%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:55:19 AM UTC 2026
% Result : Theorem 3.04s 1.26s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 125 ( 20 unt; 11 def)
% Number of atoms : 447 ( 82 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 542 ( 220 ~; 210 |; 87 &)
% ( 14 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 12 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 212 ( 0 sgn 188 !; 24 ?)
% 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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/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(f50,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| head_of(X0) != tail_of(X1) )
& ( ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| head_of(X0) != tail_of(X1) )
& ( ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( sequential(X3,X6)
& precedes(X6,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ( sequential(X3,sK3(X0,X3,X4))
& precedes(sK3(X0,X3,X4),X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X6,sK3(X0,X3,X4))],[f54]) ).
fof(f56,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) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f57,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) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f56]) ).
fof(f58,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) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f58]) ).
fof(f61,plain,
( ( ( tail_of(sK9) = tail_of(sK12)
& head_of(sK10) = head_of(sK12) )
| tail_of(sK9) = head_of(sK10)
| head_of(sK10) = head_of(sK9) )
& shortest_path(sK7,sK8,sK11)
& precedes(sK9,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f44]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f86,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f96,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ shortest_path(X0,X1,X4)
| head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f109,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
( head_of(sK10) = head_of(sK12)
| tail_of(sK9) = head_of(sK10)
| head_of(sK10) = head_of(sK9) ),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
( tail_of(sK9) = tail_of(sK12)
| tail_of(sK9) = head_of(sK10)
| head_of(sK10) = head_of(sK9) ),
inference(cnf_transformation,[],[f61]) ).
fof(f121,definition,
( spl13_1
<=> head_of(sK10) = head_of(sK9) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f123,plain,
( head_of(sK10) = head_of(sK9)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl13_2
<=> tail_of(sK9) = head_of(sK10) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f127,plain,
( tail_of(sK9) = head_of(sK10)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f129,definition,
( spl13_3
<=> head_of(sK10) = head_of(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f131,plain,
( head_of(sK10) = head_of(sK12)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f111,f129,f125,f121]) ).
fof(f134,definition,
( spl13_4
<=> tail_of(sK9) = tail_of(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f136,plain,
( tail_of(sK9) = tail_of(sK12)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl13_1
| spl13_2
| spl13_4 ),
inference(avatar_split_clause,[],[f112,f134,f125,f121]) ).
fof(f157,plain,
! [X0,X1] :
( on_path(sK10,sK11)
| ~ path(X0,X1,sK11) ),
inference(resolution,[],[f92,f109]) ).
fof(f159,definition,
( spl13_7
<=> ! [X0,X1] : ~ path(X0,X1,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f160,plain,
( ! [X0,X1] : ~ path(X0,X1,sK11)
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,definition,
( spl13_8
<=> on_path(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f164,plain,
( on_path(sK10,sK11)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl13_7
| spl13_8 ),
inference(avatar_split_clause,[],[f157,f162,f159]) ).
fof(f166,plain,
( ! [X0,X1] : ~ shortest_path(X0,X1,sK11)
| ~ spl13_7 ),
inference(resolution,[],[f160,f96]) ).
fof(f167,plain,
! [X0,X1] :
( on_path(sK9,sK11)
| ~ path(X0,X1,sK11) ),
inference(resolution,[],[f93,f109]) ).
fof(f168,plain,
( $false
| ~ spl13_7 ),
inference(resolution,[],[f166,f110]) ).
fof(f169,plain,
~ spl13_7,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f171,definition,
( spl13_9
<=> on_path(sK9,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f173,plain,
( on_path(sK9,sK11)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( spl13_7
| spl13_9 ),
inference(avatar_split_clause,[],[f167,f171,f159]) ).
fof(f177,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK11)
| edge(sK10) )
| ~ spl13_8 ),
inference(resolution,[],[f164,f78]) ).
fof(f179,definition,
( spl13_10
<=> edge(sK10) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f181,plain,
( edge(sK10)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl13_10
| spl13_7
| ~ spl13_8 ),
inference(avatar_split_clause,[],[f177,f162,f159,f179]) ).
