%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 09:55:20 AM UTC 2026
% Result : Theorem 2.70s 1.32s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 138 ( 24 unt; 15 def)
% Number of atoms : 439 ( 61 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 534 ( 233 ~; 230 |; 46 &)
% ( 17 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 11 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 199 ( 0 sgn 184 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
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/theBenchmark.p',sequential_defn) ).
fof(f13,axiom,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(f18,axiom,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
fof(f19,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f25,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) )
| ~ complete ),
inference(ennf_transformation,[],[f18]) ).
fof(f26,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) )
| ~ complete ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
& complete ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ! [X0,X1,X2,X3,X4] :
( ( edge(sK0(X2,X3))
& head_of(X3) = tail_of(sK0(X2,X3))
& tail_of(X2) = head_of(sK0(X2,X3)) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X5,sK0(X2,X3))],[f26]) ).
fof(f35,plain,
( ! [X5] : ~ triangle(sK3,sK4,X5)
& shortest_path(sK1,sK2,sK5)
& precedes(sK3,sK4,sK5)
& sequential(sK3,sK4)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5)],[f28]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f38,plain,
! [X2,X3,X0,X1,X4] :
( tail_of(X2) = head_of(sK0(X2,X3))
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ complete ),
inference(cnf_transformation,[],[f34]) ).
fof(f39,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X3) = tail_of(sK0(X2,X3))
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ complete ),
inference(cnf_transformation,[],[f34]) ).
fof(f40,plain,
! [X2,X3,X0,X1,X4] :
( edge(sK0(X2,X3))
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ complete ),
inference(cnf_transformation,[],[f34]) ).
fof(f41,plain,
complete,
inference(cnf_transformation,[],[f35]) ).
fof(f42,plain,
sequential(sK3,sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f43,plain,
precedes(sK3,sK4,sK5),
inference(cnf_transformation,[],[f35]) ).
fof(f44,plain,
shortest_path(sK1,sK2,sK5),
inference(cnf_transformation,[],[f35]) ).
fof(f45,plain,
! [X5] : ~ triangle(sK3,sK4,X5),
inference(cnf_transformation,[],[f35]) ).
fof(f46,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| edge(sK0(X2,X3))
| sP6(X4,X3) ),
inference(cnf_transformation,[],[f56_D]) ).
fof(f56_D,definition,
! [X3,X4] :
( ! [X2] :
( ~ precedes(X2,X3,X4)
| edge(sK0(X2,X3)) )
<=> ~ sP6(X4,X3) ),
introduced(definition,[new_symbols(definition,[sP6])],[general_splitting_component_introduction]) ).
fof(f57,plain,
! [X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ complete
| ~ sP6(X4,X3) ),
inference(general_splitting,[],[f40,f56_D]) ).
fof(f58,plain,
! [X3,X4] :
( ~ sP6(X4,X3)
| sP7(X4) ),
inference(cnf_transformation,[],[f58_D]) ).
fof(f58_D,definition,
! [X4] :
( ! [X3] : ~ sP6(X4,X3)
<=> ~ sP7(X4) ),
introduced(definition,[new_symbols(definition,[sP7])],[general_splitting_component_introduction]) ).
fof(f59,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ complete
| ~ sP7(X4) ),
inference(general_splitting,[],[f57,f58_D]) ).
fof(f60,plain,
! [X2,X3,X4] :
( head_of(X3) = tail_of(sK0(X2,X3))
| ~ precedes(X2,X3,X4)
| sP8(X4,X3) ),
inference(cnf_transformation,[],[f60_D]) ).
fof(f60_D,definition,
! [X3,X4] :
( ! [X2] :
( head_of(X3) = tail_of(sK0(X2,X3))
| ~ precedes(X2,X3,X4) )
<=> ~ sP8(X4,X3) ),
introduced(definition,[new_symbols(definition,[sP8])],[general_splitting_component_introduction]) ).
fof(f61,plain,
! [X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ complete
| ~ sP8(X4,X3) ),
inference(general_splitting,[],[f39,f60_D]) ).
