TSTP Solution File: SET637+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n013.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 00:52:47 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 10 unt; 0 def)
% Number of atoms : 115 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 119 ( 50 ~; 51 |; 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 : 96 ( 15 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(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(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_th119,conjecture,
! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th119) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',not_equal_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(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_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,X4,X5,X7] :
( ( member(esk3_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk3_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])])])])])])]) ).
fof(c_0_10,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_11,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = X2
| member(esk4_2(X1,X2),X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( member(esk3_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk3_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( X1 = empty_set
| member(esk4_2(X1,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
inference(assume_negation,[status(cth)],[prove_th119]) ).
cnf(c_0_19,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( intersect(X1,X2)
| ~ intersect(X3,X2)
| ~ member(esk3_2(X3,X2),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( member(esk3_2(intersection(X1,X2),X3),X1)
| ~ intersect(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( X1 = empty_set
| intersect(X2,X1)
| ~ member(esk4_2(X1,empty_set),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
fof(c_0_23,negated_conjecture,
( ( ~ intersect(esk1_0,esk2_0)
| ~ not_equal(intersection(esk1_0,esk2_0),empty_set) )
& ( intersect(esk1_0,esk2_0)
| not_equal(intersection(esk1_0,esk2_0),empty_set) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_24,plain,
! [X3,X4,X3,X4] :
( ( ~ not_equal(X3,X4)
| X3 != X4 )
& ( X3 = X4
| not_equal(X3,X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[not_equal_defn])])])]) ).
cnf(c_0_25,plain,
( intersect(X1,X2)
| ~ intersect(X2,X3)
| ~ member(esk3_2(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_26,plain,
( member(esk3_2(X1,intersection(X2,X3)),X3)
| ~ intersect(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_27,plain,
( intersect(X1,X2)
| ~ intersect(intersection(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( X1 = empty_set
| intersect(X1,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_12]),c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( ~ not_equal(intersection(esk1_0,esk2_0),empty_set)
| ~ intersect(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( intersect(X1,X2)
| ~ intersect(X2,intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( intersection(X1,X2) = empty_set
| intersect(X1,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_34,negated_conjecture,
( intersection(esk1_0,esk2_0) = empty_set
| ~ intersect(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( intersection(X1,X2) = empty_set
| intersect(X2,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_38,negated_conjecture,
intersection(esk1_0,esk2_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
( X1 != X2
| ~ not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_11]) ).
cnf(c_0_41,negated_conjecture,
( not_equal(intersection(esk1_0,esk2_0),empty_set)
| intersect(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_42,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( ~ intersect(X1,esk2_0)
| ~ member(esk3_2(X1,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_14]) ).
cnf(c_0_44,negated_conjecture,
intersect(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_38]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_16]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n013.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 Jul 10 23:34:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.015 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 46
% 0.22/1.41 # Proof object clause steps : 31
% 0.22/1.41 # Proof object formula steps : 15
% 0.22/1.41 # Proof object conjectures : 11
% 0.22/1.41 # Proof object clause conjectures : 8
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 13
% 0.22/1.41 # Proof object initial formulas used : 7
% 0.22/1.41 # Proof object generating inferences : 16
% 0.22/1.41 # Proof object simplifying inferences : 9
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 9
% 0.22/1.41 # Removed by relevancy pruning/SinE : 1
% 0.22/1.41 # Initial clauses : 17
% 0.22/1.41 # Removed in clause preprocessing : 2
% 0.22/1.41 # Initial clauses in saturation : 15
% 0.22/1.41 # Processed clauses : 103
% 0.22/1.41 # ...of these trivial : 2
% 0.22/1.41 # ...subsumed : 45
% 0.22/1.41 # ...remaining for further processing : 56
% 0.22/1.41 # Other redundant clauses eliminated : 1
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 0
% 0.22/1.41 # Backward-rewritten : 5
% 0.22/1.41 # Generated clauses : 367
% 0.22/1.41 # ...of the previous two non-trivial : 339
% 0.22/1.41 # Contextual simplify-reflections : 1
% 0.22/1.41 # Paramodulations : 356
% 0.22/1.41 # Factorizations : 10
% 0.22/1.41 # Equation resolutions : 1
% 0.22/1.41 # Current number of processed clauses : 50
% 0.22/1.41 # Positive orientable unit clauses : 7
% 0.22/1.41 # Positive unorientable unit clauses: 1
% 0.22/1.41 # Negative unit clauses : 4
% 0.22/1.41 # Non-unit-clauses : 38
% 0.22/1.41 # Current number of unprocessed clauses: 247
% 0.22/1.41 # ...number of literals in the above : 713
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 5
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 265
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 219
% 0.22/1.41 # Non-unit clause-clause subsumptions : 20
% 0.22/1.41 # Unit Clause-clause subsumption calls : 31
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 5
% 0.22/1.41 # BW rewrite match successes : 5
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 4351
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.021 s
% 0.22/1.41 # System time : 0.003 s
% 0.22/1.41 # Total time : 0.024 s
% 0.22/1.41 # Maximum resident set size: 3032 pages
%------------------------------------------------------------------------------