%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRA010+2 : 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 : n019.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 12:31:30 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 65 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 71 ( 23 ~; 25 |; 15 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 13 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complete_means_sequential_pairs_and_triangles,conjecture,
( complete
=> ! [X4,X2,X3] :
( ( ! [X7,X8] :
( ( sequential(X7,X8)
& on_path(X8,X4)
& on_path(X7,X4) )
=> ? [X9] : triangle(X7,X8,X9) )
& path(X2,X3,X4) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(sequential_pairs_and_triangles,axiom,
! [X4,X2,X3] :
( ( ! [X7,X8] :
( ( sequential(X7,X8)
& on_path(X8,X4)
& on_path(X7,X4) )
=> ? [X9] : triangle(X7,X8,X9) )
& path(X2,X3,X4) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(c_0_2,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( ( ! [X7,X8] :
( ( sequential(X7,X8)
& on_path(X8,X4)
& on_path(X7,X4) )
=> ? [X9] : triangle(X7,X8,X9) )
& path(X2,X3,X4) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
inference(assume_negation,[status(cth)],[complete_means_sequential_pairs_and_triangles]) ).
fof(c_0_3,plain,
! [X19,X20,X21,X24] :
( ( number_of_in(sequential_pairs,X19) = number_of_in(triangles,X19)
| ~ path(X20,X21,X19)
| ~ triangle(esk5_1(X19),esk6_1(X19),X24) )
& ( number_of_in(sequential_pairs,X19) = number_of_in(triangles,X19)
| ~ path(X20,X21,X19)
| sequential(esk5_1(X19),esk6_1(X19)) )
& ( number_of_in(sequential_pairs,X19) = number_of_in(triangles,X19)
| ~ path(X20,X21,X19)
| on_path(esk6_1(X19),X19) )
& ( number_of_in(sequential_pairs,X19) = number_of_in(triangles,X19)
| ~ path(X20,X21,X19)
| on_path(esk5_1(X19),X19) ) ),
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)],[sequential_pairs_and_triangles])])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X16,X17] :
( number_of_in(sequential_pairs,esk1_0) != number_of_in(triangles,esk1_0)
& ( triangle(X16,X17,esk4_2(X16,X17))
| ~ sequential(X16,X17)
| ~ on_path(X17,esk1_0)
| ~ on_path(X16,esk1_0) )
& path(esk2_0,esk3_0,esk1_0)
& complete ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).
cnf(c_0_5,plain,
( ~ path(X3,X4,X1)
| ~ triangle(esk5_1(X1),esk6_1(X1),X2)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( ~ sequential(X1,X2)
| ~ on_path(X2,esk1_0)
| ~ on_path(X1,esk1_0)
| triangle(X1,X2,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| sequential(esk5_1(X1),esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
path(esk2_0,esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
number_of_in(sequential_pairs,esk1_0) != number_of_in(triangles,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
( ~ path(X2,X3,X1)
| ~ on_path(esk5_1(X1),esk1_0)
| ~ on_path(esk6_1(X1),esk1_0)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
cnf(c_0_13,negated_conjecture,
on_path(esk6_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_14,negated_conjecture,
on_path(esk5_1(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_10]) ).
cnf(c_0_15,negated_conjecture,
~ path(X1,X2,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_10]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_9,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 18:24:50 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.45 % Version: 3.5.1
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % new_bool_1 with pid 668300 completed with status 0
% 0.15/0.45 % Result found by new_bool_1
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.45 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.15/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.45 % SubtermCWHack with pid 668303 completed with status 0
% 0.15/0.45 % Result found by SubtermCWHack
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.45 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.15/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.45 % Preprocessing time : 0.002 s
% 0.15/0.45
% 0.15/0.45 % Proof found!
