%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO089+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:51:30 AM UTC 2026
% Result : Theorem 4.18s 1.58s
% Output : Refutation 5.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 137 ( 18 unt; 10 def)
% Number of atoms : 509 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 633 ( 261 ~; 301 |; 51 &)
% ( 16 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 107 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).
fof(f3,axiom,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( ( part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) )
=> ( part_of(X2,X3)
| part_of(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn) ).
fof(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( incident_c(X0,X1)
& ~ end_point(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn) ).
fof(f17,conjecture,
! [X0,X1] :
( ? [X2] :
( part_of(X2,X0)
& inner_point(X1,X2) )
=> inner_point(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_11) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ? [X2] :
( part_of(X2,X0)
& inner_point(X1,X2) )
=> inner_point(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
? [X0,X1] :
( ~ inner_point(X1,X0)
& ? [X2] :
( part_of(X2,X0)
& inner_point(X1,X2) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
( ~ inner_point(sK1,sK0)
& part_of(sK2,sK0)
& inner_point(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21]) ).
fof(f29,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) )
| ~ end_point(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f30,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) )
| ~ end_point(X0,X1) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X4,X5] :
( part_of(X4,X5)
| part_of(X5,X4)
| ~ part_of(X4,X1)
| ~ part_of(X5,X1)
| ~ incident_c(X0,X4)
| ~ incident_c(X0,X5) ) )
| ~ end_point(X0,X1) ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ( ~ part_of(sK3(X0,X1),sK4(X0,X1))
& ~ part_of(sK4(X0,X1),sK3(X0,X1))
& part_of(sK3(X0,X1),X1)
& part_of(sK4(X0,X1),X1)
& incident_c(X0,sK3(X0,X1))
& incident_c(X0,sK4(X0,X1)) ) )
& ( ( incident_c(X0,X1)
& ! [X4,X5] :
( part_of(X4,X5)
| part_of(X5,X4)
| ~ part_of(X4,X1)
| ~ part_of(X5,X1)
| ~ incident_c(X0,X4)
| ~ incident_c(X0,X5) ) )
| ~ end_point(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3(X0,X1)),skolemize(X3,sK4(X0,X1))],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) )
| ~ part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f34,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(rectify,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK5(X0,X1),X0)
& incident_c(sK5(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f34]) ).
fof(f38,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f39,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
inner_point(sK1,sK2),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
part_of(sK2,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
~ inner_point(sK1,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X0,X1,X4,X5] :
( ~ end_point(X0,X1)
| part_of(X5,X4)
| ~ part_of(X4,X1)
| ~ part_of(X5,X1)
| ~ incident_c(X0,X4)
| ~ incident_c(X0,X5)
| part_of(X4,X5) ),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
! [X0,X1] :
( incident_c(X0,sK4(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f47,plain,
! [X0,X1] :
( incident_c(X0,sK3(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f48,plain,
! [X0,X1] :
( part_of(sK4(X0,X1),X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X0,X1] :
( part_of(sK3(X0,X1),X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X0,X1] :
( ~ part_of(sK4(X0,X1),sK3(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X0,X1] :
( ~ part_of(sK3(X0,X1),sK4(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
! [X0,X1] :
( incident_c(sK5(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0,X1] :
( part_of(X1,X0)
| ~ incident_c(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
! [X0,X1] :
( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
( ~ incident_c(sK1,sK0)
| end_point(sK1,sK0) ),
inference(resolution,[],[f59,f42]) ).
fof(f62,definition,
( spl9_1
<=> end_point(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f64,plain,
( end_point(sK1,sK0)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f66,definition,
( spl9_2
<=> incident_c(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f68,plain,
( ~ incident_c(sK1,sK0)
| spl9_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f60,f66,f62]) ).
fof(f70,plain,
( ! [X0] :
( ~ part_of(X0,sK0)
| ~ incident_c(sK1,X0) )
| spl9_2 ),
inference(resolution,[],[f68,f52]) ).
fof(f72,plain,
( ~ incident_c(sK1,sK2)
| spl9_2 ),
inference(resolution,[],[f70,f41]) ).
fof(f75,plain,
( ~ inner_point(sK1,sK2)
| spl9_2 ),
inference(resolution,[],[f72,f58]) ).
