%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU376+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:48:36 PM UTC 2026
% Result : Theorem 2.27s 1.19s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 134 ( 28 unt; 15 def)
% Number of atoms : 597 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 758 ( 295 ~; 330 |; 88 &)
% ( 24 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 16 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 173 ( 0 sgn 144 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( related(X1,X3,X4)
=> in(apply_netmap(X0,X1,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_waybel_0) ).
fof(f9,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X3,X4)
& in(apply_netmap(X0,X1,X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_waybel_0) ).
fof(f10,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& rel_str(X0) )
=> ( directed_relstr(X0)
<=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X1,X3)
& related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_yellow_6) ).
fof(f20,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(f54,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_yellow_6) ).
fof(f55,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& transitive_relstr(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f65,plain,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
inference(pure_predicate_removal,[],[f55]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X3,X4)
& in(apply_netmap(X0,X1,X4),X2) )
| ~ element(X3,the_carrier(X1)) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X3,X4)
& in(apply_netmap(X0,X1,X4),X2) )
| ~ element(X3,the_carrier(X1)) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ( directed_relstr(X0)
<=> ! [X1] :
( ! [X2] :
( ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X1,X3)
& related(X0,X2,X3) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) ) )
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f85,plain,
! [X0] :
( ( directed_relstr(X0)
<=> ! [X1] :
( ! [X2] :
( ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X1,X3)
& related(X0,X2,X3) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) ) )
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f84]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f110,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ is_often_in(X0,X1,X2)
& is_eventually_in(X0,X1,X2) )
& ~ empty_carrier(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f111,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ is_often_in(X0,X1,X2)
& is_eventually_in(X0,X1,X2) )
& ~ empty_carrier(X1)
& directed_relstr(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f110]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ? [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X1))
& ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) ) )
| ~ is_eventually_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ? [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) )
& ( ? [X5] :
( element(X5,the_carrier(X1))
& ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,X5,X6)
| ~ element(X6,the_carrier(X1)) ) )
| ~ is_eventually_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ( ~ in(apply_netmap(X0,X1,sK0(X0,X1,X2,X3)),X2)
& related(X1,X3,sK0(X0,X1,X2,X3))
& element(sK0(X0,X1,X2,X3),the_carrier(X1)) ) ) )
& ( ( element(sK1(X0,X1,X2),the_carrier(X1))
& ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,sK1(X0,X1,X2),X6)
| ~ element(X6,the_carrier(X1)) ) )
| ~ is_eventually_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0(X0,X1,X2,X3)),skolemize(X5,sK1(X0,X1,X2))],[f122]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_often_in(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ related(X1,X3,X4)
| ~ in(apply_netmap(X0,X1,X4),X2) )
& element(X3,the_carrier(X1)) ) )
& ( ! [X3] :
( ? [X4] :
( element(X4,the_carrier(X1))
& related(X1,X3,X4)
& in(apply_netmap(X0,X1,X4),X2) )
| ~ element(X3,the_carrier(X1)) )
| ~ is_often_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f83]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_often_in(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ related(X1,X3,X4)
| ~ in(apply_netmap(X0,X1,X4),X2) )
& element(X3,the_carrier(X1)) ) )
& ( ! [X5] :
( ? [X6] :
( element(X6,the_carrier(X1))
& related(X1,X5,X6)
& in(apply_netmap(X0,X1,X6),X2) )
| ~ element(X5,the_carrier(X1)) )
| ~ is_often_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_often_in(X0,X1,X2)
| ( ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ related(X1,sK2(X0,X1,X2),X4)
| ~ in(apply_netmap(X0,X1,X4),X2) )
& element(sK2(X0,X1,X2),the_carrier(X1)) ) )
& ( ! [X5] :
( ( element(sK3(X0,X1,X2,X5),the_carrier(X1))
& related(X1,X5,sK3(X0,X1,X2,X5))
& in(apply_netmap(X0,X1,sK3(X0,X1,X2,X5)),X2) )
| ~ element(X5,the_carrier(X1)) )
| ~ is_often_in(X0,X1,X2) ) )
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X6,sK3(X0,X1,X2,X5))],[f125]) ).
