%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:31:29 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 46 ( 20 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 55 ( 23 ~; 11 |; 17 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 40 ( 2 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(shortest_path_properties,axiom,
! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ( ~ precedes(X8,X7,X4)
& ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(no_short_cut_edge,conjecture,
! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7)
& edge(X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_short_cut_edge) ).
fof(c_0_2,plain,
! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ( ~ precedes(X8,X7,X4)
& ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7) ) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_properties]) ).
fof(c_0_3,negated_conjecture,
~ ! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7)
& edge(X9) ) ),
inference(assume_negation,[status(cth)],[no_short_cut_edge]) ).
fof(c_0_4,plain,
! [X33,X34,X35,X36,X37,X38] :
( ( ~ precedes(X35,X36,X37)
| ~ shortest_path(X33,X34,X37)
| ~ precedes(X36,X35,X37) )
& ( ~ precedes(X35,X36,X37)
| ~ shortest_path(X33,X34,X37)
| head_of(X38) != head_of(X36)
| tail_of(X38) != tail_of(X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).
fof(c_0_5,negated_conjecture,
( head_of(esk6_0) = head_of(esk4_0)
& tail_of(esk6_0) = tail_of(esk3_0)
& edge(esk6_0)
& precedes(esk3_0,esk4_0,esk5_0)
& shortest_path(esk1_0,esk2_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( ~ precedes(X2,X3,X6)
| ~ shortest_path(X4,X5,X6)
| head_of(X1) != head_of(X3)
| tail_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
shortest_path(esk1_0,esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( ~ precedes(X3,X2,esk5_0)
| tail_of(X1) != tail_of(X3)
| head_of(X1) != head_of(X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
precedes(esk3_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
head_of(esk6_0) = head_of(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
tail_of(esk6_0) = tail_of(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( tail_of(X1) != tail_of(esk6_0)
| head_of(X1) != head_of(esk6_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n020.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 18:20:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/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/sandbox/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 % new_bool_3 with pid 948793 completed with status 0
% 0.10/0.43 % Result found by new_bool_3
% 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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.43 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % SubtermCWHack with pid 948798 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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.43 % Search class: FGHSF-FFMS31-SFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 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 : 18
% 0.10/0.43 % Removed by relevancy pruning/SinE : 11
% 0.10/0.43 % Initial clauses : 25
% 0.10/0.43 % Removed in clause preprocessing : 0
% 0.10/0.43 % Initial clauses in saturation : 25
% 0.10/0.43 % Processed clauses : 39
% 0.10/0.43 % ...of these trivial : 0
% 0.10/0.43 % ...subsumed : 2
% 0.10/0.43 % ...remaining for further processing : 37
% 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 : 2
% 0.10/0.43 % Generated clauses : 23
% 0.10/0.43 % ...of the previous two non-redundant : 20
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 0
% 0.10/0.43 % Paramodulations : 20
% 0.10/0.43 % Factorizations : 0
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 3
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 5
% 0.10/0.43 % ...of those cached : 0
% 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 : 33
% 0.10/0.43 % Positive orientable unit clauses : 8
% 0.10/0.43 % Positive unorientable unit clauses: 0
% 0.10/0.43 % Negative unit clauses : 5
% 0.10/0.43 % Non-unit-clauses : 20
% 0.10/0.43 % Current number of unprocessed clauses: 6
% 0.10/0.43 % ...number of literals in the above : 27
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 2
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 73
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 44
% 0.10/0.43 % Non-unit clause-clause subsumptions : 0
% 0.10/0.43 % Unit Clause-clause subsumption calls : 8
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 2
% 0.10/0.43 % BW rewrite match successes : 2
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 2401
% 0.10/0.43 % Search garbage collected termcells : 687
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.006 s
% 0.10/0.43 % System time : 0.001 s
% 0.10/0.43 % Total time : 0.008 s
% 0.10/0.43 % Maximum resident set size: 3668 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.009 s
% 0.10/0.43 % System time : 0.005 s
% 0.10/0.43 % Total time : 0.014 s
% 0.10/0.43 % Maximum resident set size: 4864 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------