%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA002+4 : TPTP v9.2.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 : 300s
% DateTime : Tue May 5 04:22:55 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 66 ( 17 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 60 ( 22 ~; 20 |; 8 &)
% ( 1 <=>; 9 =>; 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 : 56 ( 9 sgn 39 !; 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/sandbox2/benchmark/theBenchmark.p',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(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,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_7,plain,
! [X124,X125,X126,X127,X128,X129,X130] :
( ( path(X124,X125,X126)
| ~ shortest_path(X124,X125,X126) )
& ( X124 != X125
| ~ shortest_path(X124,X125,X126) )
& ( ~ path(X124,X125,X127)
| less_or_equal(length_of(X126),length_of(X127))
| ~ shortest_path(X124,X125,X126) )
& ( path(X128,X129,esk6_3(X128,X129,X130))
| ~ path(X128,X129,X130)
| X128 = X129
| shortest_path(X128,X129,X130) )
& ( ~ less_or_equal(length_of(X130),length_of(esk6_3(X128,X129,X130)))
| ~ path(X128,X129,X130)
| X128 = X129
| shortest_path(X128,X129,X130) ) ),
inference(distribute,[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)],[shortest_path_defn])])])])])]) ).
fof(c_0_8,negated_conjecture,
( complete
& shortest_path(esk10_0,esk11_0,esk9_0)
& ~ less_or_equal(minus(length_of(esk9_0),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,lemma,
! [X155,X156,X157] :
( ~ complete
| ~ shortest_path(X156,X157,X155)
| number_of_in(sequential_pairs,X155) = number_of_in(triangles,X155) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangles_and_sequential_pairs])])]) ).
fof(c_0_10,plain,
! [X141,X142,X143] :
( ~ path(X141,X142,X143)
| length_of(X143) = number_of_in(edges,X143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[length_defn])]) ).
cnf(c_0_11,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,lemma,
( number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3)
| ~ complete
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_15,plain,
! [X144,X145,X146] :
( ~ path(X144,X145,X146)
| number_of_in(sequential_pairs,X146) = minus(length_of(X146),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
cnf(c_0_16,plain,
( length_of(X3) = number_of_in(edges,X3)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
path(esk10_0,esk11_0,esk9_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_18,plain,
! [X153,X154] : less_or_equal(number_of_in(X153,X154),number_of_in(X153,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_19,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_13,c_0_14])]) ).
cnf(c_0_20,plain,
( number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
length_of(esk9_0) = number_of_in(edges,esk9_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
number_of_in(triangles,esk9_0) = number_of_in(sequential_pairs,esk9_0),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_24,negated_conjecture,
~ less_or_equal(minus(length_of(esk9_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
minus(number_of_in(edges,esk9_0),n1) = number_of_in(sequential_pairs,esk9_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
less_or_equal(number_of_in(sequential_pairs,esk9_0),number_of_in(triangles,graph)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_21]),c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA002+4 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:10:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------