%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA003+1 : 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 : n004.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 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 212 ( 45 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 259 ( 92 ~; 86 |; 64 &)
% ( 3 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 119 ( 20 sgn 71 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(vertices_and_edges,conjecture,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( vertex(X2)
& vertex(X3)
& X2 != X3
& edge(X7)
& edge(X8)
& X7 != X8
& path(X2,X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vertices_and_edges) ).
fof(precedes_properties,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/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(path_properties,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> ( vertex(X2)
& vertex(X3)
& ? [X1] :
( edge(X1)
& X2 = tail_of(X1)
& ( ( X3 = head_of(X1)
& X4 = path_cons(X1,empty) )
<~> ? [X5] :
( path(head_of(X1),X3,X5)
& X4 = path_cons(X1,X5) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',path_properties) ).
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(on_path_properties,axiom,
! [X2,X3,X4,X1] :
( ( path(X2,X3,X4)
& on_path(X1,X4) )
=> ( edge(X1)
& in_path(head_of(X1),X4)
& in_path(tail_of(X1),X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(shortest_path_properties,axiom,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( ~ ? [X9] :
( tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) )
& ~ precedes(X8,X7,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(c_0_6,negated_conjecture,
~ ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( vertex(X2)
& vertex(X3)
& X2 != X3
& edge(X7)
& edge(X8)
& X7 != X8
& path(X2,X3,X4) ) ),
inference(assume_negation,[status(cth)],[vertices_and_edges]) ).
fof(c_0_7,plain,
! [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) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[precedes_properties]) ).
fof(c_0_8,plain,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> ( vertex(X2)
& vertex(X3)
& ? [X1] :
( edge(X1)
& X2 = tail_of(X1)
& ~ ( ( X3 = head_of(X1)
& X4 = path_cons(X1,empty) )
<=> ? [X5] :
( path(head_of(X1),X3,X5)
& X4 = path_cons(X1,X5) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[path_properties]) ).
fof(c_0_9,plain,
! [X123,X124,X125,X126,X127,X128,X129] :
( ( path(X123,X124,X125)
| ~ shortest_path(X123,X124,X125) )
& ( X123 != X124
| ~ shortest_path(X123,X124,X125) )
& ( ~ path(X123,X124,X126)
| less_or_equal(length_of(X125),length_of(X126))
| ~ shortest_path(X123,X124,X125) )
& ( path(X127,X128,esk6_3(X127,X128,X129))
| ~ path(X127,X128,X129)
| X127 = X128
| shortest_path(X127,X128,X129) )
& ( ~ less_or_equal(length_of(X129),length_of(esk6_3(X127,X128,X129)))
| ~ path(X127,X128,X129)
| X127 = X128
| shortest_path(X127,X128,X129) ) ),
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_10,negated_conjecture,
( shortest_path(esk9_0,esk10_0,esk13_0)
& precedes(esk11_0,esk12_0,esk13_0)
& ( ~ vertex(esk9_0)
| ~ vertex(esk10_0)
| esk9_0 = esk10_0
| ~ edge(esk11_0)
| ~ edge(esk12_0)
| esk11_0 = esk12_0
| ~ path(esk9_0,esk10_0,esk13_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_11,plain,
! [X116,X117,X118,X119,X120,X121] :
( ( on_path(X119,X116)
| ~ precedes(X119,X120,X116)
| ~ path(X117,X118,X116) )
& ( on_path(X120,X116)
| ~ precedes(X119,X120,X116)
| ~ path(X117,X118,X116) )
& ( ~ sequential(X119,X120)
| ~ sequential(X119,X121)
| ~ precedes(X121,X120,X116)
| ~ precedes(X119,X120,X116)
| ~ path(X117,X118,X116) )
& ( sequential(X119,esk5_3(X116,X119,X120))
| sequential(X119,X120)
| ~ precedes(X119,X120,X116)
| ~ path(X117,X118,X116) )
& ( precedes(esk5_3(X116,X119,X120),X120,X116)
| sequential(X119,X120)
| ~ precedes(X119,X120,X116)
| ~ path(X117,X118,X116) ) ),
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)],[c_0_7])])])])])]) ).