fof(f188,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK11)
| ~ precedes(X1,X0,sK11) ),
inference(resolution,[],[f99,f110]) ).
fof(f192,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK11)
| edge(sK9) )
| ~ spl13_9 ),
inference(resolution,[],[f173,f78]) ).
fof(f194,definition,
( spl13_12
<=> edge(sK9) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f196,plain,
( edge(sK9)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,plain,
( spl13_12
| spl13_7
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f192,f171,f159,f194]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ precedes(X2,X0,sK11)
| tail_of(X2) != tail_of(X1)
| head_of(X0) != head_of(X1) ),
inference(resolution,[],[f100,f110]) ).
fof(f461,plain,
~ precedes(sK10,sK9,sK11),
inference(resolution,[],[f188,f109]) ).
fof(f462,plain,
! [X0] : ~ precedes(X0,X0,sK11),
inference(factoring,[],[f188]) ).
fof(f463,plain,
! [X0] :
( head_of(X0) != head_of(sK10)
| tail_of(X0) != tail_of(sK9) ),
inference(resolution,[],[f311,f109]) ).
fof(f581,plain,
( head_of(sK10) != head_of(sK10)
| tail_of(sK9) != tail_of(sK12)
| ~ spl13_3 ),
inference(superposition,[],[f463,f131]) ).
fof(f583,plain,
( tail_of(sK9) != tail_of(sK12)
| ~ spl13_3 ),
inference(trivial_inequality_removal,[],[f581]) ).
fof(f584,plain,
( $false
| ~ spl13_3
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f583,f136]) ).
fof(f585,plain,
( ~ spl13_3
| ~ spl13_4 ),
inference(avatar_contradiction_clause,[],[f584]) ).
fof(f590,plain,
( ! [X0] :
( head_of(X0) != head_of(sK9)
| tail_of(X0) != tail_of(sK9) )
| ~ spl13_1 ),
inference(superposition,[],[f463,f123]) ).
fof(f806,plain,
( tail_of(sK9) != tail_of(sK9)
| ~ spl13_1 ),
inference(equality_resolution,[],[f590]) ).
fof(f807,plain,
( $false
| ~ spl13_1 ),
inference(trivial_inequality_removal,[],[f806]) ).
fof(f808,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[],[f807]) ).
fof(f824,plain,
( ! [X0] :
( head_of(X0) != head_of(sK10)
| ~ edge(X0)
| ~ edge(sK9)
| sK9 = X0
| sequential(X0,sK9) )
| ~ spl13_2 ),
inference(superposition,[],[f86,f127]) ).
fof(f825,plain,
( ! [X0] :
( head_of(X0) != head_of(sK10)
| ~ edge(X0)
| sK9 = X0
| sequential(X0,sK9) )
| ~ spl13_2
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f824,f196]) ).
fof(f831,plain,
( ~ edge(sK10)
| sK9 = sK10
| sequential(sK10,sK9)
| ~ spl13_2
| ~ spl13_12 ),
inference(equality_resolution,[],[f825]) ).
fof(f832,plain,
( sK9 = sK10
| sequential(sK10,sK9)
| ~ spl13_2
| ~ spl13_10
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f831,f181]) ).
fof(f834,definition,
( spl13_70
<=> sequential(sK10,sK9) ),
introduced(definition,[new_symbols(definition,[spl13_70])],[avatar_definition]) ).
fof(f836,plain,
( sequential(sK10,sK9)
| ~ spl13_70 ),
inference(avatar_component_clause,[],[f834]) ).
fof(f838,definition,
( spl13_71
<=> sK9 = sK10 ),
introduced(definition,[new_symbols(definition,[spl13_71])],[avatar_definition]) ).
fof(f840,plain,
( sK9 = sK10
| ~ spl13_71 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f841,plain,
( spl13_70
| spl13_71
| ~ spl13_2
| ~ spl13_10
| ~ spl13_12 ),
inference(avatar_split_clause,[],[f832,f194,f179,f125,f838,f834]) ).