fof(f127,plain,
! [X0] :
( ( ( directed_relstr(X0)
| ? [X1] :
( ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ related(X0,X1,X3)
| ~ related(X0,X2,X3) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) ) )
& ( ! [X1] :
( ! [X2] :
( ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X1,X3)
& related(X0,X2,X3) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ directed_relstr(X0) ) )
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f85]) ).
fof(f128,plain,
! [X0] :
( ( ( directed_relstr(X0)
| ? [X1] :
( ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ related(X0,X1,X3)
| ~ related(X0,X2,X3) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( ? [X6] :
( element(X6,the_carrier(X0))
& related(X0,X4,X6)
& related(X0,X5,X6) )
| ~ element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) )
| ~ directed_relstr(X0) ) )
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ( ( directed_relstr(X0)
| ( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ related(X0,sK4(X0),X3)
| ~ related(X0,sK5(X0),X3) )
& element(sK5(X0),the_carrier(X0))
& element(sK4(X0),the_carrier(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( ( element(sK6(X0,X4,X5),the_carrier(X0))
& related(X0,X4,sK6(X0,X4,X5))
& related(X0,X5,sK6(X0,X4,X5)) )
| ~ element(X5,the_carrier(X0)) )
| ~ element(X4,the_carrier(X0)) )
| ~ directed_relstr(X0) ) )
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0)),skolemize(X6,sK6(X0,X4,X5))],[f128]) ).
fof(f149,plain,
( ~ is_often_in(sK25,sK26,sK27)
& is_eventually_in(sK25,sK26,sK27)
& ~ empty_carrier(sK26)
& directed_relstr(sK26)
& net_str(sK26,sK25)
& ~ empty_carrier(sK25)
& one_sorted_str(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X0,sK25),skolemize(X1,sK26),skolemize(X2,sK27)],[f111]) ).
fof(f156,plain,
! [X2,X0,X1,X6] :
( ~ is_eventually_in(X0,X1,X2)
| ~ related(X1,sK1(X0,X1,X2),X6)
| ~ element(X6,the_carrier(X1))
| in(apply_netmap(X0,X1,X6),X2)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ is_eventually_in(X0,X1,X2)
| element(sK1(X0,X1,X2),the_carrier(X1))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f164,plain,
! [X2,X0,X1] :
( is_often_in(X0,X1,X2)
| element(sK2(X0,X1,X2),the_carrier(X1))
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f165,plain,
! [X2,X0,X1,X4] :
( is_often_in(X0,X1,X2)
| ~ element(X4,the_carrier(X1))
| ~ related(X1,sK2(X0,X1,X2),X4)
| ~ in(apply_netmap(X0,X1,X4),X2)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f166,plain,
! [X0,X4,X5] :
( ~ directed_relstr(X0)
| ~ element(X5,the_carrier(X0))
| ~ element(X4,the_carrier(X0))
| related(X0,X5,sK6(X0,X4,X5))
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f167,plain,
! [X0,X4,X5] :
( ~ directed_relstr(X0)
| ~ element(X5,the_carrier(X0))
| ~ element(X4,the_carrier(X0))
| related(X0,X4,sK6(X0,X4,X5))
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f168,plain,
! [X0,X4,X5] :
( ~ directed_relstr(X0)
| ~ element(X5,the_carrier(X0))
| ~ element(X4,the_carrier(X0))
| element(sK6(X0,X4,X5),the_carrier(X0))
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f176,plain,
! [X0,X1] :
( rel_str(X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f227,plain,
one_sorted_str(sK25),
inference(cnf_transformation,[],[f149]) ).
fof(f228,plain,
~ empty_carrier(sK25),
inference(cnf_transformation,[],[f149]) ).
fof(f229,plain,
net_str(sK26,sK25),
inference(cnf_transformation,[],[f149]) ).
fof(f230,plain,
directed_relstr(sK26),
inference(cnf_transformation,[],[f149]) ).
fof(f231,plain,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f149]) ).
fof(f232,plain,
is_eventually_in(sK25,sK26,sK27),
inference(cnf_transformation,[],[f149]) ).
fof(f233,plain,
~ is_often_in(sK25,sK26,sK27),
inference(cnf_transformation,[],[f149]) ).
fof(f264,definition,
( spl29_2
<=> one_sorted_str(sK25) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f265,plain,
( ~ one_sorted_str(sK25)
| spl29_2 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,plain,
( $false
| spl29_2 ),
inference(resolution,[],[f265,f227]) ).