fof(f62,plain,
! [X3,X4] :
( ~ sP8(X4,X3)
| sP9(X4) ),
inference(cnf_transformation,[],[f62_D]) ).
fof(f62_D,definition,
! [X4] :
( ! [X3] : ~ sP8(X4,X3)
<=> ~ sP9(X4) ),
introduced(definition,[new_symbols(definition,[sP9])],[general_splitting_component_introduction]) ).
fof(f63,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ complete
| ~ sP9(X4) ),
inference(general_splitting,[],[f61,f62_D]) ).
fof(f64,plain,
! [X2,X3,X4] :
( tail_of(X2) = head_of(sK0(X2,X3))
| ~ precedes(X2,X3,X4)
| sP10(X4,X3) ),
inference(cnf_transformation,[],[f64_D]) ).
fof(f64_D,definition,
! [X3,X4] :
( ! [X2] :
( tail_of(X2) = head_of(sK0(X2,X3))
| ~ precedes(X2,X3,X4) )
<=> ~ sP10(X4,X3) ),
introduced(definition,[new_symbols(definition,[sP10])],[general_splitting_component_introduction]) ).
fof(f65,plain,
! [X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ complete
| ~ sP10(X4,X3) ),
inference(general_splitting,[],[f38,f64_D]) ).
fof(f66,plain,
! [X3,X4] :
( ~ sP10(X4,X3)
| sP11(X4) ),
inference(cnf_transformation,[],[f66_D]) ).
fof(f66_D,definition,
! [X4] :
( ! [X3] : ~ sP10(X4,X3)
<=> ~ sP11(X4) ),
introduced(definition,[new_symbols(definition,[sP11])],[general_splitting_component_introduction]) ).
fof(f67,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ complete
| ~ sP11(X4) ),
inference(general_splitting,[],[f65,f66_D]) ).
fof(f78,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ sP7(X4) ),
inference(forward_subsumption_resolution,[],[f59,f41]) ).
fof(f79,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ sP9(X4) ),
inference(forward_subsumption_resolution,[],[f63,f41]) ).
fof(f80,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ sP11(X4) ),
inference(forward_subsumption_resolution,[],[f67,f41]) ).
fof(f81,plain,
edge(sK4),
inference(resolution,[],[f42,f51]) ).
fof(f82,plain,
edge(sK3),
inference(resolution,[],[f42,f52]) ).
fof(f105,plain,
! [X0] :
( ~ edge(sK3)
| ~ edge(sK4)
| ~ edge(X0)
| ~ sequential(sK3,sK4)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(resolution,[],[f45,f54]) ).
fof(f106,plain,
! [X0] :
( ~ edge(sK4)
| ~ edge(X0)
| ~ sequential(sK3,sK4)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f105,f52]) ).
fof(f107,plain,
! [X0] :
( ~ edge(X0)
| ~ sequential(sK3,sK4)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f106,f52]) ).
fof(f108,plain,
! [X0] :
( ~ sequential(sK3,sK4)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f107,f52]) ).
fof(f109,plain,
! [X0] :
( ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f108,f42]) ).
fof(f110,plain,
~ sP7(sK5),
inference(resolution,[],[f78,f44]) ).
fof(f111,plain,
~ sP9(sK5),
inference(resolution,[],[f79,f44]) ).
fof(f112,plain,
~ sP11(sK5),
inference(resolution,[],[f80,f44]) ).
fof(f116,plain,
( edge(sK0(sK3,sK4))
| sP6(sK5,sK4) ),
inference(resolution,[],[f56,f43]) ).
fof(f118,definition,
( spl17_5
<=> sP6(sK5,sK4) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f120,plain,
( sP6(sK5,sK4)
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f122,definition,
( spl17_6
<=> edge(sK0(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
fof(f124,plain,
( edge(sK0(sK3,sK4))
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl17_5
| spl17_6 ),
inference(avatar_split_clause,[],[f116,f122,f118]) ).
fof(f126,plain,
( sP7(sK5)
| ~ spl17_5 ),
inference(resolution,[],[f120,f58]) ).