fof(f76,plain,
( $false
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f75,f40]) ).
fof(f77,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f82,plain,
( ! [X0,X1] :
( part_of(X0,X1)
| ~ part_of(X1,sK0)
| ~ part_of(X0,sK0)
| ~ incident_c(sK1,X1)
| ~ incident_c(sK1,X0)
| part_of(X1,X0) )
| ~ spl9_1 ),
inference(resolution,[],[f44,f64]) ).
fof(f84,plain,
( ! [X0,X1] :
( ~ part_of(sK4(X0,X1),sK0)
| ~ part_of(sK3(X0,X1),sK0)
| ~ incident_c(sK1,sK4(X0,X1))
| ~ incident_c(sK1,sK3(X0,X1))
| part_of(sK4(X0,X1),sK3(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
| ~ spl9_1 ),
inference(resolution,[],[f82,f51]) ).
fof(f87,plain,
( ! [X0,X1] :
( ~ incident_c(sK1,sK4(X0,X1))
| ~ part_of(sK3(X0,X1),sK0)
| ~ part_of(sK4(X0,X1),sK0)
| ~ incident_c(sK1,sK3(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f84,f50]) ).
fof(f92,plain,
( ! [X0] :
( ~ part_of(sK3(sK1,X0),sK0)
| ~ part_of(sK4(sK1,X0),sK0)
| ~ incident_c(sK1,sK3(sK1,X0))
| ~ incident_c(sK1,X0)
| end_point(sK1,X0)
| ~ incident_c(sK1,X0)
| end_point(sK1,X0) )
| ~ spl9_1 ),
inference(resolution,[],[f87,f46]) ).
fof(f95,plain,
( ! [X0] :
( ~ part_of(sK3(sK1,X0),sK0)
| ~ part_of(sK4(sK1,X0),sK0)
| ~ incident_c(sK1,sK3(sK1,X0))
| ~ incident_c(sK1,X0)
| end_point(sK1,X0) )
| ~ spl9_1 ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f96,plain,
( ! [X0] :
( ~ part_of(sK4(sK1,X0),sK0)
| ~ part_of(sK3(sK1,X0),sK0)
| ~ incident_c(sK1,X0)
| end_point(sK1,X0) )
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f95,f47]) ).
fof(f101,plain,
( ! [X0] :
( ~ incident_c(sK5(sK0,sK4(sK1,X0)),sK0)
| ~ incident_c(sK1,X0)
| end_point(sK1,X0)
| ~ part_of(sK3(sK1,X0),sK0) )
| ~ spl9_1 ),
inference(resolution,[],[f96,f54]) ).
fof(f139,plain,
( ! [X0,X1] :
( ~ part_of(sK3(sK1,X0),sK0)
| end_point(sK1,X0)
| ~ incident_c(sK1,X0)
| ~ incident_c(sK5(sK0,sK4(sK1,X0)),X1)
| ~ part_of(X1,sK0) )
| ~ spl9_1 ),
inference(resolution,[],[f101,f52]) ).
fof(f202,definition,
( spl9_6
<=> part_of(sK4(sK1,sK2),sK3(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f203,plain,
( ~ part_of(sK4(sK1,sK2),sK3(sK1,sK2))
| spl9_6 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f204,plain,
( part_of(sK4(sK1,sK2),sK3(sK1,sK2))
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f212,plain,
( ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| ~ spl9_6 ),
inference(resolution,[],[f204,f50]) ).
fof(f214,definition,
( spl9_8
<=> end_point(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
fof(f215,plain,
( ~ end_point(sK1,sK2)
| spl9_8 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( end_point(sK1,sK2)
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f218,definition,
( spl9_9
<=> incident_c(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
fof(f219,plain,
( incident_c(sK1,sK2)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f220,plain,
( ~ incident_c(sK1,sK2)
| spl9_9 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,plain,
( spl9_8
| ~ spl9_9
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f212,f202,f218,f214]) ).
fof(f224,plain,
( ~ inner_point(sK1,sK2)
| spl9_9 ),
inference(resolution,[],[f220,f58]) ).
fof(f225,plain,
( $false
| spl9_9 ),
inference(forward_subsumption_resolution,[],[f224,f40]) ).