fof(f268,plain,
spl29_2,
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f302,definition,
( spl29_4
<=> empty_carrier(sK26) ),
introduced(definition,[new_symbols(definition,[spl29_4])],[avatar_definition]) ).
fof(f303,plain,
( empty_carrier(sK26)
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f309,definition,
( spl29_6
<=> empty_carrier(sK25) ),
introduced(definition,[new_symbols(definition,[spl29_6])],[avatar_definition]) ).
fof(f310,plain,
( empty_carrier(sK25)
| ~ spl29_6 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f333,plain,
( $false
| ~ spl29_4 ),
inference(resolution,[],[f303,f231]) ).
fof(f334,plain,
~ spl29_4,
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f408,plain,
( element(sK1(sK25,sK26,sK27),the_carrier(sK26))
| empty_carrier(sK26)
| ~ net_str(sK26,sK25)
| empty_carrier(sK25)
| ~ one_sorted_str(sK25) ),
inference(resolution,[],[f157,f232]) ).
fof(f410,definition,
( spl29_24
<=> net_str(sK26,sK25) ),
introduced(definition,[new_symbols(definition,[spl29_24])],[avatar_definition]) ).
fof(f411,plain,
( ~ net_str(sK26,sK25)
| spl29_24 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f413,definition,
( spl29_25
<=> element(sK1(sK25,sK26,sK27),the_carrier(sK26)) ),
introduced(definition,[new_symbols(definition,[spl29_25])],[avatar_definition]) ).
fof(f415,plain,
( ~ spl29_2
| spl29_6
| ~ spl29_24
| spl29_4
| spl29_25 ),
inference(avatar_split_clause,[],[f408,f413,f302,f410,f309,f264]) ).
fof(f423,plain,
( $false
| spl29_24 ),
inference(resolution,[],[f411,f229]) ).
fof(f424,plain,
spl29_24,
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f425,plain,
( element(sK2(sK25,sK26,sK27),the_carrier(sK26))
| empty_carrier(sK26)
| ~ net_str(sK26,sK25)
| empty_carrier(sK25)
| ~ one_sorted_str(sK25) ),
inference(resolution,[],[f164,f233]) ).
fof(f427,definition,
( spl29_26
<=> element(sK2(sK25,sK26,sK27),the_carrier(sK26)) ),
introduced(definition,[new_symbols(definition,[spl29_26])],[avatar_definition]) ).
fof(f429,plain,
( ~ spl29_2
| spl29_6
| ~ spl29_24
| spl29_4
| spl29_26 ),
inference(avatar_split_clause,[],[f425,f427,f302,f410,f309,f264]) ).
fof(f430,plain,
( $false
| ~ spl29_6 ),
inference(resolution,[],[f310,f228]) ).
fof(f431,plain,
~ spl29_6,
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f441,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK26))
| ~ element(X1,the_carrier(sK26))
| related(sK26,X0,sK6(sK26,X1,X0))
| empty_carrier(sK26)
| ~ rel_str(sK26) ),
inference(resolution,[],[f166,f230]) ).
fof(f449,definition,
( spl29_28
<=> rel_str(sK26) ),
introduced(definition,[new_symbols(definition,[spl29_28])],[avatar_definition]) ).
fof(f450,plain,
( ~ rel_str(sK26)
| spl29_28 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f452,definition,
( spl29_29
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(sK26))
| related(sK26,X0,sK6(sK26,X1,X0))
| ~ element(X1,the_carrier(sK26)) ) ),
introduced(definition,[new_symbols(definition,[spl29_29])],[avatar_definition]) ).
fof(f453,plain,
( ! [X0,X1] :
( related(sK26,X0,sK6(sK26,X1,X0))
| ~ element(X0,the_carrier(sK26))
| ~ element(X1,the_carrier(sK26)) )
| ~ spl29_29 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f454,plain,
( ~ spl29_28
| spl29_4
| spl29_29 ),
inference(avatar_split_clause,[],[f441,f452,f302,f449]) ).
fof(f455,plain,
( ! [X0] :
( ~ net_str(sK26,X0)
| ~ one_sorted_str(X0) )
| spl29_28 ),
inference(resolution,[],[f450,f176]) ).
