TSTP Solution File: SET600+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n022.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 00:52:20 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 85 ( 40 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 84 ( 31 ~; 39 |; 9 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 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 : 47 ( 12 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th59,conjecture,
! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th59) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',equal_member_defn) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
inference(assume_negation,[status(cth)],[prove_th59]) ).
fof(c_0_5,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(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)],[union_defn])])])])]) ).
fof(c_0_6,negated_conjecture,
( ( union(esk1_0,esk2_0) != empty_set
| esk1_0 != empty_set
| esk2_0 != empty_set )
& ( esk1_0 = empty_set
| union(esk1_0,esk2_0) = empty_set )
& ( esk2_0 = empty_set
| union(esk1_0,esk2_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set_defn])]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk3_2(X4,X5),X4)
| ~ member(esk3_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk3_2(X4,X5),X4)
| member(esk3_2(X4,X5),X5)
| 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)],[equal_member_defn])])])])])])]) ).
cnf(c_0_9,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( union(esk1_0,esk2_0) = empty_set
| esk2_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( union(esk1_0,esk2_0) = empty_set
| esk1_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( empty_set = esk2_0
| ~ member(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_16,plain,
( X1 = empty_set
| member(esk3_2(X1,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( empty_set = esk1_0
| ~ member(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
cnf(c_0_18,negated_conjecture,
empty_set = esk2_0,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( esk2_0 = esk1_0
| ~ member(X1,esk1_0) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( X1 = esk2_0
| member(esk3_2(X1,esk2_0),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_18]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
esk2_0 = esk1_0,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,plain,
( X1 = esk1_0
| member(esk3_2(X1,esk1_0),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( esk2_0 != empty_set
| esk1_0 != empty_set
| union(esk1_0,esk2_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,plain,
( union(X1,X2) = esk1_0
| member(esk3_2(union(X1,X2),esk1_0),X1)
| member(esk3_2(union(X1,X2),esk1_0),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( union(esk1_0,esk2_0) != esk2_0
| esk2_0 != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_18]),c_0_18]),c_0_18])]) ).
cnf(c_0_27,plain,
( X1 = X2
| ~ member(esk3_2(X1,X2),X2)
| ~ member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,plain,
( union(X1,X1) = esk1_0
| member(esk3_2(union(X1,X1),esk1_0),X1) ),
inference(ef,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
union(esk1_0,esk1_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_21]),c_0_21]),c_0_21])]) ).
cnf(c_0_30,plain,
~ member(esk3_2(union(esk1_0,esk1_0),esk1_0),union(esk1_0,esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n022.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 : Sat Jul 9 23:20:10 EDT 2022
% 0.13/0.34 % 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 : 0.014 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 : 23
% 0.23/1.41 # Proof object formula steps : 9
% 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 : 4
% 0.23/1.41 # Proof object generating inferences : 9
% 0.23/1.41 # Proof object simplifying inferences : 17
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 9
% 0.23/1.41 # Removed by relevancy pruning/SinE : 4
% 0.23/1.41 # Initial clauses : 12
% 0.23/1.41 # Removed in clause preprocessing : 2
% 0.23/1.41 # Initial clauses in saturation : 10
% 0.23/1.41 # Processed clauses : 41
% 0.23/1.41 # ...of these trivial : 0
% 0.23/1.41 # ...subsumed : 11
% 0.23/1.41 # ...remaining for further processing : 30
% 0.23/1.41 # Other redundant clauses eliminated : 0
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 0
% 0.23/1.41 # Backward-rewritten : 16
% 0.23/1.41 # Generated clauses : 80
% 0.23/1.41 # ...of the previous two non-trivial : 79
% 0.23/1.41 # Contextual simplify-reflections : 0
% 0.23/1.41 # Paramodulations : 76
% 0.23/1.41 # Factorizations : 4
% 0.23/1.41 # Equation resolutions : 0
% 0.23/1.41 # Current number of processed clauses : 14
% 0.23/1.41 # Positive orientable unit clauses : 2
% 0.23/1.41 # Positive unorientable unit clauses: 1
% 0.23/1.41 # Negative unit clauses : 2
% 0.23/1.41 # Non-unit-clauses : 9
% 0.23/1.41 # Current number of unprocessed clauses: 26
% 0.23/1.41 # ...number of literals in the above : 65
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 16
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 31
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 28
% 0.23/1.41 # Non-unit clause-clause subsumptions : 9
% 0.23/1.41 # Unit Clause-clause subsumption calls : 1
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 4
% 0.23/1.41 # BW rewrite match successes : 4
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 1480
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.015 s
% 0.23/1.41 # System time : 0.002 s
% 0.23/1.41 # Total time : 0.017 s
% 0.23/1.41 # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------