fof(f842,plain,
( precedes(sK9,sK9,sK11)
| ~ spl13_71 ),
inference(superposition,[],[f109,f840]) ).
fof(f881,plain,
( $false
| ~ spl13_71 ),
inference(forward_subsumption_resolution,[],[f842,f462]) ).
fof(f882,plain,
~ spl13_71,
inference(avatar_contradiction_clause,[],[f881]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( ~ on_path(sK10,X0)
| ~ on_path(sK9,X0)
| precedes(sK10,sK9,X0)
| ~ path(X1,X2,X0) )
| ~ spl13_70 ),
inference(resolution,[],[f836,f88]) ).
fof(f943,plain,
( ! [X0,X1] :
( ~ on_path(sK9,sK11)
| precedes(sK10,sK9,sK11)
| ~ path(X0,X1,sK11) )
| ~ spl13_8
| ~ spl13_70 ),
inference(resolution,[],[f887,f164]) ).
fof(f944,plain,
( ! [X0,X1] :
( precedes(sK10,sK9,sK11)
| ~ path(X0,X1,sK11) )
| ~ spl13_8
| ~ spl13_9
| ~ spl13_70 ),
inference(forward_subsumption_resolution,[],[f943,f173]) ).
fof(f945,plain,
( ! [X0,X1] : ~ path(X0,X1,sK11)
| ~ spl13_8
| ~ spl13_9
| ~ spl13_70 ),
inference(forward_subsumption_resolution,[],[f944,f461]) ).
fof(f946,plain,
( spl13_7
| ~ spl13_8
| ~ spl13_9
| ~ spl13_70 ),
inference(avatar_split_clause,[],[f945,f834,f171,f162,f159]) ).
cnf(s1,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(sat_conversion,[],[f132]) ).
cnf(s2,plain,
( spl13_1
| spl13_2
| spl13_4 ),
inference(sat_conversion,[],[f137]) ).
cnf(s5,plain,
( spl13_7
| spl13_8 ),
inference(sat_conversion,[],[f165]) ).
cnf(s6,plain,
~ spl13_7,
inference(sat_conversion,[],[f169]) ).
cnf(s7,plain,
( spl13_7
| spl13_9 ),
inference(sat_conversion,[],[f174]) ).
cnf(s8,plain,
( spl13_7
| ~ spl13_8
| spl13_10 ),
inference(sat_conversion,[],[f182]) ).
cnf(s10,plain,
( spl13_7
| ~ spl13_9
| spl13_12 ),
inference(sat_conversion,[],[f197]) ).
cnf(s60,plain,
( ~ spl13_3
| ~ spl13_4 ),
inference(sat_conversion,[],[f585]) ).
cnf(s84,plain,
~ spl13_1,
inference(sat_conversion,[],[f808]) ).
cnf(s88,plain,
( ~ spl13_2
| ~ spl13_10
| ~ spl13_12
| spl13_70
| spl13_71 ),
inference(sat_conversion,[],[f841]) ).
cnf(s91,plain,
~ spl13_71,
inference(sat_conversion,[],[f882]) ).
cnf(s99,plain,
( spl13_7
| ~ spl13_8
| ~ spl13_9
| ~ spl13_70 ),
inference(sat_conversion,[],[f946]) ).
cnf(s100,plain,
( ~ spl13_2
| ~ spl13_10
| ~ spl13_12
| spl13_70 ),
inference(rat,[],[s88,s91]) ).
cnf(s101,plain,
spl13_9,
inference(rat,[],[s7,s6]) ).
cnf(s103,plain,
spl13_12,
inference(rat,[],[s10,s6,s101]) ).
cnf(s108,plain,
spl13_8,
inference(rat,[],[s5,s6]) ).
cnf(s109,plain,
~ spl13_70,
inference(rat,[],[s99,s101,s6,s108]) ).
cnf(s112,plain,
spl13_10,
inference(rat,[],[s8,s6,s108]) ).
cnf(s115,plain,
~ spl13_2,
inference(rat,[],[s100,s109,s103,s112]) ).
cnf(s124,plain,
spl13_4,
inference(rat,[],[s2,s115,s84]) ).
cnf(s125,plain,
~ spl13_3,
inference(rat,[],[s60,s124]) ).
cnf(s126,plain,
$false,
inference(rat,[],[s1,s125,s115,s84]) ).
fof(f947,plain,
$false,
inference(avatar_sat_refutation,[],[s126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 08:46:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.04/1.26 % (1727103)Detected formulas, will run a generic FOF schedule.