fof(f226,plain,
spl9_9,
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f243,plain,
( ~ part_of(sK3(sK1,sK2),sK0)
| ~ part_of(sK4(sK1,sK2),sK0)
| ~ incident_c(sK1,sK3(sK1,sK2))
| ~ incident_c(sK1,sK4(sK1,sK2))
| part_of(sK3(sK1,sK2),sK4(sK1,sK2))
| ~ spl9_1
| spl9_6 ),
inference(resolution,[],[f203,f82]) ).
fof(f246,definition,
( spl9_10
<=> part_of(sK3(sK1,sK2),sK4(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
fof(f248,plain,
( part_of(sK3(sK1,sK2),sK4(sK1,sK2))
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl9_11
<=> incident_c(sK1,sK4(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f252,plain,
( ~ incident_c(sK1,sK4(sK1,sK2))
| spl9_11 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl9_12
<=> incident_c(sK1,sK3(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
fof(f256,plain,
( ~ incident_c(sK1,sK3(sK1,sK2))
| spl9_12 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl9_13
<=> part_of(sK4(sK1,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
fof(f260,plain,
( ~ part_of(sK4(sK1,sK2),sK0)
| spl9_13 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f262,definition,
( spl9_14
<=> part_of(sK3(sK1,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition]) ).
fof(f263,plain,
( part_of(sK3(sK1,sK2),sK0)
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( ~ part_of(sK3(sK1,sK2),sK0)
| spl9_14 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_13
| ~ spl9_14
| ~ spl9_1
| spl9_6 ),
inference(avatar_split_clause,[],[f243,f202,f62,f262,f258,f254,f250,f246]) ).
fof(f289,plain,
( ~ inner_point(sK1,sK2)
| ~ spl9_8 ),
inference(resolution,[],[f216,f57]) ).
fof(f291,plain,
( $false
| ~ spl9_8 ),
inference(forward_subsumption_resolution,[],[f289,f40]) ).
fof(f292,plain,
~ spl9_8,
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f309,plain,
( ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| ~ spl9_10 ),
inference(resolution,[],[f248,f51]) ).
fof(f310,plain,
( end_point(sK1,sK2)
| ~ spl9_9
| ~ spl9_10 ),
inference(forward_subsumption_resolution,[],[f309,f219]) ).
fof(f311,plain,
( $false
| spl9_8
| ~ spl9_9
| ~ spl9_10 ),
inference(forward_subsumption_resolution,[],[f310,f215]) ).
fof(f312,plain,
( spl9_8
| ~ spl9_9
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f313,plain,
( ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| spl9_11 ),
inference(resolution,[],[f252,f46]) ).
fof(f316,plain,
( end_point(sK1,sK2)
| ~ spl9_9
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f313,f219]) ).
fof(f317,plain,
( $false
| spl9_8
| ~ spl9_9
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f316,f215]) ).
fof(f318,plain,
( spl9_8
| ~ spl9_9
| spl9_11 ),
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f333,plain,
( ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| spl9_12 ),
inference(resolution,[],[f256,f47]) ).
fof(f336,plain,
( end_point(sK1,sK2)
| ~ spl9_9
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f333,f219]) ).
fof(f337,plain,
( $false
| spl9_8
| ~ spl9_9
| spl9_12 ),
inference(forward_subsumption_resolution,[],[f336,f215]) ).
fof(f338,plain,
( spl9_8
| ~ spl9_9
| spl9_12 ),
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f534,plain,
( ~ incident_c(sK5(sK0,sK3(sK1,sK2)),sK0)
| spl9_14 ),
inference(resolution,[],[f264,f54]) ).
fof(f662,plain,
( ! [X0] :
( ~ incident_c(sK5(sK0,sK3(sK1,sK2)),X0)
| ~ part_of(X0,sK0) )
| spl9_14 ),
inference(resolution,[],[f534,f52]) ).
fof(f701,plain,
( ! [X0,X1] :
( ~ incident_c(sK5(sK0,sK3(sK1,sK2)),X1)
| ~ part_of(X0,sK0)
| ~ part_of(X1,X0) )
| spl9_14 ),
inference(resolution,[],[f662,f52]) ).
