TSTP Solution File: SET636+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n021.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 00:52:46 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 9 unt; 0 def)
% Number of atoms : 103 ( 23 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 105 ( 42 ~; 45 |; 11 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 13 sgn 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',equal_member_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_defn) ).
fof(prove_th118,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th118) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersect_defn) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',disjoint_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_intersection) ).
fof(c_0_7,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set_defn])]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk3_2(X4,X5),X4)
| ~ member(esk3_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk3_2(X4,X5),X4)
| member(esk3_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[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)],[equal_member_defn])])])])])])]) ).
fof(c_0_9,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])])]) ).
cnf(c_0_10,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th118]) ).
fof(c_0_13,plain,
! [X4,X5,X4,X5,X7] :
( ( member(esk4_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk4_2(X4,X5),X5)
| ~ intersect(X4,X5) )
& ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) ) ),
inference(distribute,[status(thm)],[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)],[intersect_defn])])])])])])]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( X1 = empty_set
| member(esk3_2(X1,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_16,plain,
! [X3,X4,X3,X4] :
( ( ~ disjoint(X3,X4)
| ~ intersect(X3,X4) )
& ( intersect(X3,X4)
| disjoint(X3,X4) ) ),
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)],[disjoint_defn])])])])]) ).
fof(c_0_17,negated_conjecture,
( ( ~ disjoint(esk1_0,esk2_0)
| intersection(esk1_0,esk2_0) != empty_set )
& ( disjoint(esk1_0,esk2_0)
| intersection(esk1_0,esk2_0) = empty_set ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_18,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( intersection(X1,X2) = empty_set
| member(esk3_2(intersection(X1,X2),empty_set),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
( ~ intersect(X1,X2)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( intersection(esk1_0,esk2_0) = empty_set
| disjoint(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( intersection(X1,X2) = empty_set
| intersect(X3,X1)
| ~ member(esk3_2(intersection(X1,X2),empty_set),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( intersection(X1,X2) = X3
| member(esk3_2(intersection(X1,X2),X3),X3)
| member(esk3_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
fof(c_0_25,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_26,negated_conjecture,
( intersection(esk1_0,esk2_0) = empty_set
| ~ intersect(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( intersection(X1,X2) = empty_set
| intersect(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_10]) ).
cnf(c_0_28,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
intersection(esk1_0,esk2_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
( intersection(esk1_0,esk2_0) != empty_set
| ~ disjoint(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_10]) ).
cnf(c_0_34,plain,
( member(esk4_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,negated_conjecture,
( intersect(esk1_0,esk2_0)
| intersection(esk1_0,esk2_0) != empty_set ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( ~ intersect(X1,esk2_0)
| ~ member(esk4_2(X1,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( member(esk4_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,negated_conjecture,
intersect(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_30])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n021.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 : Mon Jul 11 04:08:08 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.016 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 40
% 0.24/1.42 # Proof object clause steps : 25
% 0.24/1.42 # Proof object formula steps : 15
% 0.24/1.42 # Proof object conjectures : 12
% 0.24/1.42 # Proof object clause conjectures : 9
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 13
% 0.24/1.42 # Proof object initial formulas used : 7
% 0.24/1.42 # Proof object generating inferences : 11
% 0.24/1.42 # Proof object simplifying inferences : 8
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 12
% 0.24/1.42 # Removed by relevancy pruning/SinE : 4
% 0.24/1.42 # Initial clauses : 17
% 0.24/1.42 # Removed in clause preprocessing : 2
% 0.24/1.42 # Initial clauses in saturation : 15
% 0.24/1.42 # Processed clauses : 201
% 0.24/1.42 # ...of these trivial : 7
% 0.24/1.42 # ...subsumed : 111
% 0.24/1.42 # ...remaining for further processing : 83
% 0.24/1.42 # Other redundant clauses eliminated : 0
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 0
% 0.24/1.42 # Backward-rewritten : 7
% 0.24/1.42 # Generated clauses : 842
% 0.24/1.42 # ...of the previous two non-trivial : 774
% 0.24/1.42 # Contextual simplify-reflections : 0
% 0.24/1.42 # Paramodulations : 830
% 0.24/1.42 # Factorizations : 12
% 0.24/1.42 # Equation resolutions : 0
% 0.24/1.42 # Current number of processed clauses : 76
% 0.24/1.42 # Positive orientable unit clauses : 9
% 0.24/1.42 # Positive unorientable unit clauses: 1
% 0.24/1.42 # Negative unit clauses : 4
% 0.24/1.42 # Non-unit-clauses : 62
% 0.24/1.42 # Current number of unprocessed clauses: 588
% 0.24/1.42 # ...number of literals in the above : 1842
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 7
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 778
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 674
% 0.24/1.42 # Non-unit clause-clause subsumptions : 73
% 0.24/1.42 # Unit Clause-clause subsumption calls : 9
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 3
% 0.24/1.42 # BW rewrite match successes : 3
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 9737
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.033 s
% 0.24/1.42 # System time : 0.001 s
% 0.24/1.42 # Total time : 0.034 s
% 0.24/1.42 # Maximum resident set size: 3304 pages
%------------------------------------------------------------------------------