% 0.15/0.45 % SZS status Theorem
% 0.15/0.45 % SZS output start CNFRefutation
% See solution above
% 0.15/0.45 % Parsed axioms : 19
% 0.15/0.45 % Removed by relevancy pruning/SinE : 7
% 0.15/0.45 % Initial clauses : 44
% 0.15/0.45 % Removed in clause preprocessing : 1
% 0.15/0.45 % Initial clauses in saturation : 43
% 0.15/0.45 % Processed clauses : 147
% 0.15/0.45 % ...of these trivial : 0
% 0.15/0.45 % ...subsumed : 26
% 0.15/0.45 % ...remaining for further processing : 121
% 0.15/0.45 % Other redundant clauses eliminated : 4
% 0.15/0.45 % Clauses deleted for lack of memory : 0
% 0.15/0.45 % Backward-subsumed : 9
% 0.15/0.45 % Backward-rewritten : 0
% 0.15/0.45 % Generated clauses : 262
% 0.15/0.45 % ...of the previous two non-redundant : 228
% 0.15/0.45 % ...aggressively subsumed : 0
% 0.15/0.45 % Contextual simplify-reflections : 12
% 0.15/0.45 % Paramodulations : 256
% 0.15/0.45 % Factorizations : 0
% 0.15/0.45 % NegExts : 0
% 0.15/0.45 % Equation resolutions : 5
% 0.15/0.45 % Disequality decompositions : 0
% 0.15/0.45 % Total rewrite steps : 55
% 0.15/0.45 % ...of those cached : 46
% 0.15/0.45 % Propositional unsat checks : 0
% 0.15/0.45 % Propositional check models : 0
% 0.15/0.45 % Propositional check unsatisfiable : 0
% 0.15/0.45 % Propositional clauses : 0
% 0.15/0.45 % Propositional clauses after purity: 0
% 0.15/0.45 % Propositional unsat core size : 0
% 0.15/0.45 % Propositional preprocessing time : 0.000
% 0.15/0.45 % Propositional encoding time : 0.000
% 0.15/0.45 % Propositional solver time : 0.000
% 0.15/0.45 % Success case prop preproc time : 0.000
% 0.15/0.45 % Success case prop encoding time : 0.000
% 0.15/0.45 % Success case prop solver time : 0.000
% 0.15/0.45 % Current number of processed clauses : 109
% 0.15/0.45 % Positive orientable unit clauses : 10
% 0.15/0.45 % Positive unorientable unit clauses: 0
% 0.15/0.45 % Negative unit clauses : 6
% 0.15/0.45 % Non-unit-clauses : 93
% 0.15/0.45 % Current number of unprocessed clauses: 124
% 0.15/0.45 % ...number of literals in the above : 718
% 0.15/0.45 % Current number of archived formulas : 0
% 0.15/0.45 % Current number of archived clauses : 10
% 0.15/0.45 % Clause-clause subsumption calls (NU) : 2122
% 0.15/0.45 % Rec. Clause-clause subsumption calls : 729
% 0.15/0.45 % Non-unit clause-clause subsumptions : 38
% 0.15/0.45 % Unit Clause-clause subsumption calls : 150
% 0.15/0.45 % Rewrite failures with RHS unbound : 0
% 0.15/0.45 % BW rewrite match attempts : 0
% 0.15/0.45 % BW rewrite match successes : 0
% 0.15/0.45 % Condensation attempts : 0
% 0.15/0.45 % Condensation successes : 0
% 0.15/0.45 % Termbank termtop insertions : 10014
% 0.15/0.45 % Search garbage collected termcells : 1044
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.016 s
% 0.15/0.45 % System time : 0.006 s
% 0.15/0.45 % Total time : 0.022 s
% 0.15/0.45 % Maximum resident set size: 3668 pages
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.019 s
% 0.15/0.45 % System time : 0.009 s
% 0.15/0.45 % Total time : 0.029 s
% 0.15/0.45 % Maximum resident set size: 4864 pages
% 0.15/0.45 % E exiting
%------------------------------------------------------------------------------