fof(f1048,plain,
( ! [X0] :
( ~ part_of(X0,sK0)
| ~ part_of(sK3(sK1,sK2),X0)
| part_of(sK3(sK1,sK2),sK0) )
| spl9_14 ),
inference(resolution,[],[f701,f53]) ).
fof(f1053,plain,
( ! [X0] :
( ~ part_of(sK3(sK1,sK2),X0)
| ~ part_of(X0,sK0) )
| spl9_14 ),
inference(forward_subsumption_resolution,[],[f1048,f264]) ).
fof(f1055,plain,
( ~ part_of(sK2,sK0)
| ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| spl9_14 ),
inference(resolution,[],[f1053,f49]) ).
fof(f1075,plain,
( ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| spl9_14 ),
inference(forward_subsumption_resolution,[],[f1055,f41]) ).
fof(f1076,plain,
( end_point(sK1,sK2)
| ~ spl9_9
| spl9_14 ),
inference(forward_subsumption_resolution,[],[f1075,f219]) ).
fof(f1077,plain,
( $false
| spl9_8
| ~ spl9_9
| spl9_14 ),
inference(forward_subsumption_resolution,[],[f1076,f215]) ).
fof(f1078,plain,
( spl9_8
| ~ spl9_9
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f1077]) ).
fof(f1122,plain,
( ! [X0] :
( end_point(sK1,sK2)
| ~ incident_c(sK1,sK2)
| ~ incident_c(sK5(sK0,sK4(sK1,sK2)),X0)
| ~ part_of(X0,sK0) )
| ~ spl9_1
| ~ spl9_14 ),
inference(resolution,[],[f263,f139]) ).
fof(f1125,plain,
( ! [X0] :
( ~ incident_c(sK1,sK2)
| ~ incident_c(sK5(sK0,sK4(sK1,sK2)),X0)
| ~ part_of(X0,sK0) )
| ~ spl9_1
| spl9_8
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1122,f215]) ).
fof(f1126,plain,
( ! [X0] :
( ~ incident_c(sK5(sK0,sK4(sK1,sK2)),X0)
| ~ part_of(X0,sK0) )
| ~ spl9_1
| spl9_8
| ~ spl9_9
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1125,f219]) ).
fof(f1172,plain,
( ! [X0,X1] :
( ~ incident_c(sK5(sK0,sK4(sK1,sK2)),X1)
| ~ part_of(X0,sK0)
| ~ part_of(X1,X0) )
| ~ spl9_1
| spl9_8
| ~ spl9_9
| ~ spl9_14 ),
inference(resolution,[],[f1126,f52]) ).
fof(f1195,plain,
( ! [X0] :
( ~ part_of(X0,sK0)
| ~ part_of(sK4(sK1,sK2),X0)
| part_of(sK4(sK1,sK2),sK0) )
| ~ spl9_1
| spl9_8
| ~ spl9_9
| ~ spl9_14 ),
inference(resolution,[],[f1172,f53]) ).
fof(f1200,plain,
( ! [X0] :
( ~ part_of(sK4(sK1,sK2),X0)
| ~ part_of(X0,sK0) )
| ~ spl9_1
| spl9_8
| ~ spl9_9
| spl9_13
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1195,f260]) ).
fof(f1207,plain,
( ~ part_of(sK2,sK0)
| ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| ~ spl9_1
| spl9_8
| ~ spl9_9
| spl9_13
| ~ spl9_14 ),
inference(resolution,[],[f1200,f48]) ).
fof(f1225,plain,
( ~ incident_c(sK1,sK2)
| end_point(sK1,sK2)
| ~ spl9_1
| spl9_8
| ~ spl9_9
| spl9_13
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1207,f41]) ).
fof(f1226,plain,
( end_point(sK1,sK2)
| ~ spl9_1
| spl9_8
| ~ spl9_9
| spl9_13
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1225,f219]) ).
fof(f1227,plain,
( $false
| ~ spl9_1
| spl9_8
| ~ spl9_9
| spl9_13
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1226,f215]) ).
fof(f1228,plain,
( ~ spl9_1
| spl9_8
| ~ spl9_9
| spl9_13
| ~ spl9_14 ),
inference(avatar_contradiction_clause,[],[f1227]) ).