fof(f127,plain,
( $false
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f126,f110]) ).
fof(f128,plain,
~ spl17_5,
inference(avatar_contradiction_clause,[],[f127]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( head_of(X0) != head_of(X1)
| ~ edge(X1)
| ~ edge(sK0(X2,X0))
| sK0(X2,X0) = X1
| sequential(X1,sK0(X2,X0))
| ~ precedes(X2,X0,X3)
| sP8(X3,X0) ),
inference(superposition,[],[f53,f60]) ).
fof(f132,plain,
! [X2,X0,X1] :
( head_of(X0) != head_of(sK0(X1,X0))
| ~ edge(sK0(X1,X0))
| ~ precedes(X1,X0,X2)
| sP8(X2,X0) ),
inference(superposition,[],[f46,f60]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( tail_of(X0) != tail_of(X2)
| ~ edge(sK0(X0,X1))
| ~ edge(X2)
| sK0(X0,X1) = X2
| sequential(sK0(X0,X1),X2)
| ~ precedes(X0,X1,X3)
| sP10(X3,X1) ),
inference(superposition,[],[f53,f64]) ).
fof(f167,plain,
! [X2,X0,X1] :
( sequential(X0,sK0(X1,X0))
| ~ edge(sK0(X1,X0))
| sK0(X1,X0) = X0
| ~ edge(X0)
| ~ precedes(X1,X0,X2)
| sP8(X2,X0) ),
inference(equality_resolution,[],[f131]) ).
fof(f178,plain,
! [X2,X0,X1] :
( sequential(sK0(X0,X1),X0)
| ~ edge(X0)
| sK0(X0,X1) = X0
| ~ edge(sK0(X0,X1))
| ~ precedes(X0,X1,X2)
| sP10(X2,X1) ),
inference(equality_resolution,[],[f137]) ).
fof(f192,plain,
! [X0,X1] :
( ~ edge(sK0(X0,sK4))
| sK4 = sK0(X0,sK4)
| ~ edge(sK4)
| ~ precedes(X0,sK4,X1)
| sP8(X1,sK4)
| ~ sequential(sK0(X0,sK4),sK3) ),
inference(resolution,[],[f167,f109]) ).
fof(f196,plain,
! [X0,X1] :
( sK4 = sK0(X0,sK4)
| ~ edge(sK4)
| ~ precedes(X0,sK4,X1)
| sP8(X1,sK4)
| ~ sequential(sK0(X0,sK4),sK3) ),
inference(forward_subsumption_resolution,[],[f192,f52]) ).
fof(f197,plain,
! [X0,X1] :
( ~ sequential(sK0(X0,sK4),sK3)
| ~ precedes(X0,sK4,X1)
| sP8(X1,sK4)
| sK4 = sK0(X0,sK4) ),
inference(forward_subsumption_resolution,[],[f196,f81]) ).
fof(f200,plain,
! [X0,X1] :
( ~ edge(sK3)
| sK3 = sK0(sK3,sK4)
| ~ edge(sK0(sK3,sK4))
| ~ precedes(sK3,sK4,X0)
| sP10(X0,sK4)
| ~ precedes(sK3,sK4,X1)
| sP8(X1,sK4)
| sK4 = sK0(sK3,sK4) ),
inference(resolution,[],[f178,f197]) ).
fof(f204,plain,
! [X0,X1] :
( sK3 = sK0(sK3,sK4)
| ~ edge(sK0(sK3,sK4))
| ~ precedes(sK3,sK4,X0)
| sP10(X0,sK4)
| ~ precedes(sK3,sK4,X1)
| sP8(X1,sK4)
| sK4 = sK0(sK3,sK4) ),
inference(forward_subsumption_resolution,[],[f200,f82]) ).
fof(f206,plain,
( ! [X0,X1] :
( sK3 = sK0(sK3,sK4)
| ~ precedes(sK3,sK4,X0)
| sP10(X0,sK4)
| ~ precedes(sK3,sK4,X1)
| sP8(X1,sK4)
| sK4 = sK0(sK3,sK4) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f204,f124]) ).
