TSTP Solution File: SET664+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n004.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 00:52:59 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 128 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 144 ( 55 ~; 53 |; 12 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p28,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p28) ).
fof(p33,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p33) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p6) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p3) ).
fof(prove_relset_1_27,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ilf_type(X3,relation_type(X2,empty_set))
=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_relset_1_27) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p13) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X1,empty_set)
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p1) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( ( domain_of(X1) = empty_set
| range_of(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p2) ).
fof(c_0_8,plain,
! [X4,X5,X6] :
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p28])])])])]) ).
fof(c_0_9,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[p33]) ).
fof(c_0_10,plain,
! [X5,X6,X7,X8] :
( ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6)))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])])]) ).
fof(c_0_11,plain,
! [X4,X5,X6] :
( ( subset(domain_of(X6),X4)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( subset(range_of(X6),X5)
| ~ ilf_type(X6,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ilf_type(X3,relation_type(X2,empty_set))
=> X3 = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_27]) ).
fof(c_0_13,plain,
! [X2] :
( ( relation_like(X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ilf_type(X2,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
cnf(c_0_14,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_18,plain,
( subset(range_of(X3),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk14_0,esk13_0))
& ilf_type(esk15_0,relation_type(esk14_0,empty_set))
& esk15_0 != empty_set ),
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_12])])])])]) ).
cnf(c_0_20,plain,
( ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15])]) ).
cnf(c_0_22,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15]),c_0_15])]) ).
cnf(c_0_23,plain,
( X1 = empty_set
| ~ subset(X1,empty_set)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( subset(range_of(X1),X2)
| ~ ilf_type(X1,relation_type(X3,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15]),c_0_15])]) ).
cnf(c_0_25,negated_conjecture,
ilf_type(esk15_0,relation_type(esk14_0,empty_set)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
ilf_type(esk15_0,relation_type(esk14_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_29,plain,
! [X2] :
( ( domain_of(X2) != empty_set
| X2 = empty_set
| ~ ilf_type(X2,binary_relation_type) )
& ( range_of(X2) != empty_set
| X2 = empty_set
| ~ ilf_type(X2,binary_relation_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
cnf(c_0_30,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_15])]) ).
cnf(c_0_31,negated_conjecture,
subset(range_of(esk15_0),empty_set),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15])]) ).
cnf(c_0_33,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( X1 = empty_set
| ~ ilf_type(X1,binary_relation_type)
| range_of(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
range_of(esk15_0) = empty_set,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
esk15_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[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 : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n004.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 11:00:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42 # Preprocessing time : 0.015 s
% 0.23/1.42
% 0.23/1.42 # Failure: Out of unprocessed clauses!
% 0.23/1.42 # OLD status GaveUp
% 0.23/1.42 # Parsed axioms : 35
% 0.23/1.42 # Removed by relevancy pruning/SinE : 29
% 0.23/1.42 # Initial clauses : 12
% 0.23/1.42 # Removed in clause preprocessing : 0
% 0.23/1.42 # Initial clauses in saturation : 12
% 0.23/1.42 # Processed clauses : 12
% 0.23/1.42 # ...of these trivial : 1
% 0.23/1.42 # ...subsumed : 0
% 0.23/1.42 # ...remaining for further processing : 11
% 0.23/1.42 # Other redundant clauses eliminated : 0
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 0
% 0.23/1.42 # Backward-rewritten : 2
% 0.23/1.42 # Generated clauses : 2
% 0.23/1.42 # ...of the previous two non-trivial : 0
% 0.23/1.42 # Contextual simplify-reflections : 0
% 0.23/1.42 # Paramodulations : 2
% 0.23/1.42 # Factorizations : 0
% 0.23/1.42 # Equation resolutions : 0
% 0.23/1.42 # Current number of processed clauses : 9
% 0.23/1.42 # Positive orientable unit clauses : 5
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 2
% 0.23/1.42 # Non-unit-clauses : 2
% 0.23/1.42 # Current number of unprocessed clauses: 0
% 0.23/1.42 # ...number of literals in the above : 0
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 2
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 0
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 0
% 0.23/1.42 # Non-unit clause-clause subsumptions : 0
% 0.23/1.42 # Unit Clause-clause subsumption calls : 0
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 2
% 0.23/1.42 # BW rewrite match successes : 2
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 1093
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.014 s
% 0.23/1.42 # System time : 0.002 s
% 0.23/1.42 # Total time : 0.015 s
% 0.23/1.42 # Maximum resident set size: 2732 pages
% 0.23/1.42 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.23/1.42 # Preprocessing time : 0.019 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 39
% 0.23/1.42 # Proof object clause steps : 22
% 0.23/1.42 # Proof object formula steps : 17
% 0.23/1.42 # Proof object conjectures : 11
% 0.23/1.42 # Proof object clause conjectures : 8
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 10
% 0.23/1.42 # Proof object initial formulas used : 8
% 0.23/1.42 # Proof object generating inferences : 6
% 0.23/1.42 # Proof object simplifying inferences : 17
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 35
% 0.23/1.42 # Removed by relevancy pruning/SinE : 0
% 0.23/1.42 # Initial clauses : 65
% 0.23/1.42 # Removed in clause preprocessing : 5
% 0.23/1.42 # Initial clauses in saturation : 60
% 0.23/1.42 # Processed clauses : 74
% 0.23/1.42 # ...of these trivial : 16
% 0.23/1.42 # ...subsumed : 0
% 0.23/1.42 # ...remaining for further processing : 58
% 0.23/1.42 # Other redundant clauses eliminated : 0
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 0
% 0.23/1.42 # Backward-rewritten : 4
% 0.23/1.42 # Generated clauses : 55
% 0.23/1.42 # ...of the previous two non-trivial : 46
% 0.23/1.42 # Contextual simplify-reflections : 1
% 0.23/1.42 # Paramodulations : 55
% 0.23/1.42 # Factorizations : 0
% 0.23/1.42 # Equation resolutions : 0
% 0.23/1.42 # Current number of processed clauses : 54
% 0.23/1.42 # Positive orientable unit clauses : 17
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 3
% 0.23/1.42 # Non-unit-clauses : 34
% 0.23/1.42 # Current number of unprocessed clauses: 30
% 0.23/1.42 # ...number of literals in the above : 62
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 4
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 165
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 51
% 0.23/1.42 # Non-unit clause-clause subsumptions : 1
% 0.23/1.42 # Unit Clause-clause subsumption calls : 74
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 3
% 0.23/1.42 # BW rewrite match successes : 3
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 5630
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.020 s
% 0.23/1.42 # System time : 0.002 s
% 0.23/1.42 # Total time : 0.022 s
% 0.23/1.42 # Maximum resident set size: 3024 pages
%------------------------------------------------------------------------------