fof(f456,plain,
( ~ one_sorted_str(sK25)
| spl29_28 ),
inference(resolution,[],[f455,f229]) ).
fof(f457,plain,
( ~ spl29_2
| spl29_28 ),
inference(avatar_split_clause,[],[f456,f449,f264]) ).
fof(f458,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK26))
| ~ element(X1,the_carrier(sK26))
| related(sK26,X1,sK6(sK26,X1,X0))
| empty_carrier(sK26)
| ~ rel_str(sK26) ),
inference(resolution,[],[f167,f230]) ).
fof(f466,definition,
( spl29_30
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(sK26))
| ~ element(X1,the_carrier(sK26))
| related(sK26,X1,sK6(sK26,X1,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_30])],[avatar_definition]) ).
fof(f467,plain,
( ! [X0,X1] :
( related(sK26,X1,sK6(sK26,X1,X0))
| ~ element(X1,the_carrier(sK26))
| ~ element(X0,the_carrier(sK26)) )
| ~ spl29_30 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f468,plain,
( ~ spl29_28
| spl29_4
| spl29_30 ),
inference(avatar_split_clause,[],[f458,f466,f302,f449]) ).
fof(f601,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK26))
| ~ element(X1,the_carrier(sK26))
| element(sK6(sK26,X1,X0),the_carrier(sK26))
| empty_carrier(sK26)
| ~ rel_str(sK26) ),
inference(resolution,[],[f168,f230]) ).
fof(f609,definition,
( spl29_57
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(sK26))
| ~ element(X1,the_carrier(sK26))
| element(sK6(sK26,X1,X0),the_carrier(sK26)) ) ),
introduced(definition,[new_symbols(definition,[spl29_57])],[avatar_definition]) ).
fof(f610,plain,
( ! [X0,X1] :
( element(sK6(sK26,X1,X0),the_carrier(sK26))
| ~ element(X1,the_carrier(sK26))
| ~ element(X0,the_carrier(sK26)) )
| ~ spl29_57 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f611,plain,
( ~ spl29_28
| spl29_4
| spl29_57 ),
inference(avatar_split_clause,[],[f601,f609,f302,f449]) ).
fof(f2419,plain,
! [X0] :
( ~ related(sK26,sK1(sK25,sK26,sK27),X0)
| ~ element(X0,the_carrier(sK26))
| in(apply_netmap(sK25,sK26,X0),sK27)
| empty_carrier(sK26)
| ~ net_str(sK26,sK25)
| empty_carrier(sK25)
| ~ one_sorted_str(sK25) ),
inference(resolution,[],[f156,f232]) ).
fof(f2427,definition,
( spl29_399
<=> ! [X0] :
( ~ related(sK26,sK1(sK25,sK26,sK27),X0)
| in(apply_netmap(sK25,sK26,X0),sK27)
| ~ element(X0,the_carrier(sK26)) ) ),
introduced(definition,[new_symbols(definition,[spl29_399])],[avatar_definition]) ).
fof(f2428,plain,
( ! [X0] :
( ~ related(sK26,sK1(sK25,sK26,sK27),X0)
| in(apply_netmap(sK25,sK26,X0),sK27)
| ~ element(X0,the_carrier(sK26)) )
| ~ spl29_399 ),
inference(avatar_component_clause,[],[f2427]) ).
fof(f2429,plain,
( ~ spl29_2
| spl29_6
| ~ spl29_24
| spl29_4
| spl29_399 ),
inference(avatar_split_clause,[],[f2419,f2427,f302,f410,f309,f264]) ).
fof(f2430,plain,
( ! [X0] :
( in(apply_netmap(sK25,sK26,sK6(sK26,X0,sK1(sK25,sK26,sK27))),sK27)
| ~ element(sK6(sK26,X0,sK1(sK25,sK26,sK27)),the_carrier(sK26))
| ~ element(sK1(sK25,sK26,sK27),the_carrier(sK26))
| ~ element(X0,the_carrier(sK26)) )
| ~ spl29_29
| ~ spl29_399 ),
inference(resolution,[],[f2428,f453]) ).
