TSTP Solution File: SET597+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n012.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 00:52:18 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% 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_th56,conjecture,
! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( subset(X2,X1)
& subset(X3,X1)
& ! [X4] :
( ( subset(X2,X4)
& subset(X3,X4) )
=> subset(X1,X4) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th56) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_union) ).
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(union_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(union(X1,X3),X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_subset) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( subset(X2,X1)
& subset(X3,X1)
& ! [X4] :
( ( subset(X2,X4)
& subset(X3,X4) )
=> subset(X1,X4) ) ) ),
inference(assume_negation,[status(cth)],[prove_th56]) ).
fof(c_0_6,plain,
! [X3,X4] : subset(X3,union(X3,X4)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
fof(c_0_7,negated_conjecture,
! [X9] :
( ( subset(esk2_0,esk4_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| esk1_0 != union(esk2_0,esk3_0) )
& ( subset(esk3_0,esk4_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| esk1_0 != union(esk2_0,esk3_0) )
& ( ~ subset(esk1_0,esk4_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk3_0,esk1_0)
| esk1_0 != union(esk2_0,esk3_0) )
& ( subset(esk2_0,esk1_0)
| esk1_0 = union(esk2_0,esk3_0) )
& ( subset(esk3_0,esk1_0)
| esk1_0 = union(esk2_0,esk3_0) )
& ( ~ subset(esk2_0,X9)
| ~ subset(esk3_0,X9)
| subset(esk1_0,X9)
| esk1_0 = union(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] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_9,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
union(X1,X2) = union(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(X6,X5)
| subset(union(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_subset])]) ).
cnf(c_0_14,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk1_0,X1)
| ~ subset(esk3_0,X1)
| ~ subset(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0)
| ~ subset(esk1_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
subset(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( esk1_0 = union(esk2_0,esk3_0)
| subset(esk3_0,esk1_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(union(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| subset(esk1_0,union(esk2_0,X1))
| ~ subset(esk3_0,union(esk2_0,X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( subset(esk3_0,esk4_0)
| esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( subset(esk2_0,esk4_0)
| esk1_0 != union(esk2_0,esk3_0)
| ~ subset(esk3_0,esk1_0)
| ~ subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk4_0)
| ~ subset(esk3_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_25,negated_conjecture,
subset(esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( X1 = union(X2,X3)
| ~ subset(X1,union(X2,X3))
| ~ subset(X3,X1)
| ~ subset(X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( union(esk2_0,esk3_0) = esk1_0
| subset(esk1_0,union(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( subset(esk3_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk3_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
( subset(esk2_0,esk4_0)
| union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk3_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16])]) ).
cnf(c_0_30,negated_conjecture,
( union(esk2_0,esk3_0) != esk1_0
| ~ subset(esk1_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_31,negated_conjecture,
union(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(esk3_0,esk4_0)
| union(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(esk2_0,esk4_0)
| union(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(esk1_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
( subset(esk1_0,X1)
| ~ subset(esk3_0,X1)
| ~ subset(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
subset(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_31])]) ).
cnf(c_0_37,negated_conjecture,
subset(esk2_0,esk4_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
% 0.07/0.12 % Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 15:41:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.014 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 39
% 0.24/1.42 # Proof object clause steps : 28
% 0.24/1.42 # Proof object formula steps : 11
% 0.24/1.42 # Proof object conjectures : 25
% 0.24/1.42 # Proof object clause conjectures : 22
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 10
% 0.24/1.42 # Proof object initial formulas used : 5
% 0.24/1.42 # Proof object generating inferences : 9
% 0.24/1.42 # Proof object simplifying inferences : 24
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 9
% 0.24/1.42 # Removed by relevancy pruning/SinE : 3
% 0.24/1.42 # Initial clauses : 13
% 0.24/1.42 # Removed in clause preprocessing : 0
% 0.24/1.42 # Initial clauses in saturation : 13
% 0.24/1.42 # Processed clauses : 43
% 0.24/1.42 # ...of these trivial : 2
% 0.24/1.42 # ...subsumed : 1
% 0.24/1.42 # ...remaining for further processing : 40
% 0.24/1.42 # Other redundant clauses eliminated : 2
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 2
% 0.24/1.42 # Backward-rewritten : 16
% 0.24/1.42 # Generated clauses : 82
% 0.24/1.42 # ...of the previous two non-trivial : 66
% 0.24/1.42 # Contextual simplify-reflections : 0
% 0.24/1.42 # Paramodulations : 80
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 2
% 0.24/1.42 # Current number of processed clauses : 20
% 0.24/1.42 # Positive orientable unit clauses : 8
% 0.24/1.42 # Positive unorientable unit clauses: 1
% 0.24/1.42 # Negative unit clauses : 1
% 0.24/1.42 # Non-unit-clauses : 10
% 0.24/1.42 # Current number of unprocessed clauses: 20
% 0.24/1.42 # ...number of literals in the above : 60
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 18
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 56
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 38
% 0.24/1.42 # Non-unit clause-clause subsumptions : 2
% 0.24/1.42 # Unit Clause-clause subsumption calls : 14
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 11
% 0.24/1.42 # BW rewrite match successes : 7
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 1626
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.015 s
% 0.24/1.42 # System time : 0.003 s
% 0.24/1.42 # Total time : 0.018 s
% 0.24/1.42 # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------