%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n004.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 0.21s 1.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 81 ( 40 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 85 ( 37 ~; 23 |; 20 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 4 sgn 22 !; 1 ?)
% 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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t10_tops_2) ).
fof(t46_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t46_setfam_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t8_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc2_subset_1) ).
fof(fc6_membered,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc6_membered) ).
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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',involutiveness_k7_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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k7_setfam_1) ).
fof(c_0_7,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_8,plain,
! [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_9,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_7])])])]) ).
fof(c_0_10,plain,
! [X3,X4] :
( ~ empty(X3)
| X3 = X4
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_11,plain,
! [X3] :
( element(esk5_1(X3),powerset(X3))
& empty(esk5_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_12,plain,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( complements_of_subsets(esk1_0,esk2_0) = empty_set
| esk2_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
empty(esk5_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc6_membered]) ).
cnf(c_0_18,negated_conjecture,
empty_set = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
fof(c_0_19,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_20,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_21,plain,
( X1 = esk5_1(X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
empty(esk2_0),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( esk2_0 != empty_set
| complements_of_subsets(esk1_0,esk2_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( X1 = esk2_0
| complements_of_subsets(X2,X1) != esk2_0
| ~ element(X1,powerset(powerset(X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_18]),c_0_18]) ).
cnf(c_0_25,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
element(esk5_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,plain,
esk5_1(X1) = esk2_0,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
complements_of_subsets(esk1_0,esk2_0) != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_18]),c_0_18])]) ).
cnf(c_0_30,plain,
( complements_of_subsets(X1,X2) = esk2_0
| X2 != esk2_0
| ~ element(X2,powerset(powerset(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,plain,
element(esk2_0,powerset(X1)),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n004.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 19:04:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.21/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.40 # Preprocessing time : 0.016 s
% 0.21/1.40
% 0.21/1.40 # Proof found!
% 0.21/1.40 # SZS status Theorem
% 0.21/1.40 # SZS output start CNFRefutation
% See solution above
% 0.21/1.40 # Proof object total steps : 33
% 0.21/1.40 # Proof object clause steps : 19
% 0.21/1.40 # Proof object formula steps : 14
% 0.21/1.40 # Proof object conjectures : 9
% 0.21/1.40 # Proof object clause conjectures : 6
% 0.21/1.40 # Proof object formula conjectures : 3
% 0.21/1.40 # Proof object initial clauses used : 10
% 0.21/1.40 # Proof object initial formulas used : 7
% 0.21/1.40 # Proof object generating inferences : 5
% 0.21/1.40 # Proof object simplifying inferences : 12
% 0.21/1.40 # Training examples: 0 positive, 0 negative
% 0.21/1.40 # Parsed axioms : 38
% 0.21/1.40 # Removed by relevancy pruning/SinE : 16
% 0.21/1.40 # Initial clauses : 52
% 0.21/1.40 # Removed in clause preprocessing : 2
% 0.21/1.40 # Initial clauses in saturation : 50
% 0.21/1.40 # Processed clauses : 135
% 0.21/1.40 # ...of these trivial : 6
% 0.21/1.40 # ...subsumed : 19
% 0.21/1.40 # ...remaining for further processing : 110
% 0.21/1.40 # Other redundant clauses eliminated : 0
% 0.21/1.40 # Clauses deleted for lack of memory : 0
% 0.21/1.40 # Backward-subsumed : 1
% 0.21/1.40 # Backward-rewritten : 14
% 0.21/1.40 # Generated clauses : 168
% 0.21/1.40 # ...of the previous two non-trivial : 136
% 0.21/1.40 # Contextual simplify-reflections : 4
% 0.21/1.40 # Paramodulations : 168
% 0.21/1.40 # Factorizations : 0
% 0.21/1.40 # Equation resolutions : 0
% 0.21/1.40 # Current number of processed clauses : 95
% 0.21/1.40 # Positive orientable unit clauses : 15
% 0.21/1.40 # Positive unorientable unit clauses: 0
% 0.21/1.40 # Negative unit clauses : 3
% 0.21/1.40 # Non-unit-clauses : 77
% 0.21/1.40 # Current number of unprocessed clauses: 19
% 0.21/1.40 # ...number of literals in the above : 69
% 0.21/1.40 # Current number of archived formulas : 0
% 0.21/1.40 # Current number of archived clauses : 15
% 0.21/1.40 # Clause-clause subsumption calls (NU) : 892
% 0.21/1.40 # Rec. Clause-clause subsumption calls : 861
% 0.21/1.40 # Non-unit clause-clause subsumptions : 23
% 0.21/1.40 # Unit Clause-clause subsumption calls : 46
% 0.21/1.40 # Rewrite failures with RHS unbound : 0
% 0.21/1.40 # BW rewrite match attempts : 5
% 0.21/1.40 # BW rewrite match successes : 5
% 0.21/1.40 # Condensation attempts : 0
% 0.21/1.40 # Condensation successes : 0
% 0.21/1.40 # Termbank termtop insertions : 4508
% 0.21/1.40
% 0.21/1.40 # -------------------------------------------------
% 0.21/1.40 # User time : 0.017 s
% 0.21/1.40 # System time : 0.005 s
% 0.21/1.40 # Total time : 0.022 s
% 0.21/1.40 # Maximum resident set size: 3012 pages
%------------------------------------------------------------------------------