TSTP Solution File: GRA002+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 1.41s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 144 ( 25 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 162 ( 60 ~; 69 |; 20 &)
% ( 1 <=>; 11 =>; 1 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 106 ( 21 sgn 57 !; 3 ?)
% 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/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',maximal_path_length) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(sequential_is_triangle,lemma,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sequential_is_triangle) ).
fof(precedes_defn,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
<= ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(sequential_pairs_and_triangles,axiom,
! [X4,X2,X3] :
( ( path(X2,X3,X4)
& ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sequential_pairs_and_triangles) ).
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/sandbox2/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/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',graph_has_them_all) ).
fof(c_0_7,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_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])])])])])])]) ).
fof(c_0_9,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_7])])])])]) ).
fof(c_0_10,lemma,
! [X10,X11,X12,X13,X14] :
( ~ complete
| ~ shortest_path(X10,X11,X14)
| ~ precedes(X12,X13,X14)
| ~ sequential(X12,X13)
| triangle(X12,X13,esk7_4(X10,X11,X12,X13)) ),
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)],[sequential_is_triangle])])])])])]) ).
fof(c_0_11,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( ~ sequential(X13,X14)
| ~ on_path(X13,X10)
| ~ on_path(X14,X10)
| precedes(X13,X14,X10)
| ~ path(X11,X12,X10) )
& ( ~ sequential(X13,X15)
| ~ precedes(X15,X14,X10)
| ~ on_path(X13,X10)
| ~ on_path(X14,X10)
| precedes(X13,X14,X10)
| ~ path(X11,X12,X10) ) ),
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)],[inference(fof_simplification,[status(thm)],[precedes_defn])])])])])])]) ).
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_9]) ).
fof(c_0_14,plain,
! [X10,X11,X12,X15] :
( ( on_path(esk5_1(X10),X10)
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) )
& ( on_path(esk6_1(X10),X10)
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) )
& ( sequential(esk5_1(X10),esk6_1(X10))
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) )
& ( ~ triangle(esk5_1(X10),esk6_1(X10),X15)
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) ) ),
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)],[sequential_pairs_and_triangles])])])])])])]) ).
cnf(c_0_15,lemma,
( triangle(X1,X2,esk7_4(X3,X4,X1,X2))
| ~ sequential(X1,X2)
| ~ precedes(X1,X2,X5)
| ~ shortest_path(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( precedes(X4,X5,X3)
| ~ path(X1,X2,X3)
| ~ on_path(X5,X3)
| ~ on_path(X4,X3)
| ~ sequential(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
path(esk2_0,esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk6_1(X1),X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,lemma,
( triangle(X1,X2,esk7_4(X3,X4,X1,X2))
| ~ shortest_path(X3,X4,X5)
| ~ precedes(X1,X2,X5)
| ~ sequential(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_21,negated_conjecture,
( precedes(X1,X2,esk1_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk1_0)
| ~ on_path(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| on_path(esk6_1(esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk5_1(X1),X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| sequential(esk5_1(X1),esk6_1(X1))
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1)
| ~ triangle(esk5_1(X1),esk6_1(X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( triangle(X1,X2,esk7_4(esk2_0,esk3_0,X1,X2))
| ~ precedes(X1,X2,esk1_0)
| ~ sequential(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| precedes(X1,esk6_1(esk1_0),esk1_0)
| ~ sequential(X1,esk6_1(esk1_0))
| ~ on_path(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| on_path(esk5_1(esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| sequential(esk5_1(esk1_0),esk6_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
fof(c_0_30,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_31,negated_conjecture,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ precedes(esk5_1(X1),esk6_1(X1),esk1_0)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| precedes(esk5_1(esk1_0),esk6_1(esk1_0),esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_33,plain,
( number_of_in(sequential_pairs,X1) = minus(length_of(X1),n1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,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_35,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| ~ path(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_37,negated_conjecture,
minus(length_of(esk1_0),n1) = number_of_in(sequential_pairs,esk1_0),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_38,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_40,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk1_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue May 31 03:06:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.24/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41 # Preprocessing time : 0.028 s
% 0.24/1.41
% 0.24/1.41 # Proof found!
% 0.24/1.41 # SZS status Theorem
% 0.24/1.41 # SZS output start CNFRefutation
% See solution above
% 0.24/1.41 # Proof object total steps : 42
% 0.24/1.41 # Proof object clause steps : 27
% 0.24/1.41 # Proof object formula steps : 15
% 0.24/1.41 # Proof object conjectures : 20
% 0.24/1.41 # Proof object clause conjectures : 17
% 0.24/1.41 # Proof object formula conjectures : 3
% 0.24/1.41 # Proof object initial clauses used : 12
% 0.24/1.41 # Proof object initial formulas used : 7
% 0.24/1.41 # Proof object generating inferences : 13
% 0.24/1.41 # Proof object simplifying inferences : 6
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 19
% 0.24/1.41 # Removed by relevancy pruning/SinE : 5
% 0.24/1.41 # Initial clauses : 45
% 0.24/1.41 # Removed in clause preprocessing : 1
% 0.24/1.41 # Initial clauses in saturation : 44
% 0.24/1.41 # Processed clauses : 158
% 0.24/1.41 # ...of these trivial : 0
% 0.24/1.41 # ...subsumed : 25
% 0.24/1.41 # ...remaining for further processing : 133
% 0.24/1.41 # Other redundant clauses eliminated : 2
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 2
% 0.24/1.41 # Backward-rewritten : 30
% 0.24/1.41 # Generated clauses : 244
% 0.24/1.41 # ...of the previous two non-trivial : 232
% 0.24/1.41 # Contextual simplify-reflections : 46
% 0.24/1.41 # Paramodulations : 236
% 0.24/1.41 # Factorizations : 1
% 0.24/1.41 # Equation resolutions : 7
% 0.24/1.41 # Current number of processed clauses : 99
% 0.24/1.41 # Positive orientable unit clauses : 6
% 0.24/1.41 # Positive unorientable unit clauses: 0
% 0.24/1.41 # Negative unit clauses : 3
% 0.24/1.41 # Non-unit-clauses : 90
% 0.24/1.41 # Current number of unprocessed clauses: 57
% 0.24/1.41 # ...number of literals in the above : 397
% 0.24/1.41 # Current number of archived formulas : 0
% 0.24/1.41 # Current number of archived clauses : 32
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 3734
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 1409
% 0.24/1.41 # Non-unit clause-clause subsumptions : 70
% 0.24/1.41 # Unit Clause-clause subsumption calls : 91
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 2
% 0.24/1.41 # BW rewrite match successes : 2
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 9262
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.043 s
% 0.24/1.41 # System time : 0.004 s
% 0.24/1.41 # Total time : 0.047 s
% 0.24/1.41 # Maximum resident set size: 3332 pages
%------------------------------------------------------------------------------