TSTP Solution File: SET585+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n006.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 00:52:10 EDT 2022
% Result : Theorem 0.27s 1.44s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 31 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 5 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 5 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_subset_of_union,conjecture,
! [X1,X2,X3] : subset(intersection(X1,X2),union(X1,X3)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_intersection_subset_of_union) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_of_union) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_union) ).
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(transitivity_of_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',transitivity_of_subset) ).
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(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] : subset(intersection(X1,X2),union(X1,X3)),
inference(assume_negation,[status(cth)],[prove_intersection_subset_of_union]) ).
fof(c_0_7,plain,
! [X3,X4] : subset(X3,union(X3,X4)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
fof(c_0_8,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_9,negated_conjecture,
~ subset(intersection(esk1_0,esk2_0),union(esk1_0,esk3_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_11,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_subset])]) ).
cnf(c_0_12,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
cnf(c_0_15,negated_conjecture,
~ subset(intersection(esk1_0,esk2_0),union(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ subset(intersection(esk2_0,esk1_0),union(esk3_0,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_16]) ).
cnf(c_0_21,plain,
( subset(X1,union(X2,X3))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : run_ET %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 13:55:36 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.27/1.44 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.27/1.44 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.27/1.44 # Preprocessing time : 0.016 s
% 0.27/1.44
% 0.27/1.44 # Proof found!
% 0.27/1.44 # SZS status Theorem
% 0.27/1.44 # SZS output start CNFRefutation
% See solution above
% 0.27/1.44 # Proof object total steps : 24
% 0.27/1.44 # Proof object clause steps : 11
% 0.27/1.44 # Proof object formula steps : 13
% 0.27/1.44 # Proof object conjectures : 6
% 0.27/1.44 # Proof object clause conjectures : 3
% 0.27/1.44 # Proof object formula conjectures : 3
% 0.27/1.44 # Proof object initial clauses used : 6
% 0.27/1.44 # Proof object initial formulas used : 6
% 0.27/1.44 # Proof object generating inferences : 4
% 0.27/1.44 # Proof object simplifying inferences : 4
% 0.27/1.44 # Training examples: 0 positive, 0 negative
% 0.27/1.44 # Parsed axioms : 11
% 0.27/1.44 # Removed by relevancy pruning/SinE : 0
% 0.27/1.44 # Initial clauses : 20
% 0.27/1.44 # Removed in clause preprocessing : 2
% 0.27/1.44 # Initial clauses in saturation : 18
% 0.27/1.44 # Processed clauses : 48
% 0.27/1.44 # ...of these trivial : 8
% 0.27/1.44 # ...subsumed : 8
% 0.27/1.44 # ...remaining for further processing : 32
% 0.27/1.44 # Other redundant clauses eliminated : 0
% 0.27/1.44 # Clauses deleted for lack of memory : 0
% 0.27/1.44 # Backward-subsumed : 0
% 0.27/1.44 # Backward-rewritten : 1
% 0.27/1.44 # Generated clauses : 135
% 0.27/1.44 # ...of the previous two non-trivial : 104
% 0.27/1.44 # Contextual simplify-reflections : 0
% 0.27/1.44 # Paramodulations : 133
% 0.27/1.44 # Factorizations : 2
% 0.27/1.44 # Equation resolutions : 0
% 0.27/1.44 # Current number of processed clauses : 31
% 0.27/1.44 # Positive orientable unit clauses : 10
% 0.27/1.44 # Positive unorientable unit clauses: 2
% 0.27/1.44 # Negative unit clauses : 1
% 0.27/1.44 # Non-unit-clauses : 18
% 0.27/1.44 # Current number of unprocessed clauses: 74
% 0.27/1.44 # ...number of literals in the above : 145
% 0.27/1.44 # Current number of archived formulas : 0
% 0.27/1.44 # Current number of archived clauses : 1
% 0.27/1.44 # Clause-clause subsumption calls (NU) : 33
% 0.27/1.44 # Rec. Clause-clause subsumption calls : 33
% 0.27/1.44 # Non-unit clause-clause subsumptions : 8
% 0.27/1.44 # Unit Clause-clause subsumption calls : 2
% 0.27/1.44 # Rewrite failures with RHS unbound : 0
% 0.27/1.44 # BW rewrite match attempts : 16
% 0.27/1.44 # BW rewrite match successes : 6
% 0.27/1.44 # Condensation attempts : 0
% 0.27/1.44 # Condensation successes : 0
% 0.27/1.44 # Termbank termtop insertions : 2116
% 0.27/1.44
% 0.27/1.44 # -------------------------------------------------
% 0.27/1.44 # User time : 0.016 s
% 0.27/1.44 # System time : 0.002 s
% 0.27/1.44 # Total time : 0.018 s
% 0.27/1.44 # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------