%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.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 00:47:32 EDT 2022
% Result : Theorem 0.24s 1.43s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 66 ( 19 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 26 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 14 sgn 37 !; 0 ?)
% 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_intersection_difference_empty_set,conjecture,
! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_intersection_difference_empty_set) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',difference_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_6,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set_defn])]) ).
fof(c_0_7,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_8,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_9,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
inference(assume_negation,[status(cth)],[prove_intersection_difference_empty_set]) ).
fof(c_0_12,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(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)],[inference(fof_simplification,[status(thm)],[difference_defn])])])])])]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| member(esk3_2(X1,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_15,negated_conjecture,
intersection(difference(esk1_0,esk2_0),esk2_0) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_16,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_17,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( intersection(X1,X2) = empty_set
| member(esk3_2(intersection(X1,X2),empty_set),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
intersection(difference(esk1_0,esk2_0),esk2_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( intersection(difference(X1,X2),X3) = empty_set
| ~ member(esk3_2(intersection(difference(X1,X2),X3),empty_set),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,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_19,c_0_10]) ).
cnf(c_0_24,negated_conjecture,
intersection(esk2_0,difference(esk1_0,esk2_0)) != empty_set,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
intersection(X1,difference(X2,X1)) = empty_set,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_9]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 01:16:33 EDT 2022
% 0.13/0.35 % 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 : 0.014 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 : 27
% 0.24/1.43 # Proof object clause steps : 14
% 0.24/1.43 # Proof object formula steps : 13
% 0.24/1.43 # Proof object conjectures : 6
% 0.24/1.43 # Proof object clause conjectures : 3
% 0.24/1.43 # Proof object formula conjectures : 3
% 0.24/1.43 # Proof object initial clauses used : 7
% 0.24/1.43 # Proof object initial formulas used : 6
% 0.24/1.43 # Proof object generating inferences : 5
% 0.24/1.43 # Proof object simplifying inferences : 5
% 0.24/1.43 # Training examples: 0 positive, 0 negative
% 0.24/1.43 # Parsed axioms : 10
% 0.24/1.43 # Removed by relevancy pruning/SinE : 4
% 0.24/1.43 # Initial clauses : 13
% 0.24/1.43 # Removed in clause preprocessing : 2
% 0.24/1.43 # Initial clauses in saturation : 11
% 0.24/1.43 # Processed clauses : 84
% 0.24/1.43 # ...of these trivial : 3
% 0.24/1.43 # ...subsumed : 41
% 0.24/1.43 # ...remaining for further processing : 40
% 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 : 1
% 0.24/1.43 # Backward-rewritten : 2
% 0.24/1.43 # Generated clauses : 271
% 0.24/1.43 # ...of the previous two non-trivial : 226
% 0.24/1.43 # Contextual simplify-reflections : 4
% 0.24/1.43 # Paramodulations : 257
% 0.24/1.43 # Factorizations : 14
% 0.24/1.43 # Equation resolutions : 0
% 0.24/1.43 # Current number of processed clauses : 37
% 0.24/1.43 # Positive orientable unit clauses : 5
% 0.24/1.43 # Positive unorientable unit clauses: 1
% 0.24/1.43 # Negative unit clauses : 1
% 0.24/1.43 # Non-unit-clauses : 30
% 0.24/1.43 # Current number of unprocessed clauses: 150
% 0.24/1.43 # ...number of literals in the above : 402
% 0.24/1.43 # Current number of archived formulas : 0
% 0.24/1.43 # Current number of archived clauses : 3
% 0.24/1.43 # Clause-clause subsumption calls (NU) : 209
% 0.24/1.43 # Rec. Clause-clause subsumption calls : 176
% 0.24/1.43 # Non-unit clause-clause subsumptions : 40
% 0.24/1.43 # Unit Clause-clause subsumption calls : 6
% 0.24/1.43 # Rewrite failures with RHS unbound : 0
% 0.24/1.43 # BW rewrite match attempts : 7
% 0.24/1.43 # BW rewrite match successes : 3
% 0.24/1.43 # Condensation attempts : 0
% 0.24/1.43 # Condensation successes : 0
% 0.24/1.43 # Termbank termtop insertions : 3794
% 0.24/1.43
% 0.24/1.43 # -------------------------------------------------
% 0.24/1.43 # User time : 0.019 s
% 0.24/1.43 # System time : 0.001 s
% 0.24/1.43 # Total time : 0.020 s
% 0.24/1.43 # Maximum resident set size: 3040 pages
%------------------------------------------------------------------------------