fof(f208,definition,
( spl17_7
<=> sK4 = sK0(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f210,plain,
( sK4 = sK0(sK3,sK4)
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f212,definition,
( spl17_8
<=> ! [X1] :
( ~ precedes(sK3,sK4,X1)
| sP8(X1,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
fof(f213,plain,
( ! [X1] :
( ~ precedes(sK3,sK4,X1)
| sP8(X1,sK4) )
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,definition,
( spl17_9
<=> ! [X0] :
( ~ precedes(sK3,sK4,X0)
| sP10(X0,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl17_9])],[avatar_definition]) ).
fof(f216,plain,
( ! [X0] :
( ~ precedes(sK3,sK4,X0)
| sP10(X0,sK4) )
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,definition,
( spl17_10
<=> sK3 = sK0(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl17_10])],[avatar_definition]) ).
fof(f220,plain,
( sK3 = sK0(sK3,sK4)
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,plain,
( spl17_7
| spl17_8
| spl17_9
| spl17_10
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f206,f122,f218,f215,f212,f208]) ).
fof(f226,plain,
( ! [X0] :
( head_of(sK4) != head_of(sK4)
| ~ edge(sK4)
| ~ precedes(sK3,sK4,X0)
| sP8(X0,sK4) )
| ~ spl17_7 ),
inference(superposition,[],[f132,f210]) ).
fof(f232,plain,
( ! [X0] :
( ~ edge(sK4)
| ~ precedes(sK3,sK4,X0)
| sP8(X0,sK4) )
| ~ spl17_7 ),
inference(trivial_inequality_removal,[],[f226]) ).
fof(f246,plain,
( ! [X0] :
( ~ precedes(sK3,sK4,X0)
| sP8(X0,sK4) )
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f232,f81]) ).
fof(f252,definition,
( spl17_15
<=> head_of(sK4) = tail_of(sK3) ),
introduced(definition,[new_symbols(definition,[spl17_15])],[avatar_definition]) ).
fof(f254,plain,
( head_of(sK4) = tail_of(sK3)
| ~ spl17_15 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f262,plain,
( spl17_8
| ~ spl17_7 ),
inference(avatar_split_clause,[],[f246,f208,f212]) ).
fof(f280,plain,
( sP8(sK5,sK4)
| ~ spl17_8 ),
inference(resolution,[],[f213,f43]) ).
fof(f285,plain,
( sP9(sK5)
| ~ spl17_8 ),
inference(resolution,[],[f280,f62]) ).
fof(f286,plain,
( $false
| ~ spl17_8 ),
inference(forward_subsumption_resolution,[],[f285,f111]) ).
fof(f287,plain,
~ spl17_8,
inference(avatar_contradiction_clause,[],[f286]) ).
fof(f292,plain,
( sP10(sK5,sK4)
| ~ spl17_9 ),
inference(resolution,[],[f216,f43]) ).
fof(f297,plain,
( sP11(sK5)
| ~ spl17_9 ),
inference(resolution,[],[f292,f66]) ).
fof(f298,plain,
( $false
| ~ spl17_9 ),
inference(forward_subsumption_resolution,[],[f297,f112]) ).
fof(f299,plain,
~ spl17_9,
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f307,plain,
( ! [X0] :
( head_of(sK4) = tail_of(sK3)
| ~ precedes(sK3,sK4,X0)
| sP8(X0,sK4) )
| ~ spl17_10 ),
inference(superposition,[],[f60,f220]) ).
fof(f308,plain,
( ! [X0] :
( tail_of(sK3) = head_of(sK3)
| ~ precedes(sK3,sK4,X0)
| sP10(X0,sK4) )
| ~ spl17_10 ),
inference(superposition,[],[f64,f220]) ).
fof(f310,plain,
( ! [X0] :
( head_of(sK4) != head_of(sK3)
| ~ edge(sK3)
| ~ precedes(sK3,sK4,X0)
| sP8(X0,sK4) )
| ~ spl17_10 ),
inference(superposition,[],[f132,f220]) ).
