TSTP Solution File: NUM410+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n029.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 : Mon Jul 18 09:32:10 EDT 2022
% Result : Theorem 0.24s 1.43s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 69 ( 27 ~; 24 |; 10 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 16 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t46_ordinal1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t46_ordinal1) ).
fof(d8_ordinal1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d8_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_r1_tarski) ).
fof(d7_ordinal1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( transfinite_sequence(X1)
<=> ordinal(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d7_ordinal1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
inference(assume_negation,[status(cth)],[t46_ordinal1]) ).
fof(c_0_5,plain,
! [X3,X4] :
( ( ~ transfinite_sequence_of(X4,X3)
| subset(relation_rng(X4),X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) )
& ( ~ subset(relation_rng(X4),X3)
| transfinite_sequence_of(X4,X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).
fof(c_0_6,plain,
! [X3] : subset(X3,X3),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_7,plain,
! [X2] :
( ( ~ transfinite_sequence(X2)
| ordinal(relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( ~ ordinal(relation_dom(X2))
| transfinite_sequence(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_ordinal1])])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk1_0)
& function(esk1_0)
& ordinal(relation_dom(esk1_0))
& ~ transfinite_sequence_of(esk1_0,relation_rng(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_9,plain,
( transfinite_sequence_of(X1,X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
ordinal(relation_dom(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
~ transfinite_sequence_of(esk1_0,relation_rng(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( transfinite_sequence_of(X1,relation_rng(X1))
| ~ transfinite_sequence(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,negated_conjecture,
transfinite_sequence(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n029.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 : Tue Jul 5 15:16:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.24/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43 # Preprocessing time : 0.017 s
% 0.24/1.43
% 0.24/1.43 # Proof found!
% 0.24/1.43 # SZS status Theorem
% 0.24/1.43 # SZS output start CNFRefutation
% See solution above
% 0.24/1.43 # Proof object total steps : 19
% 0.24/1.43 # Proof object clause steps : 10
% 0.24/1.43 # Proof object formula steps : 9
% 0.24/1.43 # Proof object conjectures : 9
% 0.24/1.43 # Proof object clause conjectures : 6
% 0.24/1.43 # Proof object formula conjectures : 3
% 0.24/1.43 # Proof object initial clauses used : 7
% 0.24/1.43 # Proof object initial formulas used : 4
% 0.24/1.43 # Proof object generating inferences : 3
% 0.24/1.43 # Proof object simplifying inferences : 7
% 0.24/1.43 # Training examples: 0 positive, 0 negative
% 0.24/1.43 # Parsed axioms : 45
% 0.24/1.43 # Removed by relevancy pruning/SinE : 12
% 0.24/1.43 # Initial clauses : 58
% 0.24/1.43 # Removed in clause preprocessing : 0
% 0.24/1.43 # Initial clauses in saturation : 58
% 0.24/1.43 # Processed clauses : 93
% 0.24/1.43 # ...of these trivial : 1
% 0.24/1.43 # ...subsumed : 7
% 0.24/1.43 # ...remaining for further processing : 85
% 0.24/1.43 # Other redundant clauses eliminated : 0
% 0.24/1.43 # Clauses deleted for lack of memory : 0
% 0.24/1.43 # Backward-subsumed : 1
% 0.24/1.43 # Backward-rewritten : 8
% 0.24/1.43 # Generated clauses : 73
% 0.24/1.43 # ...of the previous two non-trivial : 55
% 0.24/1.43 # Contextual simplify-reflections : 11
% 0.24/1.43 # Paramodulations : 73
% 0.24/1.43 # Factorizations : 0
% 0.24/1.43 # Equation resolutions : 0
% 0.24/1.43 # Current number of processed clauses : 76
% 0.24/1.43 # Positive orientable unit clauses : 30
% 0.24/1.43 # Positive unorientable unit clauses: 0
% 0.24/1.43 # Negative unit clauses : 4
% 0.24/1.43 # Non-unit-clauses : 42
% 0.24/1.43 # Current number of unprocessed clauses: 12
% 0.24/1.43 # ...number of literals in the above : 38
% 0.24/1.43 # Current number of archived formulas : 0
% 0.24/1.43 # Current number of archived clauses : 9
% 0.24/1.43 # Clause-clause subsumption calls (NU) : 369
% 0.24/1.43 # Rec. Clause-clause subsumption calls : 269
% 0.24/1.43 # Non-unit clause-clause subsumptions : 19
% 0.24/1.43 # Unit Clause-clause subsumption calls : 43
% 0.24/1.43 # Rewrite failures with RHS unbound : 0
% 0.24/1.43 # BW rewrite match attempts : 5
% 0.24/1.43 # BW rewrite match successes : 3
% 0.24/1.43 # Condensation attempts : 0
% 0.24/1.43 # Condensation successes : 0
% 0.24/1.43 # Termbank termtop insertions : 3199
% 0.24/1.43
% 0.24/1.43 # -------------------------------------------------
% 0.24/1.43 # User time : 0.017 s
% 0.24/1.43 # System time : 0.003 s
% 0.24/1.43 # Total time : 0.020 s
% 0.24/1.43 # Maximum resident set size: 3032 pages
%------------------------------------------------------------------------------