TSTP Solution File: SET083+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n003.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 00:48:54 EDT 2022
% Result : Theorem 0.23s 1.40s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 24 unt; 0 def)
% Number of atoms : 127 ( 34 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 117 ( 42 ~; 42 |; 24 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 14 sgn 42 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton_identified_by_element1,conjecture,
! [X1,X2] :
( ( singleton(X1) = singleton(X2)
& member(X1,universal_class) )
=> X1 = X2 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',singleton_identified_by_element1) ).
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(element_relation_defn,axiom,
! [X1,X2] :
( member(ordered_pair(X1,X2),element_relation)
<=> ( member(X2,universal_class)
& member(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',element_relation_defn) ).
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X1] : subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(inductive_defn,axiom,
! [X1] :
( inductive(X1)
<=> ( member(null_class,X1)
& subclass(image(successor_relation,X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inductive_defn) ).
fof(infinity,axiom,
? [X1] :
( member(X1,universal_class)
& inductive(X1)
& ! [X2] :
( inductive(X2)
=> subclass(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',infinity) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2] :
( ( singleton(X1) = singleton(X2)
& member(X1,universal_class) )
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[singleton_identified_by_element1]) ).
fof(c_0_11,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( member(X4,universal_class)
| ~ member(X4,unordered_pair(X5,X6)) )
& ( X4 = X5
| X4 = X6
| ~ member(X4,unordered_pair(X5,X6)) )
& ( X4 != X5
| ~ member(X4,universal_class)
| member(X4,unordered_pair(X5,X6)) )
& ( X4 != X6
| ~ member(X4,universal_class)
| member(X4,unordered_pair(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])])])]) ).
fof(c_0_12,negated_conjecture,
( singleton(esk8_0) = singleton(esk9_0)
& member(esk8_0,universal_class)
& esk8_0 != esk9_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_13,plain,
! [X2] : singleton(X2) = unordered_pair(X2,X2),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_14,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(singleton(X3),unordered_pair(X3,singleton(X4))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
cnf(c_0_15,plain,
( member(X1,unordered_pair(X2,X3))
| ~ member(X1,universal_class)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
singleton(esk8_0) = singleton(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X3,X4,X3,X4] :
( ( member(X4,universal_class)
| ~ member(ordered_pair(X3,X4),element_relation) )
& ( member(X3,X4)
| ~ member(ordered_pair(X3,X4),element_relation) )
& ( ~ member(X4,universal_class)
| ~ member(X3,X4)
| member(ordered_pair(X3,X4),element_relation) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[element_relation_defn])])])])]) ).
cnf(c_0_19,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
unordered_pair(esk9_0,esk9_0) = unordered_pair(esk8_0,esk8_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_22,plain,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),element_relation) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_17]) ).
cnf(c_0_24,plain,
( X1 = X3
| X1 = X2
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,negated_conjecture,
( member(esk9_0,unordered_pair(esk8_0,esk8_0))
| ~ member(esk9_0,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
esk8_0 != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,plain,
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ member(esk9_0,universal_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(X1,X2)
| ~ member(X2,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,negated_conjecture,
~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(esk8_0,esk8_0))),element_relation),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_28]) ).
cnf(c_0_31,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
| ~ member(X1,X2)
| ~ member(X2,universal_class) ),
inference(rw,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_32,negated_conjecture,
member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_33,plain,
! [X4] :
( ( member(esk6_1(X4),universal_class)
| X4 = null_class )
& ( member(esk6_1(X4),X4)
| X4 = null_class )
& ( disjoint(esk6_1(X4),X4)
| X4 = null_class ) ),
inference(distribute,[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)],[regularity])])])])])]) ).
cnf(c_0_34,negated_conjecture,
~ member(X1,esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,plain,
( X1 = null_class
| member(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_36,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subclass(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk1_2(X4,X5),X4)
| subclass(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subclass(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)],[subclass_defn])])])])])])]) ).
