TSTP Solution File: SET598+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n016.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 00:52:19 EDT 2022
% Result : Theorem 0.28s 1.45s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 115 ( 32 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 129 ( 53 ~; 55 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 4 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th57,conjecture,
! [X1,X2,X3] :
( X1 = intersection(X2,X3)
<=> ( subset(X1,X2)
& subset(X1,X3)
& ! [X4] :
( ( subset(X4,X2)
& subset(X4,X3) )
=> subset(X4,X1) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th57) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_is_subset) ).
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(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(intersection_of_subsets,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_of_subsets) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( X1 = intersection(X2,X3)
<=> ( subset(X1,X2)
& subset(X1,X3)
& ! [X4] :
( ( subset(X4,X2)
& subset(X4,X3) )
=> subset(X4,X1) ) ) ),
inference(assume_negation,[status(cth)],[prove_th57]) ).
fof(c_0_6,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
fof(c_0_7,negated_conjecture,
! [X9] :
( ( subset(esk4_0,esk2_0)
| ~ subset(esk1_0,esk2_0)
| ~ subset(esk1_0,esk3_0)
| esk1_0 != intersection(esk2_0,esk3_0) )
& ( subset(esk4_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| ~ subset(esk1_0,esk3_0)
| esk1_0 != intersection(esk2_0,esk3_0) )
& ( ~ subset(esk4_0,esk1_0)
| ~ subset(esk1_0,esk2_0)
| ~ subset(esk1_0,esk3_0)
| esk1_0 != intersection(esk2_0,esk3_0) )
& ( subset(esk1_0,esk2_0)
| esk1_0 = intersection(esk2_0,esk3_0) )
& ( subset(esk1_0,esk3_0)
| esk1_0 = intersection(esk2_0,esk3_0) )
& ( ~ subset(X9,esk2_0)
| ~ subset(X9,esk3_0)
| subset(X9,esk1_0)
| esk1_0 = intersection(esk2_0,esk3_0) ) ),
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)],[c_0_5])])])])])])]) ).
fof(c_0_8,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_9,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( esk1_0 = intersection(esk2_0,esk3_0)
| subset(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,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])])])])]) ).
fof(c_0_13,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X4,X6)
| subset(X4,intersection(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_of_subsets])]) ).
cnf(c_0_14,negated_conjecture,
( esk1_0 = intersection(esk2_0,esk3_0)
| subset(X1,esk1_0)
| ~ subset(X1,esk3_0)
| ~ subset(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0)
| ~ subset(esk4_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
subset(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( esk1_0 = intersection(esk2_0,esk3_0)
| subset(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( subset(X1,intersection(X2,X3))
| ~ subset(X1,X3)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( intersection(esk2_0,esk3_0) = esk1_0
| subset(intersection(esk2_0,X1),esk1_0)
| ~ subset(intersection(esk2_0,X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( subset(esk4_0,esk3_0)
| esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( subset(esk4_0,esk2_0)
| esk1_0 != intersection(esk2_0,esk3_0)
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( intersection(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk3_0)
| ~ subset(esk4_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_25,negated_conjecture,
subset(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( intersection(X1,X2) = X3
| ~ subset(intersection(X1,X2),X3)
| ~ subset(X3,X2)
| ~ subset(X3,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( intersection(esk2_0,esk3_0) = esk1_0
| subset(intersection(esk2_0,esk3_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( subset(esk4_0,esk3_0)
| intersection(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
( subset(esk4_0,esk2_0)
| intersection(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16])]) ).
cnf(c_0_30,negated_conjecture,
( intersection(esk2_0,esk3_0) != esk1_0
| ~ subset(esk4_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_31,negated_conjecture,
intersection(esk2_0,esk3_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]),c_0_16])]) ).
cnf(c_0_32,negated_conjecture,
( subset(esk4_0,esk3_0)
| intersection(esk2_0,esk3_0) != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_25])]) ).
cnf(c_0_33,negated_conjecture,
( subset(esk4_0,esk2_0)
| intersection(esk2_0,esk3_0) != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_25])]) ).
cnf(c_0_34,negated_conjecture,
~ subset(esk4_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
( subset(X1,esk1_0)
| ~ subset(X1,esk3_0)
| ~ subset(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
subset(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_31])]) ).
cnf(c_0_37,negated_conjecture,
subset(esk4_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_31])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.15 % Command : run_ET %s %d
% 0.15/0.36 % Computer : n016.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 : Mon Jul 11 09:04:57 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.28/1.45 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.28/1.45 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.28/1.45 # Preprocessing time : 0.015 s
% 0.28/1.45
% 0.28/1.45 # Proof found!
