%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 : Tue Sep 29 10:08:25 AM UTC 2026
% Result : Theorem 0.38s 0.48s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 139 ( 23 unt; 14 def)
% Number of atoms : 429 ( 74 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 505 ( 215 ~; 218 |; 44 &)
% ( 17 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 15 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 204 ( 0 sgn 186 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( path(X0,X1,X2)
& on_path(X3,X2) )
=> ( edge(X3)
& in_path(head_of(X3),X2)
& in_path(tail_of(X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(f9,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
| ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) )
=> precedes(X3,X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(f10,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ~ ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& ~ precedes(X3,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f18,conjecture,
! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ~ ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& head_of(X3) != tail_of(X2)
& head_of(X3) != head_of(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ~ ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& head_of(X3) != tail_of(X2)
& head_of(X3) != head_of(X2) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( edge(X3)
& in_path(head_of(X3),X2)
& in_path(tail_of(X3),X2) )
| ~ path(X0,X1,X2)
| ~ on_path(X3,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( edge(X3)
& in_path(head_of(X3),X2)
& in_path(tail_of(X3),X2) )
| ~ path(X0,X1,X2)
| ~ on_path(X3,X2) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ( ~ sequential(X3,X4)
& ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) ) ) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ( ~ sequential(X3,X4)
& ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) ) ) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(ennf_transformation,[],[f12]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(flattening,[],[f35]) ).
fof(f43,plain,
? [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
| tail_of(X2) = head_of(X3)
| head_of(X2) = head_of(X3) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
| tail_of(X2) = head_of(X3)
| head_of(X2) = head_of(X3) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) ),
inference(flattening,[],[f43]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f69,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ path(X1,X2,X0)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f81,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f82,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f36]) ).
fof(f92,plain,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| head_of(sK10) = head_of(sK12) ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| tail_of(sK9) = tail_of(sK12) ),
inference(cnf_transformation,[],[f44]) ).
fof(f94,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f44]) ).
fof(f95,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f44]) ).
fof(f114,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| ~ sequential(X0,X1) ),
inference(consistent_polarity_flipping,[],[f69]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ path(X1,X2,X0)
| ~ precedes(X5,X4,X0)
| sequential(X3,X5)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(consistent_polarity_flipping,[],[f70]) ).
fof(f124,plain,
! [X2,X0,X1] :
( shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4,X5] :
( head_of(X3) != head_of(X5)
| shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| tail_of(X2) != tail_of(X5) ),
inference(consistent_polarity_flipping,[],[f82]) ).
fof(f134,plain,
~ shortest_path(sK7,sK8,sK11),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f136,definition,
( spl13_1
<=> head_of(sK10) = head_of(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f138,plain,
( head_of(sK10) = head_of(sK12)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f140,definition,
( spl13_2
<=> head_of(sK10) = tail_of(sK9) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f142,plain,
( head_of(sK10) = tail_of(sK9)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f144,definition,
( spl13_3
<=> head_of(sK9) = head_of(sK10) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f145,plain,
( head_of(sK9) != head_of(sK10)
| spl13_3 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f146,plain,
( head_of(sK9) = head_of(sK10)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f92,f144,f140,f136]) ).
fof(f149,definition,
( spl13_4
<=> tail_of(sK9) = tail_of(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f151,plain,
( tail_of(sK9) = tail_of(sK12)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl13_4
| spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f93,f144,f140,f149]) ).
fof(f155,definition,
( spl13_5
<=> edge(sK9) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f156,plain,
( edge(sK9)
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f163,plain,
path(sK7,sK8,sK11),
inference(resolution,[],[f124,f134]) ).
fof(f168,plain,
! [X0,X1] :
( ~ path(X0,X1,sK11)
| on_path(sK10,sK11) ),
inference(resolution,[],[f75,f94]) ).
fof(f170,definition,
( spl13_7
<=> on_path(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f172,plain,
( on_path(sK10,sK11)
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,definition,
( spl13_8
<=> ! [X0,X1] : ~ path(X0,X1,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f175,plain,
( ! [X0,X1] : ~ path(X0,X1,sK11)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( spl13_7
| spl13_8 ),
inference(avatar_split_clause,[],[f168,f174,f170]) ).
fof(f177,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK11)
| edge(sK10) )
| ~ spl13_7 ),
inference(resolution,[],[f172,f61]) ).
fof(f179,definition,
( spl13_9
<=> edge(sK10) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f181,plain,
( edge(sK10)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl13_9
| spl13_8
| ~ spl13_7 ),
inference(avatar_split_clause,[],[f177,f170,f174,f179]) ).
fof(f183,plain,
! [X0,X1] :
( ~ path(X0,X1,sK11)
| on_path(sK9,sK11) ),
inference(resolution,[],[f76,f94]) ).
