% 0.24/1.43 # Paramodulations : 1865
% 0.24/1.43 # Factorizations : 0
% 0.24/1.43 # Equation resolutions : 0
% 0.24/1.43 # Current number of processed clauses : 386
% 0.24/1.43 # Positive orientable unit clauses : 63
% 0.24/1.43 # Positive unorientable unit clauses: 0
% 0.24/1.43 # Negative unit clauses : 5
% 0.24/1.43 # Non-unit-clauses : 318
% 0.24/1.43 # Current number of unprocessed clauses: 840
% 0.24/1.43 # ...number of literals in the above : 2547
% 0.24/1.43 # Current number of archived formulas : 0
% 0.24/1.43 # Current number of archived clauses : 9
% 0.24/1.43 # Clause-clause subsumption calls (NU) : 12796
% 0.24/1.43 # Rec. Clause-clause subsumption calls : 11967
% 0.24/1.43 # Non-unit clause-clause subsumptions : 231
% 0.24/1.43 # Unit Clause-clause subsumption calls : 195
% 0.24/1.43 # Rewrite failures with RHS unbound : 0
% 0.24/1.43 # BW rewrite match attempts : 77
% 0.24/1.43 # BW rewrite match successes : 4
% 0.24/1.43 # Condensation attempts : 0
% 0.24/1.43 # Condensation successes : 0
% 0.24/1.43 # Termbank termtop insertions : 25398
% 0.24/1.43
% 0.24/1.43 # -------------------------------------------------
% 0.24/1.43 # User time : 0.059 s
% 0.24/1.43 # System time : 0.005 s
% 0.24/1.43 # Total time : 0.064 s
% 0.24/1.43 # Maximum resident set size: 4412 pages
% 0.24/11.69 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.69 eprover: No such file or directory
% 0.24/11.69 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.69 eprover: No such file or directory
% 0.24/11.70 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.70 eprover: No such file or directory
% 0.24/11.70 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.70 eprover: No such file or directory
% 0.24/11.71 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.71 eprover: No such file or directory
% 0.24/11.72 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.72 eprover: No such file or directory
% 0.24/11.72 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.72 eprover: No such file or directory
% 0.24/11.73 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.73 eprover: No such file or directory
% 0.24/11.73 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.73 eprover: No such file or directory
% 0.24/11.74 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.74 eprover: No such file or directory
% 0.24/11.74 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/11.74 eprover: No such file or directory
%------------------------------------------------------------------------------