% 0.28/1.45 # SZS status Theorem
% 0.28/1.45 # SZS output start CNFRefutation
% See solution above
% 0.28/1.45 # Proof object total steps : 39
% 0.28/1.45 # Proof object clause steps : 28
% 0.28/1.45 # Proof object formula steps : 11
% 0.28/1.45 # Proof object conjectures : 25
% 0.28/1.45 # Proof object clause conjectures : 22
% 0.28/1.45 # Proof object formula conjectures : 3
% 0.28/1.45 # Proof object initial clauses used : 10
% 0.28/1.45 # Proof object initial formulas used : 5
% 0.28/1.45 # Proof object generating inferences : 9
% 0.28/1.45 # Proof object simplifying inferences : 24
% 0.28/1.45 # Training examples: 0 positive, 0 negative
% 0.28/1.45 # Parsed axioms : 9
% 0.28/1.45 # Removed by relevancy pruning/SinE : 3
% 0.28/1.45 # Initial clauses : 13
% 0.28/1.45 # Removed in clause preprocessing : 0
% 0.28/1.45 # Initial clauses in saturation : 13
% 0.28/1.45 # Processed clauses : 43
% 0.28/1.45 # ...of these trivial : 3
% 0.28/1.45 # ...subsumed : 1
% 0.28/1.45 # ...remaining for further processing : 39
% 0.28/1.45 # Other redundant clauses eliminated : 2
% 0.28/1.45 # Clauses deleted for lack of memory : 0
% 0.28/1.45 # Backward-subsumed : 2
% 0.28/1.45 # Backward-rewritten : 16
% 0.28/1.45 # Generated clauses : 80
% 0.28/1.45 # ...of the previous two non-trivial : 63
% 0.28/1.45 # Contextual simplify-reflections : 0
% 0.28/1.45 # Paramodulations : 78
% 0.28/1.45 # Factorizations : 0
% 0.28/1.45 # Equation resolutions : 2
% 0.28/1.45 # Current number of processed clauses : 19
% 0.28/1.45 # Positive orientable unit clauses : 8
% 0.28/1.45 # Positive unorientable unit clauses: 1
% 0.28/1.45 # Negative unit clauses : 1
% 0.28/1.45 # Non-unit-clauses : 9
% 0.28/1.45 # Current number of unprocessed clauses: 19
% 0.28/1.45 # ...number of literals in the above : 54
% 0.28/1.45 # Current number of archived formulas : 0
% 0.28/1.45 # Current number of archived clauses : 18
% 0.28/1.45 # Clause-clause subsumption calls (NU) : 53
% 0.28/1.45 # Rec. Clause-clause subsumption calls : 35
% 0.28/1.45 # Non-unit clause-clause subsumptions : 2
% 0.28/1.45 # Unit Clause-clause subsumption calls : 13
% 0.28/1.45 # Rewrite failures with RHS unbound : 0
% 0.28/1.45 # BW rewrite match attempts : 11
% 0.28/1.45 # BW rewrite match successes : 7
% 0.28/1.45 # Condensation attempts : 0
% 0.28/1.45 # Condensation successes : 0
% 0.28/1.45 # Termbank termtop insertions : 1636
% 0.28/1.45
% 0.28/1.45 # -------------------------------------------------
% 0.28/1.45 # User time : 0.015 s
% 0.28/1.45 # System time : 0.003 s
% 0.28/1.45 # Total time : 0.018 s
% 0.28/1.45 # Maximum resident set size: 2768 pages
%------------------------------------------------------------------------------