%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU168+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:52:13 PM UTC 2026
% Result : Theorem 1.41s 0.67s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 156 ( 8 unt; 7 def)
% Number of atoms : 530 ( 2 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 657 ( 283 ~; 300 |; 52 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 107 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,conjecture,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2] :
~ ( subset(X2,X1)
& ~ are_equipotent(X2,X1)
& ~ in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2] :
~ ( subset(X2,X1)
& ~ are_equipotent(X2,X1)
& ~ in(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
( subset(X4,X2)
=> in(X4,X3) ) ) )
& ! [X2] :
~ ( subset(X2,X1)
& ~ are_equipotent(X2,X1)
& ~ in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
fof(f10,plain,
~ ! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X4] :
( in(X4,X1)
=> in(powerset(X4),X1) )
& ! [X5] :
~ ( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) ) ),
inference(rectify,[],[f7]) ).
fof(f11,plain,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X4] :
~ ( in(X4,X1)
& ! [X5] :
~ ( in(X5,X1)
& ! [X6] :
( subset(X6,X4)
=> in(X6,X5) ) ) )
& ! [X7] :
~ ( subset(X7,X1)
& ~ are_equipotent(X7,X1)
& ~ in(X7,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f14,plain,
? [X0] :
! [X1] :
( ~ in(X0,X1)
| ? [X2,X3] :
( ~ in(X3,X1)
& in(X2,X1)
& subset(X3,X2) )
| ? [X4] :
( ~ in(powerset(X4),X1)
& in(X4,X1) )
| ? [X5] :
( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f15,plain,
? [X0] :
! [X1] :
( ~ in(X0,X1)
| ? [X2,X3] :
( ~ in(X3,X1)
& in(X2,X1)
& subset(X3,X2) )
| ? [X4] :
( ~ in(powerset(X4),X1)
& in(X4,X1) )
| ? [X5] :
( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( in(X3,X1)
| ~ in(X2,X1)
| ~ subset(X3,X2) )
& ! [X4] :
( ~ in(X4,X1)
| ? [X5] :
( in(X5,X1)
& ! [X6] :
( in(X6,X5)
| ~ subset(X6,X4) ) ) )
& ! [X7] :
( ~ subset(X7,X1)
| are_equipotent(X7,X1)
| in(X7,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( in(X3,X1)
| ~ in(X2,X1)
| ~ subset(X3,X2) )
& ! [X4] :
( ~ in(X4,X1)
| ? [X5] :
( in(X5,X1)
& ! [X6] :
( in(X6,X5)
| ~ subset(X6,X4) ) ) )
& ! [X7] :
( ~ subset(X7,X1)
| are_equipotent(X7,X1)
| in(X7,X1) ) ),
inference(flattening,[],[f16]) ).
fof(f20,plain,
! [X2,X0,X1] :
( subset(X2,X0)
| ~ in(X2,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| ~ in(sK3(X1),X1)
| subset(sK6(X1),sK5(X1))
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| ~ in(sK3(X1),X1)
| in(sK5(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| ~ in(sK3(X1),X1)
| ~ in(sK6(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X1] :
( subset(sK6(X1),sK5(X1))
| in(sK4(X1),X1)
| ~ in(sK3(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X1] :
( ~ in(sK3(X1),X1)
| in(sK4(X1),X1)
| in(sK5(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X1] :
( ~ in(sK6(X1),X1)
| in(sK4(X1),X1)
| ~ in(sK3(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f33,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| ~ are_equipotent(sK3(X1),X1)
| subset(sK6(X1),sK5(X1))
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| ~ are_equipotent(sK3(X1),X1)
| in(sK5(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| ~ are_equipotent(sK3(X1),X1)
| ~ in(sK6(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X1] :
( subset(sK6(X1),sK5(X1))
| in(sK4(X1),X1)
| ~ are_equipotent(sK3(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X1] :
( ~ are_equipotent(sK3(X1),X1)
| in(sK4(X1),X1)
| in(sK5(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X1] :
( ~ are_equipotent(sK3(X1),X1)
| in(sK4(X1),X1)
| ~ in(sK6(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| subset(sK3(X1),X1)