fof(f2438,definition,
( spl29_401
<=> ! [X0] :
( in(apply_netmap(sK25,sK26,sK6(sK26,X0,sK1(sK25,sK26,sK27))),sK27)
| ~ element(X0,the_carrier(sK26))
| ~ element(sK6(sK26,X0,sK1(sK25,sK26,sK27)),the_carrier(sK26)) ) ),
introduced(definition,[new_symbols(definition,[spl29_401])],[avatar_definition]) ).
fof(f2439,plain,
( ! [X0] :
( in(apply_netmap(sK25,sK26,sK6(sK26,X0,sK1(sK25,sK26,sK27))),sK27)
| ~ element(X0,the_carrier(sK26))
| ~ element(sK6(sK26,X0,sK1(sK25,sK26,sK27)),the_carrier(sK26)) )
| ~ spl29_401 ),
inference(avatar_component_clause,[],[f2438]) ).
fof(f2440,plain,
( ~ spl29_25
| spl29_401
| ~ spl29_29
| ~ spl29_399 ),
inference(avatar_split_clause,[],[f2430,f2427,f452,f2438,f413]) ).
fof(f2929,plain,
! [X0] :
( ~ element(X0,the_carrier(sK26))
| ~ related(sK26,sK2(sK25,sK26,sK27),X0)
| ~ in(apply_netmap(sK25,sK26,X0),sK27)
| empty_carrier(sK26)
| ~ net_str(sK26,sK25)
| empty_carrier(sK25)
| ~ one_sorted_str(sK25) ),
inference(resolution,[],[f165,f233]) ).
fof(f2937,definition,
( spl29_457
<=> ! [X0] :
( ~ element(X0,the_carrier(sK26))
| ~ in(apply_netmap(sK25,sK26,X0),sK27)
| ~ related(sK26,sK2(sK25,sK26,sK27),X0) ) ),
introduced(definition,[new_symbols(definition,[spl29_457])],[avatar_definition]) ).
fof(f2938,plain,
( ! [X0] :
( ~ related(sK26,sK2(sK25,sK26,sK27),X0)
| ~ in(apply_netmap(sK25,sK26,X0),sK27)
| ~ element(X0,the_carrier(sK26)) )
| ~ spl29_457 ),
inference(avatar_component_clause,[],[f2937]) ).
fof(f2939,plain,
( ~ spl29_2
| spl29_6
| ~ spl29_24
| spl29_4
| spl29_457 ),
inference(avatar_split_clause,[],[f2929,f2937,f302,f410,f309,f264]) ).
fof(f2941,plain,
( ! [X0] :
( ~ in(apply_netmap(sK25,sK26,sK6(sK26,sK2(sK25,sK26,sK27),X0)),sK27)
| ~ element(sK6(sK26,sK2(sK25,sK26,sK27),X0),the_carrier(sK26))
| ~ element(sK2(sK25,sK26,sK27),the_carrier(sK26))
| ~ element(X0,the_carrier(sK26)) )
| ~ spl29_30
| ~ spl29_457 ),
inference(resolution,[],[f2938,f467]) ).
fof(f2944,definition,
( spl29_458
<=> ! [X0] :
( ~ in(apply_netmap(sK25,sK26,sK6(sK26,sK2(sK25,sK26,sK27),X0)),sK27)
| ~ element(X0,the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,sK27),X0),the_carrier(sK26)) ) ),
introduced(definition,[new_symbols(definition,[spl29_458])],[avatar_definition]) ).
fof(f2945,plain,
( ! [X0] :
( ~ in(apply_netmap(sK25,sK26,sK6(sK26,sK2(sK25,sK26,sK27),X0)),sK27)
| ~ element(X0,the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,sK27),X0),the_carrier(sK26)) )
| ~ spl29_458 ),
inference(avatar_component_clause,[],[f2944]) ).
fof(f2946,plain,
( ~ spl29_26
| spl29_458
| ~ spl29_30
| ~ spl29_457 ),
inference(avatar_split_clause,[],[f2941,f2937,f466,f2944,f427]) ).
fof(f2952,plain,
( ~ element(sK1(sK25,sK26,sK27),the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,sK27),sK1(sK25,sK26,sK27)),the_carrier(sK26))
| ~ element(sK2(sK25,sK26,sK27),the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,sK27),sK1(sK25,sK26,sK27)),the_carrier(sK26))
| ~ spl29_401
| ~ spl29_458 ),
inference(resolution,[],[f2945,f2439]) ).