fof(c_0_37,plain,
! [X2] : subclass(X2,universal_class),
inference(variable_rename,[status(thm)],[class_elements_are_sets]) ).
fof(c_0_38,plain,
! [X2,X2] :
( ( member(null_class,X2)
| ~ inductive(X2) )
& ( subclass(image(successor_relation,X2),X2)
| ~ inductive(X2) )
& ( ~ member(null_class,X2)
| ~ subclass(image(successor_relation,X2),X2)
| inductive(X2) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inductive_defn])])])])]) ).
fof(c_0_39,plain,
! [X4] :
( member(esk2_0,universal_class)
& inductive(esk2_0)
& ( ~ inductive(X4)
| subclass(esk2_0,X4) ) ),
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)],[infinity])])])])])]) ).
cnf(c_0_40,negated_conjecture,
esk8_0 = null_class,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subclass(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( member(null_class,X1)
| ~ inductive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
inductive(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,negated_conjecture,
unordered_pair(esk9_0,esk9_0) = unordered_pair(null_class,null_class),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_40]),c_0_40]) ).
cnf(c_0_46,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
member(null_class,esk2_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( X1 = esk9_0
| ~ member(X1,unordered_pair(null_class,null_class)) ),
inference(spm,[status(thm)],[c_0_24,c_0_45]) ).
cnf(c_0_49,plain,
member(null_class,universal_class),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
esk9_0 != null_class,
inference(rw,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_20]),c_0_49])]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 19:47:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.23/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.40 # Preprocessing time : 0.015 s
% 0.23/1.40
% 0.23/1.40 # Failure: Out of unprocessed clauses!
% 0.23/1.40 # OLD status GaveUp
% 0.23/1.40 # Parsed axioms : 44
% 0.23/1.40 # Removed by relevancy pruning/SinE : 43
% 0.23/1.40 # Initial clauses : 3
% 0.23/1.40 # Removed in clause preprocessing : 0
% 0.23/1.40 # Initial clauses in saturation : 3
% 0.23/1.40 # Processed clauses : 3
% 0.23/1.40 # ...of these trivial : 0
% 0.23/1.40 # ...subsumed : 0
% 0.23/1.40 # ...remaining for further processing : 3
% 0.23/1.40 # Other redundant clauses eliminated : 0
% 0.23/1.40 # Clauses deleted for lack of memory : 0
% 0.23/1.40 # Backward-subsumed : 0
% 0.23/1.40 # Backward-rewritten : 0
% 0.23/1.40 # Generated clauses : 0
% 0.23/1.40 # ...of the previous two non-trivial : 0
% 0.23/1.40 # Contextual simplify-reflections : 0
% 0.23/1.40 # Paramodulations : 0
% 0.23/1.40 # Factorizations : 0
% 0.23/1.40 # Equation resolutions : 0
% 0.23/1.40 # Current number of processed clauses : 3
% 0.23/1.40 # Positive orientable unit clauses : 2
% 0.23/1.40 # Positive unorientable unit clauses: 0
% 0.23/1.40 # Negative unit clauses : 1
% 0.23/1.40 # Non-unit-clauses : 0
% 0.23/1.40 # Current number of unprocessed clauses: 0
% 0.23/1.40 # ...number of literals in the above : 0
% 0.23/1.40 # Current number of archived formulas : 0
% 0.23/1.40 # Current number of archived clauses : 0
% 0.23/1.40 # Clause-clause subsumption calls (NU) : 0
% 0.23/1.40 # Rec. Clause-clause subsumption calls : 0
% 0.23/1.40 # Non-unit clause-clause subsumptions : 0
% 0.23/1.40 # Unit Clause-clause subsumption calls : 0
% 0.23/1.40 # Rewrite failures with RHS unbound : 0
% 0.23/1.40 # BW rewrite match attempts : 0
% 0.23/1.40 # BW rewrite match successes : 0
% 0.23/1.40 # Condensation attempts : 0
% 0.23/1.40 # Condensation successes : 0
% 0.23/1.40 # Termbank termtop insertions : 579
% 0.23/1.40
% 0.23/1.40 # -------------------------------------------------
% 0.23/1.40 # User time : 0.013 s
% 0.23/1.40 # System time : 0.002 s
% 0.23/1.40 # Total time : 0.015 s
% 0.23/1.40 # Maximum resident set size: 2728 pages
% 0.23/1.40 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.23/1.40 # Preprocessing time : 0.019 s
% 0.23/1.40
% 0.23/1.40 # Proof found!