| subset(sK6(X1),sK5(X1))
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| subset(sK3(X1),X1)
| in(sK5(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f41,plain,
! [X1] :
( ~ in(powerset(sK4(X1)),X1)
| subset(sK3(X1),X1)
| ~ in(sK6(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f42,plain,
! [X1] :
( subset(sK6(X1),sK5(X1))
| in(sK4(X1),X1)
| subset(sK3(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f43,plain,
! [X1] :
( subset(sK3(X1),X1)
| in(sK4(X1),X1)
| in(sK5(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f44,plain,
! [X1] :
( ~ in(sK6(X1),X1)
| in(sK4(X1),X1)
| subset(sK3(X1),X1)
| ~ in(sK2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X6,X4] :
( ~ in(X4,sK7(X0))
| in(X6,sK8(X0,X4))
| ~ subset(X6,X4) ),
inference(cnf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0,X4] :
( in(sK8(X0,X4),sK7(X0))
| ~ in(X4,sK7(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f47,plain,
! [X2,X3,X0] :
( ~ in(X2,sK7(X0))
| ~ subset(X3,X2)
| in(X3,sK7(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0,X7] :
( are_equipotent(X7,sK7(X0))
| in(X7,sK7(X0))
| ~ subset(X7,sK7(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f49,plain,
! [X0] : in(X0,sK7(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f50,plain,
! [X2,X0] :
( ~ in(X2,powerset(X0))
| subset(X2,X0) ),
inference(equality_resolution,[],[f20]) ).
fof(f76,plain,
! [X0,X1] :
( subset(sK1(powerset(X0),X1),X0)
| subset(powerset(X0),X1) ),
inference(resolution,[],[f24,f50]) ).
fof(f101,definition,
( spl9_2
<=> in(sK5(sK7(sK2)),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f103,plain,
( in(sK5(sK7(sK2)),sK7(sK2))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl9_3
<=> in(sK4(sK7(sK2)),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f106,plain,
( ~ in(sK4(sK7(sK2)),sK7(sK2))
| spl9_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f107,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK8(X1,X2))
| in(X0,sK7(X1))
| ~ in(X2,sK7(X1)) ),
inference(resolution,[],[f47,f46]) ).
fof(f261,plain,
( ! [X0] :
( ~ subset(X0,sK5(sK7(sK2)))
| in(X0,sK7(sK2)) )
| ~ spl9_2 ),
inference(resolution,[],[f103,f47]) ).
fof(f269,plain,
( in(sK6(sK7(sK2)),sK7(sK2))
| in(sK4(sK7(sK2)),sK7(sK2))
| ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_2 ),
inference(resolution,[],[f261,f36]) ).
fof(f270,plain,
( in(sK6(sK7(sK2)),sK7(sK2))
| in(sK4(sK7(sK2)),sK7(sK2))
| ~ in(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_2 ),
inference(resolution,[],[f261,f30]) ).
fof(f271,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| ~ in(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f270,f32]) ).
fof(f272,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f269,f38]) ).
fof(f290,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| ~ in(sK3(sK7(sK2)),sK7(sK2))
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f271,f49]) ).
fof(f291,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f272,f49]) ).
fof(f293,definition,
( spl9_20
<=> in(sK3(sK7(sK2)),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_20])],[avatar_definition]) ).
fof(f295,plain,
( ~ in(sK3(sK7(sK2)),sK7(sK2))
| spl9_20 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f296,plain,
( ~ spl9_20
| spl9_3
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f290,f101,f105,f293]) ).
fof(f298,definition,
( spl9_21
<=> are_equipotent(sK3(sK7(sK2)),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_21])],[avatar_definition]) ).
fof(f300,plain,
( ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| spl9_21 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,plain,
( ~ spl9_21
| spl9_3
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f291,f101,f105,f298]) ).