fof(f185,definition,
( spl13_10
<=> on_path(sK9,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f187,plain,
( on_path(sK9,sK11)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl13_10
| spl13_8 ),
inference(avatar_split_clause,[],[f183,f174,f185]) ).
fof(f190,plain,
( $false
| ~ spl13_8 ),
inference(backward_subsumption_resolution,[],[f163,f175]) ).
fof(f191,plain,
~ spl13_8,
inference(avatar_contradiction_clause,[],[f190]) ).
fof(f193,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK11)
| edge(sK9) )
| ~ spl13_10 ),
inference(resolution,[],[f187,f61]) ).
fof(f196,plain,
( spl13_5
| spl13_8
| ~ spl13_10 ),
inference(avatar_split_clause,[],[f193,f185,f174,f155]) ).
fof(f203,definition,
( spl13_12
<=> ! [X0,X1] : shortest_path(X0,X1,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f204,plain,
( ! [X0,X1] : shortest_path(X0,X1,sK11)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f207,plain,
( ! [X0] :
( head_of(X0) != head_of(sK10)
| sK9 = X0
| ~ edge(sK9)
| ~ edge(X0)
| ~ sequential(X0,sK9) )
| ~ spl13_2 ),
inference(superposition,[],[f114,f142]) ).
fof(f208,plain,
( ! [X0] :
( head_of(X0) != head_of(sK10)
| sK9 = X0
| ~ edge(X0)
| ~ sequential(X0,sK9) )
| ~ spl13_2
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f207,f156]) ).
fof(f273,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X2)
| shortest_path(X0,X1,X2)
| tail_of(X3) != tail_of(X4) ),
inference(equality_resolution,[],[f130]) ).
fof(f285,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X5,X4,X0)
| ~ path(X1,X2,X0)
| sequential(X3,X5)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(forward_subsumption_resolution,[],[f120,f75]) ).
fof(f286,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,sK11)
| sequential(X2,sK9)
| ~ on_path(X2,sK11)
| precedes(X2,sK10,sK11) ),
inference(resolution,[],[f285,f94]) ).
fof(f288,definition,
( spl13_21
<=> ! [X2] :
( sequential(X2,sK9)
| precedes(X2,sK10,sK11)
| ~ on_path(X2,sK11) ) ),
introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition]) ).
fof(f289,plain,
( ! [X2] :
( ~ on_path(X2,sK11)
| precedes(X2,sK10,sK11)
| sequential(X2,sK9) )
| ~ spl13_21 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( spl13_21
| spl13_8 ),
inference(avatar_split_clause,[],[f286,f174,f288]) ).
fof(f322,plain,
( precedes(sK10,sK10,sK11)
| sequential(sK10,sK9)
| ~ spl13_7
| ~ spl13_21 ),
inference(resolution,[],[f289,f172]) ).
fof(f325,definition,
( spl13_26
<=> sequential(sK10,sK9) ),
introduced(definition,[new_symbols(definition,[spl13_26])],[avatar_definition]) ).
fof(f327,plain,
( sequential(sK10,sK9)
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f329,definition,
( spl13_27
<=> precedes(sK10,sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_27])],[avatar_definition]) ).
fof(f331,plain,
( precedes(sK10,sK10,sK11)
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f332,plain,
( spl13_26
| spl13_27
| ~ spl13_7
| ~ spl13_21 ),
inference(avatar_split_clause,[],[f322,f288,f170,f329,f325]) ).
fof(f346,plain,
( sK9 = sK10
| ~ edge(sK10)
| ~ sequential(sK10,sK9)
| ~ spl13_2
| ~ spl13_5 ),
inference(equality_resolution,[],[f208]) ).
fof(f347,plain,
( sK9 = sK10
| ~ sequential(sK10,sK9)
| ~ spl13_2
| ~ spl13_5
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f346,f181]) ).
fof(f349,plain,
( sK9 = sK10
| ~ spl13_2
| ~ spl13_5
| ~ spl13_9
| ~ spl13_26 ),
inference(forward_subsumption_resolution,[],[f347,f327]) ).
fof(f366,plain,
( head_of(sK9) != head_of(sK9)
| ~ spl13_2
| spl13_3
| ~ spl13_5
| ~ spl13_9
| ~ spl13_26 ),
inference(superposition,[],[f145,f349]) ).
fof(f378,plain,
( $false
| ~ spl13_2
| spl13_3
| ~ spl13_5
| ~ spl13_9
| ~ spl13_26 ),
inference(trivial_inequality_removal,[],[f366]) ).
fof(f379,plain,
( ~ spl13_2
| spl13_3
| ~ spl13_5
| ~ spl13_9
| ~ spl13_26 ),
inference(avatar_contradiction_clause,[],[f378]) ).