fof(f2954,plain,
( ~ element(sK1(sK25,sK26,sK27),the_carrier(sK26))
| ~ element(sK6(sK26,sK2(sK25,sK26,sK27),sK1(sK25,sK26,sK27)),the_carrier(sK26))
| ~ element(sK2(sK25,sK26,sK27),the_carrier(sK26))
| ~ spl29_401
| ~ spl29_458 ),
inference(duplicate_literal_removal,[],[f2952]) ).
fof(f2961,definition,
( spl29_461
<=> element(sK6(sK26,sK2(sK25,sK26,sK27),sK1(sK25,sK26,sK27)),the_carrier(sK26)) ),
introduced(definition,[new_symbols(definition,[spl29_461])],[avatar_definition]) ).
fof(f2962,plain,
( ~ element(sK6(sK26,sK2(sK25,sK26,sK27),sK1(sK25,sK26,sK27)),the_carrier(sK26))
| spl29_461 ),
inference(avatar_component_clause,[],[f2961]) ).
fof(f2963,plain,
( ~ spl29_26
| ~ spl29_461
| ~ spl29_25
| ~ spl29_401
| ~ spl29_458 ),
inference(avatar_split_clause,[],[f2954,f2944,f2438,f413,f2961,f427]) ).
fof(f3070,plain,
( ~ element(sK2(sK25,sK26,sK27),the_carrier(sK26))
| ~ element(sK1(sK25,sK26,sK27),the_carrier(sK26))
| ~ spl29_57
| spl29_461 ),
inference(resolution,[],[f2962,f610]) ).
fof(f3071,plain,
( ~ spl29_25
| ~ spl29_26
| ~ spl29_57
| spl29_461 ),
inference(avatar_split_clause,[],[f3070,f2961,f609,f427,f413]) ).
cnf(s2,plain,
spl29_2,
inference(sat_conversion,[],[f268]) ).
cnf(s8,plain,
~ spl29_4,
inference(sat_conversion,[],[f334]) ).
cnf(s20,plain,
( ~ spl29_2
| spl29_4
| spl29_6
| ~ spl29_24
| spl29_25 ),
inference(sat_conversion,[],[f415]) ).
cnf(s21,plain,
spl29_24,
inference(sat_conversion,[],[f424]) ).
cnf(s22,plain,
( ~ spl29_2
| spl29_4
| spl29_6
| ~ spl29_24
| spl29_26 ),
inference(sat_conversion,[],[f429]) ).
cnf(s23,plain,
~ spl29_6,
inference(sat_conversion,[],[f431]) ).
cnf(s25,plain,
( spl29_4
| ~ spl29_28
| spl29_29 ),
inference(sat_conversion,[],[f454]) ).
cnf(s26,plain,
( ~ spl29_2
| spl29_28 ),
inference(sat_conversion,[],[f457]) ).
cnf(s27,plain,
( spl29_4
| ~ spl29_28
| spl29_30 ),
inference(sat_conversion,[],[f468]) ).
cnf(s41,plain,
( spl29_4
| ~ spl29_28
| spl29_57 ),
inference(sat_conversion,[],[f611]) ).
cnf(s228,plain,
( ~ spl29_2
| spl29_4
| spl29_6
| ~ spl29_24
| spl29_399 ),
inference(sat_conversion,[],[f2429]) ).
cnf(s230,plain,
( ~ spl29_25
| ~ spl29_29
| ~ spl29_399
| spl29_401 ),
inference(sat_conversion,[],[f2440]) ).
cnf(s263,plain,
( ~ spl29_2
| spl29_4
| spl29_6
| ~ spl29_24
| spl29_457 ),
inference(sat_conversion,[],[f2939]) ).
cnf(s264,plain,
( ~ spl29_26
| ~ spl29_30
| ~ spl29_457
| spl29_458 ),
inference(sat_conversion,[],[f2946]) ).
cnf(s267,plain,
( ~ spl29_25
| ~ spl29_26
| ~ spl29_401
| ~ spl29_458
| ~ spl29_461 ),
inference(sat_conversion,[],[f2963]) ).