fof(f435,plain,
( ! [X0] :
( ~ subset(X0,sK4(sK7(sK2)))
| in(X0,sK8(sK2,sK4(sK7(sK2)))) )
| ~ spl9_3 ),
inference(resolution,[],[f45,f107]) ).
fof(f461,plain,
( ! [X0] :
( in(sK1(powerset(sK4(sK7(sK2))),X0),sK8(sK2,sK4(sK7(sK2))))
| subset(powerset(sK4(sK7(sK2))),X0) )
| ~ spl9_3 ),
inference(resolution,[],[f435,f76]) ).
fof(f492,plain,
! [X0] :
( in(sK3(sK7(X0)),sK7(X0))
| ~ subset(sK3(sK7(X0)),sK7(X0))
| in(sK4(sK7(X0)),sK7(X0))
| ~ in(sK6(sK7(X0)),sK7(X0))
| ~ in(sK2,sK7(X0)) ),
inference(resolution,[],[f48,f38]) ).
fof(f493,plain,
! [X0] :
( in(sK3(sK7(X0)),sK7(X0))
| ~ subset(sK3(sK7(X0)),sK7(X0))
| in(sK4(sK7(X0)),sK7(X0))
| in(sK5(sK7(X0)),sK7(X0))
| ~ in(sK2,sK7(X0)) ),
inference(resolution,[],[f48,f37]) ).
fof(f494,plain,
! [X0] :
( in(sK3(sK7(X0)),sK7(X0))
| in(sK4(sK7(X0)),sK7(X0))
| in(sK5(sK7(X0)),sK7(X0))
| ~ in(sK2,sK7(X0)) ),
inference(forward_subsumption_resolution,[],[f493,f43]) ).
fof(f495,plain,
! [X0] :
( in(sK3(sK7(X0)),sK7(X0))
| in(sK4(sK7(X0)),sK7(X0))
| ~ in(sK6(sK7(X0)),sK7(X0))
| ~ in(sK2,sK7(X0)) ),
inference(forward_subsumption_resolution,[],[f492,f44]) ).
fof(f497,plain,
! [X0] :
( ~ in(sK2,sK7(X0))
| in(sK5(sK7(X0)),sK7(X0))
| in(sK4(sK7(X0)),sK7(X0)) ),
inference(forward_subsumption_resolution,[],[f494,f31]) ).
fof(f498,plain,
! [X0] :
( ~ in(sK6(sK7(X0)),sK7(X0))
| in(sK4(sK7(X0)),sK7(X0))
| ~ in(sK2,sK7(X0)) ),
inference(forward_subsumption_resolution,[],[f495,f32]) ).
fof(f500,plain,
( in(sK5(sK7(sK2)),sK7(sK2))
| in(sK4(sK7(sK2)),sK7(sK2)) ),
inference(resolution,[],[f497,f49]) ).
fof(f2170,plain,
( subset(powerset(sK4(sK7(sK2))),sK8(sK2,sK4(sK7(sK2))))
| subset(powerset(sK4(sK7(sK2))),sK8(sK2,sK4(sK7(sK2))))
| ~ spl9_3 ),
inference(resolution,[],[f461,f25]) ).
fof(f2172,plain,
( subset(powerset(sK4(sK7(sK2))),sK8(sK2,sK4(sK7(sK2))))
| ~ spl9_3 ),
inference(duplicate_literal_removal,[],[f2170]) ).
fof(f2174,plain,
( in(powerset(sK4(sK7(sK2))),sK7(sK2))
| ~ in(sK4(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2172,f144]) ).
fof(f2179,plain,
( in(powerset(sK4(sK7(sK2))),sK7(sK2))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2174,f107]) ).
fof(f2183,plain,
( ~ in(sK3(sK7(sK2)),sK7(sK2))
| subset(sK6(sK7(sK2)),sK5(sK7(sK2)))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f27]) ).
fof(f2184,plain,
( ~ in(sK3(sK7(sK2)),sK7(sK2))
| in(sK5(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f28]) ).
fof(f2185,plain,
( ~ in(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK6(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f29]) ).
fof(f2186,plain,
( ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| subset(sK6(sK7(sK2)),sK5(sK7(sK2)))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f33]) ).