fof(f333,plain,
( ! [X0] :
( head_of(sK4) != head_of(sK3)
| ~ precedes(sK3,sK4,X0)
| sP8(X0,sK4) )
| ~ spl17_10 ),
inference(forward_subsumption_resolution,[],[f310,f82]) ).
fof(f339,definition,
( spl17_24
<=> tail_of(sK3) = head_of(sK3) ),
introduced(definition,[new_symbols(definition,[spl17_24])],[avatar_definition]) ).
fof(f341,plain,
( tail_of(sK3) = head_of(sK3)
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f342,plain,
( spl17_9
| spl17_24
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f308,f218,f339,f215]) ).
fof(f343,plain,
( spl17_8
| spl17_15
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f307,f218,f252,f212]) ).
fof(f347,definition,
( spl17_25
<=> head_of(sK4) = head_of(sK3) ),
introduced(definition,[new_symbols(definition,[spl17_25])],[avatar_definition]) ).
fof(f349,plain,
( head_of(sK4) != head_of(sK3)
| spl17_25 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f350,plain,
( spl17_8
| ~ spl17_25
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f333,f218,f347,f212]) ).
fof(f355,plain,
( tail_of(sK3) != head_of(sK3)
| ~ spl17_15
| spl17_25 ),
inference(forward_demodulation,[],[f349,f254]) ).
fof(f357,plain,
( $false
| ~ spl17_15
| ~ spl17_24
| spl17_25 ),
inference(forward_subsumption_resolution,[],[f355,f341]) ).
fof(f358,plain,
( ~ spl17_15
| ~ spl17_24
| spl17_25 ),
inference(avatar_contradiction_clause,[],[f357]) ).
cnf(s4,plain,
( spl17_5
| spl17_6 ),
inference(sat_conversion,[],[f125]) ).
cnf(s5,plain,
~ spl17_5,
inference(sat_conversion,[],[f128]) ).
cnf(s6,plain,
( ~ spl17_6
| spl17_7
| spl17_8
| spl17_9
| spl17_10 ),
inference(sat_conversion,[],[f221]) ).
cnf(s13,plain,
( ~ spl17_7
| spl17_8 ),
inference(sat_conversion,[],[f262]) ).
cnf(s15,plain,
~ spl17_8,
inference(sat_conversion,[],[f287]) ).
cnf(s16,plain,
~ spl17_9,
inference(sat_conversion,[],[f299]) ).
cnf(s22,plain,
( spl17_9
| ~ spl17_10
| spl17_24 ),
inference(sat_conversion,[],[f342]) ).
cnf(s23,plain,
( spl17_8
| ~ spl17_10
| spl17_15 ),
inference(sat_conversion,[],[f343]) ).
cnf(s25,plain,
( spl17_8
| ~ spl17_10
| ~ spl17_25 ),
inference(sat_conversion,[],[f350]) ).
cnf(s27,plain,
( ~ spl17_15
| ~ spl17_24
| spl17_25 ),
inference(sat_conversion,[],[f358]) ).
cnf(s29,plain,
~ spl17_7,
inference(rat,[],[s13,s15]) ).
cnf(s30,plain,
( ~ spl17_6
| spl17_10 ),
inference(rat,[],[s6,s16,s15,s29]) ).
cnf(s31,plain,
spl17_6,
inference(rat,[],[s4,s5]) ).
cnf(s32,plain,
spl17_10,
inference(rat,[],[s30,s31]) ).
cnf(s33,plain,
~ spl17_25,
inference(rat,[],[s25,s15,s32]) ).
cnf(s35,plain,
spl17_15,
inference(rat,[],[s23,s15,s32]) ).
cnf(s36,plain,
spl17_24,
inference(rat,[],[s22,s16,s32]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s27,s33,s36,s35]) ).
fof(f359,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 08:46:51 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.70/1.32 % (4117228)Detected formulas, will run a generic FOF schedule.
