%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:31:51 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 72 ( 18 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 66 ( 24 ~; 20 |; 10 &)
% ( 2 <=>; 10 =>; 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 : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 60 ( 9 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(shortest_path_defn,axiom,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) )
& X2 != X3
& path(X2,X3,X10) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
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/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
fof(length_defn,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> length_of(X4) = number_of_in(edges,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',length_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/sandbox2/benchmark/theBenchmark.p',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/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(c_0_6,plain,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) )
& X2 != X3
& path(X2,X3,X10) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_defn]) ).
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,
! [X16,X17,X18,X19,X20,X21,X22] :
( ( shortest_path(X20,X21,X22)
| X20 = X21
| ~ path(X20,X21,X22)
| ~ less_or_equal(length_of(X22),length_of(esk4_3(X20,X21,X22))) )
& ( shortest_path(X20,X21,X22)
| X20 = X21
| ~ path(X20,X21,X22)
| path(X20,X21,esk4_3(X20,X21,X22)) )
& ( ~ shortest_path(X16,X17,X18)
| less_or_equal(length_of(X18),length_of(X19))
| ~ path(X16,X17,X19) )
& ( ~ shortest_path(X16,X17,X18)
| X16 != X17 )
& ( ~ shortest_path(X16,X17,X18)
| path(X16,X17,X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])])]) ).
fof(c_0_9,negated_conjecture,
( ~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph))
& shortest_path(esk2_0,esk3_0,esk1_0)
& complete ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,lemma,
! [X35,X36,X37] :
( number_of_in(sequential_pairs,X35) = number_of_in(triangles,X35)
| ~ shortest_path(X36,X37,X35)
| ~ complete ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangles_and_sequential_pairs])])])]) ).
fof(c_0_11,plain,
! [X38,X39,X40] :
( length_of(X40) = number_of_in(edges,X40)
| ~ path(X38,X39,X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[length_defn])])]) ).
cnf(c_0_12,plain,
( ~ shortest_path(X1,X2,X3)
| 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]) ).
cnf(c_0_14,lemma,
( ~ shortest_path(X1,X2,X3)
| ~ complete
| number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ path(X1,X2,X3)
| length_of(X3) = number_of_in(edges,X3) ),
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]) ).
fof(c_0_18,plain,
! [X26,X27,X28] :
( number_of_in(sequential_pairs,X28) = minus(length_of(X28),n1)
| ~ path(X26,X27,X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])])]) ).
fof(c_0_19,plain,
! [X24,X25] : less_or_equal(number_of_in(X24,X25),number_of_in(X24,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_20,lemma,
( ~ shortest_path(X2,X3,X1)
| number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_21,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_22,negated_conjecture,
length_of(esk1_0) = number_of_in(edges,esk1_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( ~ path(X1,X2,X3)
| number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
~ less_or_equal(minus(number_of_in(edges,esk1_0),n1),number_of_in(triangles,graph)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
minus(number_of_in(edges,esk1_0),n1) = number_of_in(sequential_pairs,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_22]) ).
cnf(c_0_28,negated_conjecture,
less_or_equal(number_of_in(sequential_pairs,esk1_0),number_of_in(triangles,graph)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 18:18:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % sh5l with pid 1011400 completed with status 0
% 0.10/0.43 % Result found by sh5l
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.43 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.43 % SubtermCWHack with pid 1011403 completed with status 0
% 0.10/0.43 % Result found by SubtermCWHack
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.43 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.43 % Preprocessing time : 0.002 s
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Theorem
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.43 % Parsed axioms : 19
% 0.10/0.43 % Removed by relevancy pruning/SinE : 0
% 0.10/0.43 % Initial clauses : 63
% 0.10/0.43 % Removed in clause preprocessing : 1
% 0.10/0.43 % Initial clauses in saturation : 62
% 0.10/0.43 % Processed clauses : 52
% 0.10/0.43 % ...of these trivial : 0
% 0.10/0.43 % ...subsumed : 1
% 0.10/0.43 % ...remaining for further processing : 51
% 0.10/0.43 % Other redundant clauses eliminated : 2
% 0.10/0.43 % Clauses deleted for lack of memory : 0
% 0.10/0.43 % Backward-subsumed : 0
% 0.10/0.43 % Backward-rewritten : 1
% 0.10/0.43 % Generated clauses : 25
% 0.10/0.43 % ...of the previous two non-redundant : 25
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 0
% 0.10/0.43 % Paramodulations : 23
% 0.10/0.43 % Factorizations : 0
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 2
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 6
% 0.10/0.43 % ...of those cached : 2
% 0.10/0.43 % Propositional unsat checks : 0
% 0.10/0.43 % Propositional check models : 0
% 0.10/0.43 % Propositional check unsatisfiable : 0
% 0.10/0.43 % Propositional clauses : 0
% 0.10/0.43 % Propositional clauses after purity: 0
% 0.10/0.43 % Propositional unsat core size : 0
% 0.10/0.43 % Propositional preprocessing time : 0.000
% 0.10/0.43 % Propositional encoding time : 0.000
% 0.10/0.43 % Propositional solver time : 0.000
% 0.10/0.43 % Success case prop preproc time : 0.000
% 0.10/0.43 % Success case prop encoding time : 0.000
% 0.10/0.43 % Success case prop solver time : 0.000
% 0.10/0.43 % Current number of processed clauses : 48
% 0.10/0.43 % Positive orientable unit clauses : 10
% 0.10/0.43 % Positive unorientable unit clauses: 0
% 0.10/0.43 % Negative unit clauses : 3
% 0.10/0.43 % Non-unit-clauses : 35
% 0.10/0.43 % Current number of unprocessed clauses: 35
% 0.10/0.43 % ...number of literals in the above : 153
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 1
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 209
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 125
% 0.10/0.43 % Non-unit clause-clause subsumptions : 1
% 0.10/0.43 % Unit Clause-clause subsumption calls : 47
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 1
% 0.10/0.43 % BW rewrite match successes : 1
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 4841
% 0.10/0.43 % Search garbage collected termcells : 1187
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.007 s
% 0.10/0.43 % System time : 0.002 s
% 0.10/0.43 % Total time : 0.010 s
% 0.10/0.43 % Maximum resident set size: 3672 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.013 s
% 0.10/0.43 % System time : 0.003 s
% 0.10/0.43 % Total time : 0.016 s
% 0.10/0.43 % Maximum resident set size: 4608 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------