fof(f2187,plain,
( ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| in(sK5(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f34]) ).
fof(f2188,plain,
( ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK6(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f35]) ).
fof(f2189,plain,
( subset(sK3(sK7(sK2)),sK7(sK2))
| subset(sK6(sK7(sK2)),sK5(sK7(sK2)))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f39]) ).
fof(f2190,plain,
( subset(sK3(sK7(sK2)),sK7(sK2))
| in(sK5(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2179,f40]) ).
fof(f2194,plain,
( ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK6(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2188,f49]) ).
fof(f2195,plain,
( ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| subset(sK6(sK7(sK2)),sK5(sK7(sK2)))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2186,f49]) ).
fof(f2196,plain,
( ~ in(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK6(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2185,f49]) ).
fof(f2197,plain,
( ~ in(sK3(sK7(sK2)),sK7(sK2))
| subset(sK6(sK7(sK2)),sK5(sK7(sK2)))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2183,f49]) ).
fof(f2199,definition,
( spl9_224
<=> in(sK6(sK7(sK2)),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_224])],[avatar_definition]) ).
fof(f2200,plain,
( in(sK6(sK7(sK2)),sK7(sK2))
| ~ spl9_224 ),
inference(avatar_component_clause,[],[f2199]) ).
fof(f2201,plain,
( ~ in(sK6(sK7(sK2)),sK7(sK2))
| spl9_224 ),
inference(avatar_component_clause,[],[f2199]) ).
fof(f2202,plain,
( ~ spl9_224
| ~ spl9_21
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2194,f105,f298,f2199]) ).
fof(f2204,definition,
( spl9_225
<=> subset(sK6(sK7(sK2)),sK5(sK7(sK2))) ),
introduced(definition,[new_symbols(definition,[spl9_225])],[avatar_definition]) ).
fof(f2206,plain,
( subset(sK6(sK7(sK2)),sK5(sK7(sK2)))
| ~ spl9_225 ),
inference(avatar_component_clause,[],[f2204]) ).
fof(f2207,plain,
( spl9_225
| ~ spl9_21
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2195,f105,f298,f2204]) ).
fof(f2208,plain,
( ~ spl9_224
| ~ spl9_20
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2196,f105,f293,f2199]) ).
fof(f2209,plain,
( spl9_225
| ~ spl9_20
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2197,f105,f293,f2204]) ).
fof(f2212,plain,
( in(sK6(sK7(sK2)),sK7(sK2))
| ~ spl9_2
| ~ spl9_225 ),
inference(resolution,[],[f2206,f261]) ).
fof(f2216,plain,
( $false
| ~ spl9_2
| spl9_224
| ~ spl9_225 ),
inference(forward_subsumption_resolution,[],[f2212,f2201]) ).
fof(f2217,plain,
( ~ spl9_2
| spl9_224
| ~ spl9_225 ),
inference(avatar_contradiction_clause,[],[f2216]) ).
fof(f2229,plain,
( ~ are_equipotent(sK3(sK7(sK2)),sK7(sK2))
| in(sK5(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2187,f49]) ).
fof(f2230,plain,
( ~ in(sK3(sK7(sK2)),sK7(sK2))
| in(sK5(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2184,f49]) ).
fof(f2231,plain,
( subset(sK3(sK7(sK2)),sK7(sK2))
| in(sK5(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2190,f49]) ).
fof(f2232,plain,
( subset(sK3(sK7(sK2)),sK7(sK2))
| subset(sK6(sK7(sK2)),sK5(sK7(sK2)))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2189,f49]) ).
fof(f2233,plain,
( spl9_2
| ~ spl9_21
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2229,f105,f298,f101]) ).
fof(f2234,plain,
( spl9_2
| ~ spl9_20
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2230,f105,f293,f101]) ).
fof(f2236,definition,
( spl9_228
<=> subset(sK3(sK7(sK2)),sK7(sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_228])],[avatar_definition]) ).