fof(f387,plain,
( ! [X2,X3,X0,X1,X4] :
( head_of(X0) != head_of(sK10)
| shortest_path(X1,X2,X3)
| ~ precedes(X4,X0,X3)
| tail_of(X4) != tail_of(sK12) )
| ~ spl13_1 ),
inference(superposition,[],[f130,f138]) ).
fof(f421,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ precedes(X4,X0,X3)
| head_of(X0) != head_of(sK10)
| shortest_path(X1,X2,X3)
| tail_of(X4) != tail_of(sK9) )
| ~ spl13_1
| ~ spl13_4 ),
inference(forward_demodulation,[],[f387,f151]) ).
fof(f427,plain,
( ! [X0,X1] :
( head_of(sK10) != head_of(sK10)
| shortest_path(X0,X1,sK11)
| tail_of(sK9) != tail_of(sK9) )
| ~ spl13_1
| ~ spl13_4 ),
inference(resolution,[],[f421,f94]) ).
fof(f428,plain,
( ! [X0,X1] : shortest_path(X0,X1,sK11)
| ~ spl13_1
| ~ spl13_4 ),
inference(trivial_inequality_removal,[],[f427]) ).
fof(f429,plain,
( spl13_12
| ~ spl13_1
| ~ spl13_4 ),
inference(avatar_split_clause,[],[f428,f149,f136,f203]) ).
fof(f430,plain,
( $false
| ~ spl13_12 ),
inference(backward_subsumption_resolution,[],[f134,f204]) ).
fof(f431,plain,
~ spl13_12,
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f449,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ precedes(X4,sK10,X3)
| shortest_path(X1,X2,X3)
| head_of(X0) != head_of(sK9)
| tail_of(X0) != tail_of(X4) )
| ~ spl13_3 ),
inference(superposition,[],[f130,f146]) ).
fof(f509,plain,
( ! [X2,X0,X1] :
( shortest_path(X0,X1,sK11)
| head_of(X2) != head_of(sK9)
| tail_of(X2) != tail_of(sK9) )
| ~ spl13_3 ),
inference(resolution,[],[f449,f94]) ).
fof(f516,definition,
( spl13_47
<=> ! [X2] :
( head_of(X2) != head_of(sK9)
| tail_of(X2) != tail_of(sK9) ) ),
introduced(definition,[new_symbols(definition,[spl13_47])],[avatar_definition]) ).
fof(f517,plain,
( ! [X2] :
( tail_of(X2) != tail_of(sK9)
| head_of(X2) != head_of(sK9) )
| ~ spl13_47 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f518,plain,
( spl13_47
| spl13_12
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f509,f144,f203,f516]) ).
fof(f645,plain,
( head_of(sK9) != head_of(sK9)
| ~ spl13_47 ),
inference(equality_resolution,[],[f517]) ).
fof(f646,plain,
( $false
| ~ spl13_47 ),
inference(trivial_inequality_removal,[],[f645]) ).
fof(f647,plain,
~ spl13_47,
inference(avatar_contradiction_clause,[],[f646]) ).
fof(f676,plain,
( ! [X0,X1] :
( shortest_path(X0,X1,sK11)
| tail_of(sK10) != tail_of(sK10) )
| ~ spl13_27 ),
inference(resolution,[],[f331,f273]) ).
fof(f678,plain,
( ! [X0,X1] : shortest_path(X0,X1,sK11)
| ~ spl13_27 ),
inference(trivial_inequality_removal,[],[f676]) ).
fof(f684,plain,
( spl13_12
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f678,f329,f203]) ).
cnf(s1,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(sat_conversion,[],[f147]) ).
cnf(s2,plain,
( spl13_2
| spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f152]) ).
cnf(s4,plain,
( spl13_7
| spl13_8 ),
inference(sat_conversion,[],[f176]) ).
cnf(s5,plain,
( ~ spl13_7
| spl13_8
| spl13_9 ),
inference(sat_conversion,[],[f182]) ).
cnf(s6,plain,
( spl13_8
| spl13_10 ),
inference(sat_conversion,[],[f188]) ).
cnf(s7,plain,
~ spl13_8,
inference(sat_conversion,[],[f191]) ).
cnf(s9,plain,
( spl13_5
| spl13_8
| ~ spl13_10 ),
inference(sat_conversion,[],[f196]) ).
cnf(s18,plain,
( spl13_8
| spl13_21 ),
inference(sat_conversion,[],[f290]) ).
cnf(s23,plain,
( ~ spl13_7
| ~ spl13_21
| spl13_26
| spl13_27 ),
inference(sat_conversion,[],[f332]) ).
cnf(s25,plain,
( ~ spl13_2
| spl13_3
| ~ spl13_5
| ~ spl13_9
| ~ spl13_26 ),
inference(sat_conversion,[],[f379]) ).