% 2.70/1.32 % (4117239)dis-21_1_sil=8000:lcm=predicate:random_seed=2656551943: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)
% 2.70/1.32 % (4117233)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=2162070470:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.32 % (4117234)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=2643809580:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.32 % (4117236)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3357698866:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.32 % (4117235)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=856736438:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.32 % (4117239)Instruction limit reached!
% 2.70/1.32 % (4117239)------------------------------
% 2.70/1.32 % (4117239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.32 % (4117239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.32 % (4117239)CaDiCaL version: 2.1.3
% 2.70/1.32 % (4117239)Termination reason: Instruction limit
% 2.70/1.32 % (4117239)Termination phase: Saturation
% 2.70/1.32 % (4117239)Time elapsed: 0.037 s
% 2.70/1.32 % (4117239)Peak memory usage: 89 MB
% 2.70/1.32 % (4117239)Instructions burned: 132 (million)
% 2.70/1.32 % (4117238)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1461577073:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.32 % (4117237)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=718632258:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.32 % (4117236)First to succeed.
% 2.70/1.32 % (4117236)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4117228"
% 2.70/1.32 % (4117237)Instruction limit reached!
% 2.70/1.32 % (4117237)------------------------------
% 2.70/1.32 % (4117237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.32 % (4117237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.32 % (4117237)CaDiCaL version: 2.1.3
% 2.70/1.32 % (4117237)Termination reason: Instruction limit
% 2.70/1.32 % (4117237)Termination phase: Saturation
% 2.70/1.32 % (4117237)Time elapsed: 0.067 s
% 2.70/1.32 % (4117237)Peak memory usage: 88 MB
% 2.70/1.32 % (4117237)Instructions burned: 119 (million)
% 2.70/1.32 % (4117238)Instruction limit reached!
% 2.70/1.32 % (4117238)------------------------------
% 2.70/1.32 % (4117238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.32 % (4117238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.32 % (4117238)CaDiCaL version: 2.1.3
% 2.70/1.32 % (4117238)Termination reason: Instruction limit
% 2.70/1.32 % (4117238)Termination phase: Saturation
% 2.70/1.32 % (4117238)Time elapsed: 0.095 s
% 2.70/1.32 % (4117238)Peak memory usage: 90 MB
% 2.70/1.32 % (4117238)Instructions burned: 140 (million)
% 2.70/1.32 % (4117247)lrs+10_1_sil=8000:sp=occurrence:random_seed=2719556359:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.70/1.32 % (4117247)Instruction limit reached!
% 2.70/1.32 % (4117247)------------------------------
% 2.70/1.32 % (4117247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.32 % (4117247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.32 % (4117247)CaDiCaL version: 2.1.3
% 2.70/1.32 % (4117247)Termination reason: Instruction limit
% 2.70/1.32 % (4117247)Termination phase: Saturation
% 2.70/1.32 % (4117247)Time elapsed: 0.092 s
% 2.70/1.32 % (4117247)Peak memory usage: 91 MB
% 2.70/1.32 % (4117247)Instructions burned: 289 (million)
% 2.70/1.32 % (4117248)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3150151537:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.70/1.32 % (4117248)Also succeeded, but the first one will report.
% 2.70/1.32 % (4117249)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2136158713:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.70/1.32 % (4117236)Refutation found. Thanks to Tanya!
% 2.70/1.32 % SZS status Theorem for theBenchmark
% 2.70/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.52 % (4117236)------------------------------
% 3.78/1.52 % (4117236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.52 % (4117236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.52 % (4117236)CaDiCaL version: 2.1.3
% 3.78/1.52 % (4117236)Termination reason: Refutation
% 3.78/1.52 % (4117236)Time elapsed: 0.014 s
% 3.78/1.52 % (4117236)Peak memory usage: 89 MB
% 3.78/1.52 % (4117236)Instructions burned: 18 (million)
% 3.78/1.52 % (4117236)------------------------------
% 3.78/1.52 % (4117236)------------------------------
% 3.78/1.52 % (4117228)Success in time 0.441 s
% 3.78/1.52 % Vampire exiting
%------------------------------------------------------------------------------