cnf(s294,plain,
( ~ spl29_25
| ~ spl29_26
| ~ spl29_57
| spl29_461 ),
inference(sat_conversion,[],[f3071]) ).
cnf(s316,plain,
( ~ spl29_2
| spl29_4
| ~ spl29_24
| spl29_26 ),
inference(rat,[],[s22,s23]) ).
cnf(s317,plain,
( ~ spl29_2
| spl29_4
| spl29_25 ),
inference(rat,[],[s20,s21,s23]) ).
cnf(s326,plain,
spl29_457,
inference(rat,[],[s263,s8,s21,s23,s2]) ).
cnf(s327,plain,
spl29_399,
inference(rat,[],[s228,s8,s21,s23,s2]) ).
cnf(s328,plain,
spl29_28,
inference(rat,[],[s26,s2]) ).
cnf(s330,plain,
spl29_26,
inference(rat,[],[s316,s8,s21,s2]) ).
cnf(s331,plain,
spl29_25,
inference(rat,[],[s317,s8,s2]) ).
cnf(s333,plain,
spl29_57,
inference(rat,[],[s41,s8,s328]) ).
cnf(s334,plain,
spl29_30,
inference(rat,[],[s27,s8,s328]) ).
cnf(s335,plain,
spl29_29,
inference(rat,[],[s25,s8,s328]) ).
cnf(s336,plain,
spl29_461,
inference(rat,[],[s294,s330,s333,s331]) ).
cnf(s359,plain,
spl29_458,
inference(rat,[],[s264,s330,s326,s334]) ).
cnf(s362,plain,
spl29_401,
inference(rat,[],[s230,s331,s327,s335]) ).
cnf(s363,plain,
$false,
inference(rat,[],[s267,s336,s331,s330,s359,s362]) ).
fof(f3072,plain,
$false,
inference(avatar_sat_refutation,[],[s363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU376+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n011.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 : Mon Sep 28 04:59:30 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 2.27/1.19 % (3027415)Detected formulas, will run a generic FOF schedule.
% 2.27/1.19 % (3027426)dis-21_1_sil=8000:lcm=predicate:random_seed=4065112049: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)
% 2.27/1.19 % (3027426)First to succeed.
% 2.27/1.19 % (3027426)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3027415"
% 2.27/1.19 % (3027423)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3094363255:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.27/1.19 % (3027420)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=2022667435:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.27/1.19 % (3027421)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=2802975067:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.27/1.19 % (3027424)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1871270426:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.27/1.19 % (3027425)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1597150267:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.27/1.19 % (3027422)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=4069940783:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.27/1.19 % (3027423)Refutation not found, incomplete strategy
% 2.27/1.19 % (3027423)------------------------------
% 2.27/1.19 % (3027423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.27/1.19 % (3027423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/1.19 % (3027423)CaDiCaL version: 2.1.3
% 2.27/1.19 % (3027423)Termination reason: Refutation not found, incomplete strategy
% 2.27/1.19 % (3027423)Time elapsed: 0.003 s
% 2.27/1.19 % (3027423)Peak memory usage: 88 MB
% 2.27/1.19 % (3027423)Instructions burned: 2 (million)
% 2.27/1.19 % (3027425)Also succeeded, but the first one will report.
% 2.27/1.19 % (3027424)Also succeeded, but the first one will report.
% 2.27/1.19 % (3027426)Refutation found. Thanks to Tanya!
% 2.27/1.19 % SZS status Theorem for theBenchmark
% 2.27/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.29 % (3027426)------------------------------
% 2.69/1.29 % (3027426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.29 % (3027426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.29 % (3027426)CaDiCaL version: 2.1.3
% 2.69/1.29 % (3027426)Termination reason: Refutation
% 2.69/1.29 % (3027426)Time elapsed: 0.022 s
% 2.69/1.29 % (3027426)Peak memory usage: 91 MB
% 2.69/1.29 % (3027426)Instructions burned: 63 (million)
% 2.69/1.29 % (3027426)------------------------------
% 2.69/1.29 % (3027426)------------------------------
% 2.69/1.29 % (3027415)Success in time 0.324 s
% 2.69/1.29 % Vampire exiting
%------------------------------------------------------------------------------