%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.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 00:49:51 EDT 2022
% Result : Theorem 0.24s 1.41s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 20 unt; 0 def)
% Number of atoms : 90 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 81 ( 32 ~; 34 |; 10 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 101 ( 22 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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(prove_absorbtion_for_intersection,conjecture,
! [X1,X2] : intersection(X1,union(X1,X2)) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_absorbtion_for_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_union) ).
fof(c_0_7,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk3_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk3_2(X4,X5),X5)
| subset(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)],[subset_defn])])])])])])]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(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)],[union_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,
( subset(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( subset(X1,union(X2,X3))
| ~ member(esk3_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(intersection(X1,X2),X3)
| member(esk3_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
subset(intersection(X1,X2),union(X1,X3)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk3_2(X1,intersection(X2,X3)),X3)
| ~ member(esk3_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_20,plain,
( member(X1,union(X2,X3))
| ~ member(X1,intersection(X2,X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_21,plain,
! [X3,X4,X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])])]) ).
cnf(c_0_22,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk3_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_23,plain,
( subset(intersection(X1,X2),X3)
| member(esk3_2(intersection(X1,X2),X3),union(X1,X4)) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_26,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
fof(c_0_27,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_28,negated_conjecture,
~ ! [X1,X2] : intersection(X1,union(X1,X2)) = X1,
inference(assume_negation,[status(cth)],[prove_absorbtion_for_intersection]) ).
cnf(c_0_29,plain,
subset(intersection(X1,X2),intersection(union(X1,X3),intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_32,negated_conjecture,
intersection(esk1_0,union(esk1_0,esk2_0)) != esk1_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_33,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_34,plain,
subset(X1,intersection(X1,union(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
intersection(esk1_0,union(esk1_0,esk2_0)) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
intersection(X1,union(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_26])]) ).
cnf(c_0_38,negated_conjecture,
intersection(esk1_0,union(esk2_0,esk1_0)) != esk1_0,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
intersection(X1,union(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n023.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 : Mon Jul 11 10:07:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41 # Preprocessing time : 0.015 s
% 0.24/1.41
% 0.24/1.41 # Proof found!
% 0.24/1.41 # SZS status Theorem
% 0.24/1.41 # SZS output start CNFRefutation
% See solution above
% 0.24/1.41 # Proof object total steps : 41
% 0.24/1.41 # Proof object clause steps : 26
% 0.24/1.41 # Proof object formula steps : 15
% 0.24/1.41 # Proof object conjectures : 6
% 0.24/1.41 # Proof object clause conjectures : 3
% 0.24/1.41 # Proof object formula conjectures : 3
% 0.24/1.41 # Proof object initial clauses used : 10
% 0.24/1.41 # Proof object initial formulas used : 7
% 0.24/1.41 # Proof object generating inferences : 14
% 0.24/1.41 # Proof object simplifying inferences : 8
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 9
% 0.24/1.41 # Removed by relevancy pruning/SinE : 0
% 0.24/1.41 # Initial clauses : 20
% 0.24/1.41 # Removed in clause preprocessing : 2
% 0.24/1.41 # Initial clauses in saturation : 18
% 0.24/1.41 # Processed clauses : 834
% 0.24/1.41 # ...of these trivial : 248
% 0.24/1.41 # ...subsumed : 378
% 0.24/1.41 # ...remaining for further processing : 208
% 0.24/1.41 # Other redundant clauses eliminated : 2
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 0
% 0.24/1.41 # Backward-rewritten : 5
% 0.24/1.41 # Generated clauses : 3154
% 0.24/1.41 # ...of the previous two non-trivial : 2304
% 0.24/1.41 # Contextual simplify-reflections : 16
% 0.24/1.41 # Paramodulations : 3142
% 0.24/1.41 # Factorizations : 10
% 0.24/1.41 # Equation resolutions : 2
% 0.24/1.41 # Current number of processed clauses : 201
% 0.24/1.41 # Positive orientable unit clauses : 87
% 0.24/1.41 # Positive unorientable unit clauses: 2
% 0.24/1.41 # Negative unit clauses : 0
% 0.24/1.41 # Non-unit-clauses : 112
% 0.24/1.41 # Current number of unprocessed clauses: 1475
% 0.24/1.41 # ...number of literals in the above : 3166
% 0.24/1.41 # Current number of archived formulas : 0
% 0.24/1.41 # Current number of archived clauses : 5
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 4036
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 3924
% 0.24/1.41 # Non-unit clause-clause subsumptions : 394
% 0.24/1.41 # Unit Clause-clause subsumption calls : 220
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 618
% 0.24/1.41 # BW rewrite match successes : 8
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 30287
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.061 s
% 0.24/1.41 # System time : 0.004 s
% 0.24/1.41 # Total time : 0.065 s
% 0.24/1.41 # Maximum resident set size: 4356 pages
%------------------------------------------------------------------------------