TSTP Solution File: GRA002+4 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 : Sat Jul 16 07:16:07 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 59 ( 13 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 55 ( 20 ~; 18 |; 8 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 47 ( 10 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maximal_path_length,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> less_or_equal(minus(length_of(X4),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',maximal_path_length) ).
fof(triangles_and_sequential_pairs,lemma,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',triangles_and_sequential_pairs) ).
fof(shortest_path_defn,axiom,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( path(X2,X3,X10)
& X2 != X3
& ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(path_length_sequential_pairs,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> number_of_in(sequential_pairs,X4) = minus(length_of(X4),n1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',path_length_sequential_pairs) ).
fof(graph_has_them_all,axiom,
! [X11,X12] : less_or_equal(number_of_in(X11,X12),number_of_in(X11,graph)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',graph_has_them_all) ).
fof(c_0_5,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> less_or_equal(minus(length_of(X4),n1),number_of_in(triangles,graph)) ) ),
inference(assume_negation,[status(cth)],[maximal_path_length]) ).
fof(c_0_6,lemma,
! [X5,X6,X7] :
( ~ complete
| ~ shortest_path(X6,X7,X5)
| number_of_in(sequential_pairs,X5) = number_of_in(triangles,X5) ),
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)],[triangles_and_sequential_pairs])])])])]) ).
fof(c_0_7,negated_conjecture,
( complete
& shortest_path(esk2_0,esk3_0,esk1_0)
& ~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph)) ),
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,
! [X11,X12,X13,X14,X11,X12,X13] :
( ( path(X11,X12,X13)
| ~ shortest_path(X11,X12,X13) )
& ( X11 != X12
| ~ shortest_path(X11,X12,X13) )
& ( ~ path(X11,X12,X14)
| less_or_equal(length_of(X13),length_of(X14))
| ~ shortest_path(X11,X12,X13) )
& ( path(X11,X12,esk4_3(X11,X12,X13))
| ~ path(X11,X12,X13)
| X11 = X12
| shortest_path(X11,X12,X13) )
& ( ~ less_or_equal(length_of(X13),length_of(esk4_3(X11,X12,X13)))
| ~ path(X11,X12,X13)
| X11 = X12
| shortest_path(X11,X12,X13) ) ),
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)],[shortest_path_defn])])])])])])]) ).
cnf(c_0_9,lemma,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ shortest_path(X2,X3,X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X5,X6,X7] :
( ~ path(X5,X6,X7)
| number_of_in(sequential_pairs,X7) = minus(length_of(X7),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
cnf(c_0_12,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
shortest_path(esk2_0,esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_14,plain,
! [X13,X14] : less_or_equal(number_of_in(X13,X14),number_of_in(X13,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_15,lemma,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ shortest_path(X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).
cnf(c_0_16,plain,
( number_of_in(sequential_pairs,X1) = minus(length_of(X1),n1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
path(esk2_0,esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_20,negated_conjecture,
~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
minus(length_of(esk1_0),n1) = number_of_in(sequential_pairs,esk1_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
less_or_equal(number_of_in(sequential_pairs,esk1_0),number_of_in(triangles,graph)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.12/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n024.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 May 31 02:26:51 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 : 0.017 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 : 24
% 0.24/1.42 # Proof object clause steps : 13
% 0.24/1.42 # Proof object formula steps : 11
% 0.24/1.42 # Proof object conjectures : 11
% 0.24/1.42 # Proof object clause conjectures : 8
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 7
% 0.24/1.42 # Proof object initial formulas used : 5
% 0.24/1.42 # Proof object generating inferences : 4
% 0.24/1.42 # Proof object simplifying inferences : 5
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 19
% 0.24/1.42 # Removed by relevancy pruning/SinE : 7
% 0.24/1.42 # Initial clauses : 34
% 0.24/1.42 # Removed in clause preprocessing : 1
% 0.24/1.42 # Initial clauses in saturation : 33
% 0.24/1.42 # Processed clauses : 41
% 0.24/1.42 # ...of these trivial : 0
% 0.24/1.42 # ...subsumed : 0
% 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 : 0
% 0.24/1.42 # Backward-rewritten : 1
% 0.24/1.42 # Generated clauses : 24
% 0.24/1.42 # ...of the previous two non-trivial : 25
% 0.24/1.42 # Contextual simplify-reflections : 1
% 0.24/1.42 # Paramodulations : 22
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 2
% 0.24/1.42 # Current number of processed clauses : 37
% 0.24/1.42 # Positive orientable unit clauses : 7
% 0.24/1.42 # Positive unorientable unit clauses: 0
% 0.24/1.42 # Negative unit clauses : 1
% 0.24/1.42 # Non-unit-clauses : 29
% 0.24/1.42 # Current number of unprocessed clauses: 17
% 0.24/1.42 # ...number of literals in the above : 74
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 1
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 144
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 39
% 0.24/1.42 # Non-unit clause-clause subsumptions : 1
% 0.24/1.42 # Unit Clause-clause subsumption calls : 52
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 1
% 0.24/1.42 # BW rewrite match successes : 1
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 2869
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.016 s
% 0.24/1.42 # System time : 0.004 s
% 0.24/1.42 # Total time : 0.020 s
% 0.24/1.42 # Maximum resident set size: 3036 pages
%------------------------------------------------------------------------------