cnf(s1,plain,
( spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s2,plain,
spl9_2,
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( ~ spl9_6
| spl9_8
| ~ spl9_9 ),
inference(sat_conversion,[],[f221]) ).
cnf(s9,plain,
spl9_9,
inference(sat_conversion,[],[f226]) ).
cnf(s10,plain,
( ~ spl9_1
| spl9_6
| spl9_10
| ~ spl9_11
| ~ spl9_12
| ~ spl9_13
| ~ spl9_14 ),
inference(sat_conversion,[],[f265]) ).
cnf(s13,plain,
~ spl9_8,
inference(sat_conversion,[],[f292]) ).
cnf(s14,plain,
( spl9_8
| ~ spl9_9
| ~ spl9_10 ),
inference(sat_conversion,[],[f312]) ).
cnf(s15,plain,
( spl9_8
| ~ spl9_9
| spl9_11 ),
inference(sat_conversion,[],[f318]) ).
cnf(s16,plain,
( spl9_8
| ~ spl9_9
| spl9_12 ),
inference(sat_conversion,[],[f338]) ).
cnf(s50,plain,
( spl9_8
| ~ spl9_9
| spl9_14 ),
inference(sat_conversion,[],[f1078]) ).
cnf(s58,plain,
( ~ spl9_1
| spl9_8
| ~ spl9_9
| spl9_13
| ~ spl9_14 ),
inference(sat_conversion,[],[f1228]) ).
cnf(s59,plain,
spl9_14,
inference(rat,[],[s50,s13,s9]) ).
cnf(s60,plain,
spl9_12,
inference(rat,[],[s16,s13,s9]) ).
cnf(s61,plain,
spl9_11,
inference(rat,[],[s15,s13,s9]) ).
cnf(s62,plain,
~ spl9_10,
inference(rat,[],[s14,s13,s9]) ).
cnf(s64,plain,
~ spl9_6,
inference(rat,[],[s8,s9,s13]) ).
cnf(s68,plain,
spl9_1,
inference(rat,[],[s1,s2]) ).
cnf(s69,plain,
spl9_13,
inference(rat,[],[s58,s59,s9,s13,s68]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s10,s59,s64,s60,s61,s62,s69,s68]) ).
fof(f1229,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO089+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n018.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 06:56:39 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 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
% 4.18/1.58 % (1975264)Detected formulas, will run a generic FOF schedule.
% 4.18/1.58 % (1975272)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3763270352:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.18/1.58 % (1975272)Refutation not found, incomplete strategy
% 4.18/1.58 % (1975272)------------------------------
% 4.18/1.58 % (1975272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975272)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975272)Termination reason: Refutation not found, incomplete strategy
% 4.18/1.58 % (1975272)Time elapsed: 0.002 s
% 4.18/1.58 % (1975272)Peak memory usage: 88 MB
% 4.18/1.58 % (1975272)Instructions burned: 2 (million)
% 4.18/1.58 % (1975269)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=3203380744:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.18/1.58 % (1975270)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=182006679:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.18/1.58 % (1975271)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=637845397:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.18/1.58 % (1975273)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4127491129:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.18/1.58 % (1975274)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3015818740:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.18/1.58 % (1975275)dis-21_1_sil=8000:lcm=predicate:random_seed=581178083: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)
% 4.18/1.58 % (1975273)Instruction limit reached!
% 4.18/1.58 % (1975273)------------------------------
% 4.18/1.58 % (1975273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975273)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975273)Termination reason: Instruction limit
% 4.18/1.58 % (1975273)Termination phase: Saturation
% 4.18/1.58 % (1975273)Time elapsed: 0.063 s
% 4.18/1.58 % (1975273)Peak memory usage: 88 MB
% 4.18/1.58 % (1975273)Instructions burned: 120 (million)
% 4.18/1.58 % (1975275)Instruction limit reached!
% 4.18/1.58 % (1975275)------------------------------
% 4.18/1.58 % (1975275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975275)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975275)Termination reason: Instruction limit
% 4.18/1.58 % (1975275)Termination phase: Saturation
% 4.18/1.58 % (1975275)Time elapsed: 0.073 s
% 4.18/1.58 % (1975275)Peak memory usage: 89 MB
% 4.18/1.58 % (1975275)Instructions burned: 129 (million)
% 4.18/1.58 % (1975274)Instruction limit reached!