cnf(s33,plain,
( ~ spl13_1
| ~ spl13_4
| spl13_12 ),
inference(sat_conversion,[],[f429]) ).
cnf(s34,plain,
~ spl13_12,
inference(sat_conversion,[],[f431]) ).
cnf(s47,plain,
( ~ spl13_3
| spl13_12
| spl13_47 ),
inference(sat_conversion,[],[f518]) ).
cnf(s64,plain,
~ spl13_47,
inference(sat_conversion,[],[f647]) ).
cnf(s71,plain,
( spl13_12
| ~ spl13_27 ),
inference(sat_conversion,[],[f684]) ).
cnf(s76,plain,
( ~ spl13_3
| spl13_12 ),
inference(rat,[],[s47,s64]) ).
cnf(s77,plain,
~ spl13_27,
inference(rat,[],[s71,s34]) ).
cnf(s78,plain,
~ spl13_3,
inference(rat,[],[s76,s34]) ).
cnf(s80,plain,
( ~ spl13_1
| ~ spl13_4 ),
inference(rat,[],[s33,s34]) ).
cnf(s82,plain,
( ~ spl13_2
| ~ spl13_5
| ~ spl13_9
| ~ spl13_26 ),
inference(rat,[],[s25,s78]) ).
cnf(s83,plain,
( ~ spl13_7
| ~ spl13_21
| spl13_26 ),
inference(rat,[],[s23,s77]) ).
cnf(s86,plain,
spl13_21,
inference(rat,[],[s18,s7]) ).
cnf(s88,plain,
spl13_10,
inference(rat,[],[s6,s7]) ).
cnf(s89,plain,
spl13_5,
inference(rat,[],[s9,s7,s88]) ).
cnf(s91,plain,
( ~ spl13_7
| spl13_9 ),
inference(rat,[],[s5,s7]) ).
cnf(s92,plain,
spl13_7,
inference(rat,[],[s4,s7]) ).
cnf(s93,plain,
spl13_26,
inference(rat,[],[s83,s86,s92]) ).
cnf(s94,plain,
spl13_9,
inference(rat,[],[s91,s92]) ).
cnf(s95,plain,
~ spl13_2,
inference(rat,[],[s82,s93,s89,s94]) ).
cnf(s96,plain,
spl13_4,
inference(rat,[],[s2,s78,s95]) ).
cnf(s97,plain,
~ spl13_1,
inference(rat,[],[s80,s96]) ).
cnf(s98,plain,
$false,
inference(rat,[],[s1,s78,s95,s97]) ).
fof(f702,plain,
$false,
inference(avatar_sat_refutation,[],[s98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 08:45:47 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.48 % (509715)Will run a generic schedule for satisfiability detection.
% 0.38/0.48 % (509724)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=546753381:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.38/0.48 % (509720)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2908737673_2999 on theBenchmark for (2999ds/0Mi)
% 0.38/0.48 % (509723)dis+10_1_sil=32000:sp=arity:random_seed=511862119:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.38/0.48 % (509722)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=771171598:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.38/0.48 % (509725)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1946109438:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.48 % (509726)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1676821672:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.38/0.48 % TRYING [1]
% 0.38/0.48 % (509721)% WARNING: option uhcvi not known.
% 0.38/0.48 % TRYING [2]
% 0.38/0.48 % TRYING [3]
% 0.38/0.48 % (509721)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1214414092:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.38/0.48 % TRYING [4]
% 0.38/0.48 % (509721) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-509715-509721"...
% 0.38/0.48 % (509724)Instruction limit reached!
% 0.38/0.48 % (509724)------------------------------
% 0.38/0.48 % (509724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.48 % (509724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.48 % (509724)CaDiCaL version: 2.1.3
% 0.38/0.48 % (509724)Termination reason: Instruction limit
% 0.38/0.48 % (509724)Termination phase: Saturation
% 0.38/0.48 % (509724)Time elapsed: 0.040 s
% 0.38/0.48 % (509724)Peak memory usage: 13 MB
% 0.38/0.48 % (509724)Instructions burned: 118 (million)
% 0.38/0.48 % (509721)...printing done.
% 0.38/0.48 % (509721)Refutation found. Thanks to Tanya!
% 0.38/0.48 % SZS status Theorem for theBenchmark
% 0.38/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.38/0.48 % (509721)------------------------------
% 0.38/0.48 % (509721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.48 % (509721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.48 % (509721)CaDiCaL version: 2.1.3
% 0.38/0.48 % (509721)Termination reason: Refutation
% 0.38/0.48 % (509721)Time elapsed: 0.021 s
% 0.38/0.48 % (509721)Peak memory usage: 13 MB
% 0.38/0.48 % (509721)Instructions burned: 23 (million)
% 0.38/0.48 % (509715)Success in time 0.068 s
% 0.38/0.48 % Vampire exiting
%------------------------------------------------------------------------------