% 3.04/1.26 % (1727114)dis-21_1_sil=8000:lcm=predicate:random_seed=1924380482:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.04/1.26 % (1727108)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2235844255:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.04/1.26 % (1727114)Instruction limit reached!
% 3.04/1.26 % (1727114)------------------------------
% 3.04/1.26 % (1727114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.26 % (1727114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.26 % (1727114)CaDiCaL version: 2.1.3
% 3.04/1.26 % (1727114)Termination reason: Instruction limit
% 3.04/1.26 % (1727114)Termination phase: Saturation
% 3.04/1.26 % (1727114)Time elapsed: 0.044 s
% 3.04/1.26 % (1727114)Peak memory usage: 90 MB
% 3.04/1.26 % (1727114)Instructions burned: 130 (million)
% 3.04/1.26 % (1727113)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3013899455:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.04/1.26 % (1727112)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1448021224:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.04/1.26 % (1727109)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3716681597:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.04/1.26 % (1727110)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2633778664:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.04/1.26 % (1727111)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3024297718:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.04/1.26 % (1727111)Refutation not found, incomplete strategy
% 3.04/1.26 % (1727111)------------------------------
% 3.04/1.26 % (1727111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.26 % (1727111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.26 % (1727111)CaDiCaL version: 2.1.3
% 3.04/1.26 % (1727111)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.26 % (1727111)Time elapsed: 0.002 s
% 3.04/1.26 % (1727111)Peak memory usage: 88 MB
% 3.04/1.26 % (1727111)Instructions burned: 1 (million)
% 3.04/1.26 % (1727112)Refutation not found, incomplete strategy
% 3.04/1.26 % (1727112)------------------------------
% 3.04/1.26 % (1727112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.26 % (1727112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.26 % (1727112)CaDiCaL version: 2.1.3
% 3.04/1.26 % (1727112)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.26 % (1727112)Time elapsed: 0.004 s
% 3.04/1.26 % (1727112)Peak memory usage: 88 MB
% 3.04/1.26 % (1727112)Instructions burned: 6 (million)
% 3.04/1.26 % (1727113)First to succeed.
% 3.04/1.26 % (1727113)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1727103"
% 3.04/1.26 % (1727122)lrs+10_1_sil=8000:sp=occurrence:random_seed=993024497:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.04/1.26 % (1727122)Also succeeded, but the first one will report.
% 3.04/1.26 % (1727111)------------------------------
% 3.04/1.26 % (1727111)------------------------------
% 3.04/1.26 % (1727112)------------------------------
% 3.04/1.26 % (1727112)------------------------------
% 3.04/1.26 % (1727113)Refutation found. Thanks to Tanya!
% 3.04/1.26 % SZS status Theorem for theBenchmark
% 3.04/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.45 % (1727113)------------------------------
% 3.67/1.45 % (1727113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.45 % (1727113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.45 % (1727113)CaDiCaL version: 2.1.3
% 3.67/1.45 % (1727113)Termination reason: Refutation
% 3.67/1.45 % (1727113)Time elapsed: 0.028 s
% 3.67/1.45 % (1727113)Peak memory usage: 90 MB
% 3.67/1.45 % (1727113)Instructions burned: 33 (million)
% 3.67/1.45 % (1727113)------------------------------
% 3.67/1.45 % (1727113)------------------------------
% 3.67/1.45 % (1727103)Success in time 0.435 s
% 3.67/1.45 % Vampire exiting
%------------------------------------------------------------------------------