TSTP Solution File: SET638+3 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n007.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 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 25 unt; 0 def)
% Number of atoms : 42 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 3 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th120,conjecture,
! [X1,X2,X3] :
( ( subset(X1,union(X2,X3))
& intersection(X1,X3) = empty_set )
=> subset(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th120) ).
fof(intersection_distributes_over_union,axiom,
! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_distributes_over_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(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_empty_set) ).
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(subset_intersection,axiom,
! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_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(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,union(X2,X3))
& intersection(X1,X3) = empty_set )
=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[prove_th120]) ).
fof(c_0_8,plain,
! [X4,X5,X6] : intersection(X4,union(X5,X6)) = union(intersection(X4,X5),intersection(X4,X6)),
inference(variable_rename,[status(thm)],[intersection_distributes_over_union]) ).
fof(c_0_9,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_10,negated_conjecture,
( subset(esk1_0,union(esk2_0,esk3_0))
& intersection(esk1_0,esk3_0) = empty_set
& ~ subset(esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_11,plain,
intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
intersection(esk1_0,esk3_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X2] : union(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
cnf(c_0_15,plain,
union(intersection(X1,X2),intersection(X3,X1)) = intersection(X1,union(X2,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
intersection(esk3_0,esk1_0) = empty_set,
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_17,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_19,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| intersection(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_intersection])]) ).
cnf(c_0_20,negated_conjecture,
intersection(esk1_0,union(X1,esk3_0)) = intersection(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
intersection(esk1_0,union(esk3_0,X1)) = intersection(esk1_0,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
subset(esk1_0,union(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_25,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
cnf(c_0_26,negated_conjecture,
( intersection(esk1_0,X1) = esk1_0
| ~ subset(esk1_0,union(esk3_0,X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
subset(esk1_0,union(esk3_0,esk2_0)),
inference(rw,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_28,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
intersection(esk2_0,esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_12]) ).
cnf(c_0_30,negated_conjecture,
~ subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 23:33:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41 # Preprocessing time : 0.015 s
% 0.23/1.41
% 0.23/1.41 # Proof found!
% 0.23/1.41 # SZS status Theorem
% 0.23/1.41 # SZS output start CNFRefutation
% See solution above
% 0.23/1.41 # Proof object total steps : 32
% 0.23/1.41 # Proof object clause steps : 17
% 0.23/1.41 # Proof object formula steps : 15
% 0.23/1.41 # Proof object conjectures : 13
% 0.23/1.41 # Proof object clause conjectures : 10
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 9
% 0.23/1.41 # Proof object initial formulas used : 7
% 0.23/1.41 # Proof object generating inferences : 6
% 0.23/1.41 # Proof object simplifying inferences : 5
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 15
% 0.23/1.41 # Removed by relevancy pruning/SinE : 1
% 0.23/1.41 # Initial clauses : 27
% 0.23/1.41 # Removed in clause preprocessing : 2
% 0.23/1.41 # Initial clauses in saturation : 25
% 0.23/1.41 # Processed clauses : 77
% 0.23/1.41 # ...of these trivial : 8
% 0.23/1.41 # ...subsumed : 15
% 0.23/1.41 # ...remaining for further processing : 54
% 0.23/1.41 # Other redundant clauses eliminated : 2
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 1
% 0.23/1.41 # Backward-rewritten : 3
% 0.23/1.41 # Generated clauses : 313
% 0.23/1.41 # ...of the previous two non-trivial : 235
% 0.23/1.41 # Contextual simplify-reflections : 0
% 0.23/1.41 # Paramodulations : 309
% 0.23/1.41 # Factorizations : 2
% 0.23/1.41 # Equation resolutions : 2
% 0.23/1.41 # Current number of processed clauses : 48
% 0.23/1.41 # Positive orientable unit clauses : 18
% 0.23/1.41 # Positive unorientable unit clauses: 2
% 0.23/1.41 # Negative unit clauses : 2
% 0.23/1.41 # Non-unit-clauses : 26
% 0.23/1.41 # Current number of unprocessed clauses: 180
% 0.23/1.41 # ...number of literals in the above : 367
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 4
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 50
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 50
% 0.23/1.41 # Non-unit clause-clause subsumptions : 11
% 0.23/1.41 # Unit Clause-clause subsumption calls : 0
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 14
% 0.23/1.41 # BW rewrite match successes : 9
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 3766
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.019 s
% 0.23/1.41 # System time : 0.002 s
% 0.23/1.41 # Total time : 0.021 s
% 0.23/1.41 # Maximum resident set size: 3044 pages
%------------------------------------------------------------------------------