fof(f2237,plain,
( ~ subset(sK3(sK7(sK2)),sK7(sK2))
| spl9_228 ),
inference(avatar_component_clause,[],[f2236]) ).
fof(f2238,plain,
( subset(sK3(sK7(sK2)),sK7(sK2))
| ~ spl9_228 ),
inference(avatar_component_clause,[],[f2236]) ).
fof(f2239,plain,
( spl9_2
| spl9_228
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2231,f105,f2236,f101]) ).
fof(f2240,plain,
( spl9_225
| spl9_228
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f2232,f105,f2236,f2204]) ).
fof(f2246,plain,
( in(sK3(sK7(sK2)),sK7(sK2))
| ~ subset(sK3(sK7(sK2)),sK7(sK2))
| spl9_21 ),
inference(resolution,[],[f300,f48]) ).
fof(f2247,plain,
( ~ subset(sK3(sK7(sK2)),sK7(sK2))
| spl9_20
| spl9_21 ),
inference(forward_subsumption_resolution,[],[f2246,f295]) ).
fof(f2258,plain,
( $false
| spl9_20
| spl9_21
| ~ spl9_228 ),
inference(forward_subsumption_resolution,[],[f2247,f2238]) ).
fof(f2259,plain,
( spl9_20
| spl9_21
| ~ spl9_228 ),
inference(avatar_contradiction_clause,[],[f2258]) ).
fof(f2274,plain,
( spl9_3
| spl9_2 ),
inference(avatar_split_clause,[],[f500,f101,f105]) ).
fof(f2279,plain,
( ! [X0] :
( ~ subset(X0,sK5(sK7(sK2)))
| in(X0,sK7(sK2)) )
| ~ spl9_2 ),
inference(resolution,[],[f103,f47]) ).
fof(f2281,plain,
( ! [X0] :
( ~ subset(X0,sK4(sK7(sK2)))
| in(X0,sK8(sK2,sK4(sK7(sK2)))) )
| ~ spl9_3 ),
inference(resolution,[],[f107,f45]) ).
fof(f2320,plain,
( in(sK6(sK7(sK2)),sK7(sK2))
| in(sK4(sK7(sK2)),sK7(sK2))
| subset(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_2 ),
inference(resolution,[],[f2279,f42]) ).
fof(f2387,plain,
( ! [X0] :
( in(sK1(powerset(sK4(sK7(sK2))),X0),sK8(sK2,sK4(sK7(sK2))))
| subset(powerset(sK4(sK7(sK2))),X0) )
| ~ spl9_3 ),
inference(resolution,[],[f2281,f76]) ).
fof(f2778,plain,
( subset(powerset(sK4(sK7(sK2))),sK8(sK2,sK4(sK7(sK2))))
| subset(powerset(sK4(sK7(sK2))),sK8(sK2,sK4(sK7(sK2))))
| ~ spl9_3 ),
inference(resolution,[],[f2387,f25]) ).
fof(f2780,plain,
( subset(powerset(sK4(sK7(sK2))),sK8(sK2,sK4(sK7(sK2))))
| ~ spl9_3 ),
inference(duplicate_literal_removal,[],[f2778]) ).
fof(f2782,plain,
( in(powerset(sK4(sK7(sK2))),sK7(sK2))
| ~ in(sK4(sK7(sK2)),sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2780,f144]) ).
fof(f2787,plain,
( in(powerset(sK4(sK7(sK2))),sK7(sK2))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f2782,f107]) ).
fof(f2799,plain,
( subset(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK6(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3 ),
inference(resolution,[],[f2787,f41]) ).
fof(f2802,plain,
( ~ in(sK6(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_3
| spl9_228 ),
inference(forward_subsumption_resolution,[],[f2799,f2237]) ).
fof(f2803,plain,
( ~ in(sK2,sK7(sK2))
| ~ spl9_3
| ~ spl9_224
| spl9_228 ),
inference(forward_subsumption_resolution,[],[f2802,f2200]) ).
fof(f2804,plain,
( $false
| ~ spl9_3
| ~ spl9_224
| spl9_228 ),
inference(forward_subsumption_resolution,[],[f2803,f49]) ).