% 0.23/1.40 # SZS status Theorem
% 0.23/1.40 # SZS output start CNFRefutation
% See solution above
% 0.23/1.40 # Proof object total steps : 52
% 0.23/1.40 # Proof object clause steps : 31
% 0.23/1.40 # Proof object formula steps : 21
% 0.23/1.40 # Proof object conjectures : 16
% 0.23/1.40 # Proof object clause conjectures : 13
% 0.23/1.40 # Proof object formula conjectures : 3
% 0.23/1.40 # Proof object initial clauses used : 14
% 0.23/1.40 # Proof object initial formulas used : 10
% 0.23/1.40 # Proof object generating inferences : 10
% 0.23/1.40 # Proof object simplifying inferences : 17
% 0.23/1.40 # Training examples: 0 positive, 0 negative
% 0.23/1.40 # Parsed axioms : 44
% 0.23/1.40 # Removed by relevancy pruning/SinE : 0
% 0.23/1.40 # Initial clauses : 92
% 0.23/1.40 # Removed in clause preprocessing : 8
% 0.23/1.40 # Initial clauses in saturation : 84
% 0.23/1.40 # Processed clauses : 138
% 0.23/1.40 # ...of these trivial : 2
% 0.23/1.40 # ...subsumed : 19
% 0.23/1.40 # ...remaining for further processing : 117
% 0.23/1.40 # Other redundant clauses eliminated : 5
% 0.23/1.40 # Clauses deleted for lack of memory : 0
% 0.23/1.40 # Backward-subsumed : 4
% 0.23/1.40 # Backward-rewritten : 11
% 0.23/1.40 # Generated clauses : 414
% 0.23/1.40 # ...of the previous two non-trivial : 384
% 0.23/1.40 # Contextual simplify-reflections : 1
% 0.23/1.40 # Paramodulations : 407
% 0.23/1.40 # Factorizations : 0
% 0.23/1.40 # Equation resolutions : 7
% 0.23/1.40 # Current number of processed clauses : 98
% 0.23/1.40 # Positive orientable unit clauses : 21
% 0.23/1.40 # Positive unorientable unit clauses: 0
% 0.23/1.40 # Negative unit clauses : 5
% 0.23/1.40 # Non-unit-clauses : 72
% 0.23/1.40 # Current number of unprocessed clauses: 216
% 0.23/1.40 # ...number of literals in the above : 583
% 0.23/1.40 # Current number of archived formulas : 0
% 0.23/1.40 # Current number of archived clauses : 23
% 0.23/1.40 # Clause-clause subsumption calls (NU) : 847
% 0.23/1.40 # Rec. Clause-clause subsumption calls : 734
% 0.23/1.40 # Non-unit clause-clause subsumptions : 11
% 0.23/1.40 # Unit Clause-clause subsumption calls : 547
% 0.23/1.40 # Rewrite failures with RHS unbound : 0
% 0.23/1.40 # BW rewrite match attempts : 18
% 0.23/1.40 # BW rewrite match successes : 4
% 0.23/1.40 # Condensation attempts : 0
% 0.23/1.40 # Condensation successes : 0
% 0.23/1.40 # Termbank termtop insertions : 15203
% 0.23/1.40
% 0.23/1.40 # -------------------------------------------------
% 0.23/1.40 # User time : 0.031 s
% 0.23/1.40 # System time : 0.001 s
% 0.23/1.40 # Total time : 0.032 s
% 0.23/1.40 # Maximum resident set size: 3632 pages
%------------------------------------------------------------------------------