% 4.18/1.58 % (1975274)------------------------------
% 4.18/1.58 % (1975274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975274)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975274)Termination reason: Instruction limit
% 4.18/1.58 % (1975274)Termination phase: Saturation
% 4.18/1.58 % (1975274)Time elapsed: 0.095 s
% 4.18/1.58 % (1975274)Peak memory usage: 89 MB
% 4.18/1.58 % (1975274)Instructions burned: 140 (million)
% 4.18/1.58 % (1975272)------------------------------
% 4.18/1.58 % (1975272)------------------------------
% 4.18/1.58 % (1975283)lrs+10_1_sil=8000:sp=occurrence:random_seed=2132214643:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.18/1.58 % (1975284)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1192880251:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.18/1.58 % (1975286)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1824496093:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.18/1.58 % (1975285)lrs+1011_1_sil=32000:sp=occurrence:random_seed=998997190:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.18/1.58 % (1975286)Instruction limit reached!
% 4.18/1.58 % (1975286)------------------------------
% 4.18/1.58 % (1975286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975286)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975286)Termination reason: Instruction limit
% 4.18/1.58 % (1975286)Termination phase: Saturation
% 4.18/1.58 % (1975286)Time elapsed: 0.072 s
% 4.18/1.58 % (1975286)Peak memory usage: 90 MB
% 4.18/1.58 % (1975286)Instructions burned: 250 (million)
% 4.18/1.58 % (1975284)Instruction limit reached!
% 4.18/1.58 % (1975284)------------------------------
% 4.18/1.58 % (1975284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975284)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975284)Termination reason: Instruction limit
% 4.18/1.58 % (1975284)Termination phase: Saturation
% 4.18/1.58 % (1975284)Time elapsed: 0.085 s
% 4.18/1.58 % (1975284)Peak memory usage: 89 MB
% 4.18/1.58 % (1975284)Instructions burned: 157 (million)
% 4.18/1.58 % (1975285)First to succeed.
% 4.18/1.58 % (1975285)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1975264"
% 4.18/1.58 % (1975283)Instruction limit reached!
% 4.18/1.58 % (1975283)------------------------------
% 4.18/1.58 % (1975283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975283)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975283)Termination reason: Instruction limit
% 4.18/1.58 % (1975283)Termination phase: Saturation
% 4.18/1.58 % (1975283)Time elapsed: 0.165 s
% 4.18/1.58 % (1975283)Peak memory usage: 91 MB
% 4.18/1.58 % (1975283)Instructions burned: 285 (million)
% 4.18/1.58 % (1975291)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2422654697:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.18/1.58 % (1975292)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3297761433:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.18/1.58 % (1975291)Instruction limit reached!
% 4.18/1.58 % (1975291)------------------------------
% 4.18/1.58 % (1975291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.58 % (1975291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.58 % (1975291)CaDiCaL version: 2.1.3
% 4.18/1.58 % (1975291)Termination reason: Instruction limit
% 4.18/1.58 % (1975291)Termination phase: Saturation
% 4.18/1.58 % (1975291)Time elapsed: 0.084 s
% 4.18/1.58 % (1975291)Peak memory usage: 88 MB
% 4.18/1.58 % (1975291)Instructions burned: 298 (million)
% 4.18/1.58 % (1975293)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=259627168:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.18/1.58 % (1975285)Refutation found. Thanks to Tanya!
% 4.18/1.58 % SZS status Theorem for theBenchmark
% 4.18/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.54/1.78 % (1975285)------------------------------
% 5.54/1.78 % (1975285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.78 % (1975285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.78 % (1975285)CaDiCaL version: 2.1.3
% 5.54/1.78 % (1975285)Termination reason: Refutation
% 5.54/1.78 % (1975285)Time elapsed: 0.080 s
% 5.54/1.78 % (1975285)Peak memory usage: 90 MB
% 5.54/1.78 % (1975285)Instructions burned: 126 (million)
% 5.54/1.78 % (1975285)------------------------------
% 5.54/1.78 % (1975285)------------------------------
% 5.54/1.78 % (1975264)Success in time 0.703 s
% 5.54/1.78 % Vampire exiting
%------------------------------------------------------------------------------