%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA002+3 : TPTP v9.2.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 04:22:54 PM UTC 2026
% Result : Theorem 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 12 unt; 0 def)
% Number of atoms : 158 ( 29 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 173 ( 62 ~; 72 |; 23 &)
% ( 1 <=>; 14 =>; 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 : 15 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 121 ( 20 sgn 68 !; 4 ?)
% 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/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
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/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
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/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(length_defn,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> length_of(X4) = number_of_in(edges,X4) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(c_0_8,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_9,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) )
=> precedes(X7,X8,X4) ) ),
inference(fof_simplification,[status(thm)],[precedes_defn]) ).
fof(c_0_10,plain,
! [X127,X128,X129,X130,X131,X132,X133] :
( ( path(X127,X128,X129)
| ~ shortest_path(X127,X128,X129) )
& ( X127 != X128
| ~ shortest_path(X127,X128,X129) )
& ( ~ path(X127,X128,X130)
| less_or_equal(length_of(X129),length_of(X130))
| ~ shortest_path(X127,X128,X129) )
& ( path(X131,X132,esk6_3(X131,X132,X133))
| ~ path(X131,X132,X133)
| X131 = X132
| shortest_path(X131,X132,X133) )
& ( ~ less_or_equal(length_of(X133),length_of(esk6_3(X131,X132,X133)))
| ~ path(X131,X132,X133)
| X131 = X132
| shortest_path(X131,X132,X133) ) ),
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_11,negated_conjecture,
( complete
& shortest_path(esk11_0,esk12_0,esk10_0)
& ~ less_or_equal(minus(length_of(esk10_0),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,lemma,
! [X158,X159,X160,X161,X162] :
( ~ complete
| ~ shortest_path(X158,X159,X162)
| ~ precedes(X160,X161,X162)
| ~ sequential(X160,X161)
| triangle(X160,X161,esk9_4(X158,X159,X160,X161)) ),
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_is_triangle])])])])]) ).
fof(c_0_13,plain,
! [X114,X115,X116,X117,X118,X119] :
( ( ~ sequential(X117,X118)
| ~ on_path(X117,X114)
| ~ on_path(X118,X114)
| precedes(X117,X118,X114)
| ~ path(X115,X116,X114) )
& ( ~ sequential(X117,X119)
| ~ precedes(X119,X118,X114)
| ~ on_path(X117,X114)
| ~ on_path(X118,X114)
| precedes(X117,X118,X114)
| ~ path(X115,X116,X114) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_14,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
shortest_path(esk11_0,esk12_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X150,X151,X152,X155] :
( ( on_path(esk7_1(X150),X150)
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) )
& ( on_path(esk8_1(X150),X150)
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) )
& ( sequential(esk7_1(X150),esk8_1(X150))
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) )
& ( ~ triangle(esk7_1(X150),esk8_1(X150),X155)
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) ) ),
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)],[sequential_pairs_and_triangles])])])])])]) ).
cnf(c_0_17,lemma,
( triangle(X4,X5,esk9_4(X1,X2,X4,X5))
| ~ complete
| ~ shortest_path(X1,X2,X3)
| ~ precedes(X4,X5,X3)
| ~ sequential(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( precedes(X1,X2,X3)
| ~ sequential(X1,X2)
| ~ on_path(X1,X3)
| ~ on_path(X2,X3)
| ~ path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
path(esk11_0,esk12_0,esk10_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( on_path(esk8_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,lemma,
( triangle(X1,X2,esk9_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_17,c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
( precedes(X1,X2,esk10_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk10_0)
| ~ on_path(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| on_path(esk8_1(esk10_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_25,plain,
( sequential(esk7_1(X1),esk8_1(X1))
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( on_path(esk7_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_27,plain,
! [X144,X145,X146] :
( ~ path(X144,X145,X146)
| length_of(X146) = number_of_in(edges,X146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[length_defn])]) ).
cnf(c_0_28,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ triangle(esk7_1(X1),esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( triangle(X1,X2,esk9_4(esk11_0,esk12_0,X1,X2))
| ~ precedes(X1,X2,esk10_0)
| ~ sequential(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| precedes(X1,esk8_1(esk10_0),esk10_0)
| ~ sequential(X1,esk8_1(esk10_0))
| ~ on_path(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| sequential(esk7_1(esk10_0),esk8_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| on_path(esk7_1(esk10_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
fof(c_0_33,plain,
! [X147,X148,X149] :
( ~ path(X147,X148,X149)
| number_of_in(sequential_pairs,X149) = minus(length_of(X149),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
cnf(c_0_34,plain,
( length_of(X3) = number_of_in(edges,X3)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ precedes(esk7_1(X1),esk8_1(X1),esk10_0)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]) ).
cnf(c_0_36,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| precedes(esk7_1(esk10_0),esk8_1(esk10_0),esk10_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_37,plain,
( number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
length_of(esk10_0) = number_of_in(edges,esk10_0),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
fof(c_0_39,plain,
! [X156,X157] : less_or_equal(number_of_in(X156,X157),number_of_in(X156,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_40,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| ~ path(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
~ less_or_equal(minus(length_of(esk10_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_42,negated_conjecture,
minus(number_of_in(edges,esk10_0),n1) = number_of_in(sequential_pairs,esk10_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_38]) ).
cnf(c_0_43,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_45,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk10_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_38]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA002+3 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n002.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:08:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------