TSTP Solution File: SET183+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET183+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 00:49:55 EDT 2022
% Result : Theorem 0.21s 1.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 70 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 25 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 9 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_intersection,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_subset_intersection) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_intersection) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_is_subset) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',equal_defn) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[prove_subset_intersection]) ).
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,negated_conjecture,
( subset(esk1_0,esk2_0)
& intersection(esk1_0,esk2_0) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
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,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,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_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( subset(esk1_0,X1)
| member(esk3_2(esk1_0,X1),esk2_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_19,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
fof(c_0_20,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_21,negated_conjecture,
( subset(esk1_0,intersection(X1,esk2_0))
| ~ member(esk3_2(esk1_0,intersection(X1,esk2_0)),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
intersection(esk1_0,esk2_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
subset(esk1_0,intersection(esk2_0,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_22]) ).
cnf(c_0_27,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
intersection(esk2_0,esk1_0) != esk1_0,
inference(rw,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : run_ET %s %d
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 22:19:40 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.21/1.39 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.39 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.39 # Preprocessing time : 0.015 s
% 0.21/1.39
% 0.21/1.39 # Proof found!
% 0.21/1.39 # SZS status Theorem
% 0.21/1.39 # SZS output start CNFRefutation
% See solution above
% 0.21/1.39 # Proof object total steps : 30
% 0.21/1.39 # Proof object clause steps : 17
% 0.21/1.39 # Proof object formula steps : 13
% 0.21/1.39 # Proof object conjectures : 11
% 0.21/1.39 # Proof object clause conjectures : 8
% 0.21/1.39 # Proof object formula conjectures : 3
% 0.21/1.39 # Proof object initial clauses used : 9
% 0.21/1.39 # Proof object initial formulas used : 6
% 0.21/1.39 # Proof object generating inferences : 7
% 0.21/1.39 # Proof object simplifying inferences : 5
% 0.21/1.39 # Training examples: 0 positive, 0 negative
% 0.21/1.39 # Parsed axioms : 8
% 0.21/1.39 # Removed by relevancy pruning/SinE : 0
% 0.21/1.39 # Initial clauses : 18
% 0.21/1.39 # Removed in clause preprocessing : 2
% 0.21/1.39 # Initial clauses in saturation : 16
% 0.21/1.39 # Processed clauses : 307
% 0.21/1.39 # ...of these trivial : 15
% 0.21/1.39 # ...subsumed : 194
% 0.21/1.39 # ...remaining for further processing : 98
% 0.21/1.39 # Other redundant clauses eliminated : 2
% 0.21/1.39 # Clauses deleted for lack of memory : 0
% 0.21/1.39 # Backward-subsumed : 0
% 0.21/1.39 # Backward-rewritten : 1
% 0.21/1.39 # Generated clauses : 687
% 0.21/1.39 # ...of the previous two non-trivial : 647
% 0.21/1.39 # Contextual simplify-reflections : 11
% 0.21/1.39 # Paramodulations : 671
% 0.21/1.39 # Factorizations : 14
% 0.21/1.39 # Equation resolutions : 2
% 0.21/1.39 # Current number of processed clauses : 95
% 0.21/1.39 # Positive orientable unit clauses : 16
% 0.21/1.39 # Positive unorientable unit clauses: 1
% 0.21/1.39 # Negative unit clauses : 1
% 0.21/1.39 # Non-unit-clauses : 77
% 0.21/1.39 # Current number of unprocessed clauses: 356
% 0.21/1.39 # ...number of literals in the above : 859
% 0.21/1.39 # Current number of archived formulas : 0
% 0.21/1.39 # Current number of archived clauses : 1
% 0.21/1.39 # Clause-clause subsumption calls (NU) : 2147
% 0.21/1.39 # Rec. Clause-clause subsumption calls : 2028
% 0.21/1.39 # Non-unit clause-clause subsumptions : 205
% 0.21/1.39 # Unit Clause-clause subsumption calls : 47
% 0.21/1.39 # Rewrite failures with RHS unbound : 0
% 0.21/1.39 # BW rewrite match attempts : 9
% 0.21/1.39 # BW rewrite match successes : 2
% 0.21/1.39 # Condensation attempts : 0
% 0.21/1.39 # Condensation successes : 0
% 0.21/1.39 # Termbank termtop insertions : 9436
% 0.21/1.39
% 0.21/1.39 # -------------------------------------------------
% 0.21/1.39 # User time : 0.029 s
% 0.21/1.39 # System time : 0.003 s
% 0.21/1.39 # Total time : 0.032 s
% 0.21/1.39 # Maximum resident set size: 3292 pages
%------------------------------------------------------------------------------