fof(c_0_12,plain,
! [X93,X94,X95,X97] :
( ( vertex(X93)
| ~ path(X93,X94,X95) )
& ( vertex(X94)
| ~ path(X93,X94,X95) )
& ( edge(esk2_3(X93,X94,X95))
| ~ path(X93,X94,X95) )
& ( X93 = tail_of(esk2_3(X93,X94,X95))
| ~ path(X93,X94,X95) )
& ( X94 != head_of(esk2_3(X93,X94,X95))
| X95 != path_cons(esk2_3(X93,X94,X95),empty)
| ~ path(head_of(esk2_3(X93,X94,X95)),X94,X97)
| X95 != path_cons(esk2_3(X93,X94,X95),X97)
| ~ path(X93,X94,X95) )
& ( path(head_of(esk2_3(X93,X94,X95)),X94,esk3_3(X93,X94,X95))
| X94 = head_of(esk2_3(X93,X94,X95))
| ~ path(X93,X94,X95) )
& ( X95 = path_cons(esk2_3(X93,X94,X95),esk3_3(X93,X94,X95))
| X94 = head_of(esk2_3(X93,X94,X95))
| ~ path(X93,X94,X95) )
& ( path(head_of(esk2_3(X93,X94,X95)),X94,esk3_3(X93,X94,X95))
| X95 = path_cons(esk2_3(X93,X94,X95),empty)
| ~ path(X93,X94,X95) )
& ( X95 = path_cons(esk2_3(X93,X94,X95),esk3_3(X93,X94,X95))
| X95 = path_cons(esk2_3(X93,X94,X95),empty)
| ~ path(X93,X94,X95) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_13,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
shortest_path(esk9_0,esk10_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X99,X100,X101,X102] :
( ( edge(X102)
| ~ path(X99,X100,X101)
| ~ on_path(X102,X101) )
& ( in_path(head_of(X102),X101)
| ~ path(X99,X100,X101)
| ~ on_path(X102,X101) )
& ( in_path(tail_of(X102),X101)
| ~ path(X99,X100,X101)
| ~ on_path(X102,X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
cnf(c_0_16,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
precedes(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( vertex(X1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
path(esk9_0,esk10_0,esk13_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( vertex(X1)
| ~ path(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( on_path(esk12_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( on_path(X1,X2)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( esk9_0 = esk10_0
| esk11_0 = esk12_0
| ~ vertex(esk9_0)
| ~ vertex(esk10_0)
| ~ edge(esk11_0)
| ~ edge(esk12_0)
| ~ path(esk9_0,esk10_0,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
vertex(esk9_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
vertex(esk10_0),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
on_path(esk12_0,esk13_0),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( on_path(esk11_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
fof(c_0_30,plain,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( ~ ? [X9] :
( tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) )
& ~ precedes(X8,X7,X4) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_properties]) ).
cnf(c_0_31,negated_conjecture,
( esk11_0 = esk12_0
| esk10_0 = esk9_0
| ~ edge(esk11_0)
| ~ edge(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_19])]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
on_path(esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
fof(c_0_34,plain,
! [X131,X132,X133,X134,X135,X136] :
( ( tail_of(X136) != tail_of(X133)
| head_of(X136) != head_of(X134)
| ~ shortest_path(X131,X132,X135)
| ~ precedes(X133,X134,X135) )
& ( ~ precedes(X134,X133,X135)
| ~ shortest_path(X131,X132,X135)
| ~ precedes(X133,X134,X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_35,negated_conjecture,
( esk10_0 = esk9_0
| esk11_0 = esk12_0
| ~ edge(esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_36,negated_conjecture,
edge(esk11_0),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_37,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( esk11_0 = esk12_0
| esk10_0 = esk9_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_39,negated_conjecture,
( ~ precedes(X1,X2,esk13_0)
| ~ precedes(X2,X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_14]) ).
cnf(c_0_40,negated_conjecture,
( esk10_0 = esk9_0
| precedes(esk12_0,esk12_0,esk13_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_41,plain,
( X1 != X2
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_42,negated_conjecture,
esk10_0 = esk9_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_40]) ).
cnf(c_0_43,plain,
~ shortest_path(X1,X1,X2),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA003+1 : 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 : n004.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 18:05:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------