fof(f2805,plain,
( ~ spl9_3
| ~ spl9_224
| spl9_228 ),
inference(avatar_contradiction_clause,[],[f2804]) ).
fof(f2808,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| subset(sK3(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f2320,f498]) ).
fof(f2814,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| ~ in(sK2,sK7(sK2))
| ~ spl9_2
| spl9_228 ),
inference(forward_subsumption_resolution,[],[f2808,f2237]) ).
fof(f2816,plain,
( in(sK4(sK7(sK2)),sK7(sK2))
| ~ spl9_2
| spl9_228 ),
inference(forward_subsumption_resolution,[],[f2814,f49]) ).
fof(f2905,plain,
( $false
| ~ spl9_2
| spl9_3
| spl9_228 ),
inference(forward_subsumption_resolution,[],[f2816,f106]) ).
fof(f2906,plain,
( ~ spl9_2
| spl9_3
| spl9_228 ),
inference(avatar_contradiction_clause,[],[f2905]) ).
cnf(s7,plain,
( ~ spl9_2
| spl9_3
| ~ spl9_20 ),
inference(sat_conversion,[],[f296]) ).
cnf(s8,plain,
( ~ spl9_2
| spl9_3
| ~ spl9_21 ),
inference(sat_conversion,[],[f301]) ).
cnf(s103,plain,
( ~ spl9_3
| ~ spl9_21
| ~ spl9_224 ),
inference(sat_conversion,[],[f2202]) ).
cnf(s104,plain,
( ~ spl9_3
| ~ spl9_21
| spl9_225 ),
inference(sat_conversion,[],[f2207]) ).
cnf(s105,plain,
( ~ spl9_3
| ~ spl9_20
| ~ spl9_224 ),
inference(sat_conversion,[],[f2208]) ).
cnf(s106,plain,
( ~ spl9_3
| ~ spl9_20
| spl9_225 ),
inference(sat_conversion,[],[f2209]) ).
cnf(s107,plain,
( ~ spl9_2
| spl9_224
| ~ spl9_225 ),
inference(sat_conversion,[],[f2217]) ).
cnf(s111,plain,
( spl9_2
| ~ spl9_3
| ~ spl9_21 ),
inference(sat_conversion,[],[f2233]) ).
cnf(s112,plain,
( spl9_2
| ~ spl9_3
| ~ spl9_20 ),
inference(sat_conversion,[],[f2234]) ).
cnf(s113,plain,
( spl9_2
| ~ spl9_3
| spl9_228 ),
inference(sat_conversion,[],[f2239]) ).
cnf(s114,plain,
( ~ spl9_3
| spl9_225
| spl9_228 ),
inference(sat_conversion,[],[f2240]) ).
cnf(s115,plain,
( spl9_20
| spl9_21
| ~ spl9_228 ),
inference(sat_conversion,[],[f2259]) ).
cnf(s119,plain,
( spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f2274]) ).
cnf(s127,plain,
( ~ spl9_3
| ~ spl9_224
| spl9_228 ),
inference(sat_conversion,[],[f2805]) ).
cnf(s154,plain,
( ~ spl9_2
| spl9_3
| spl9_228 ),
inference(sat_conversion,[],[f2906]) ).
cnf(s155,plain,
( spl9_2
| ~ spl9_3 ),
inference(rat,[],[s115,s111,s112,s113]) ).
cnf(s156,plain,
spl9_2,
inference(rat,[],[s155,s119]) ).
cnf(s157,plain,
( spl9_228
| ~ spl9_3 ),
inference(rat,[],[s107,s114,s127,s156]) ).
cnf(s158,plain,
( ~ spl9_21
| ~ spl9_3 ),
inference(rat,[],[s107,s103,s104,s156]) ).
cnf(s159,plain,
( ~ spl9_20
| ~ spl9_3 ),
inference(rat,[],[s107,s105,s106,s156]) ).
cnf(s160,plain,
~ spl9_3,
inference(rat,[],[s159,s115,s158,s157]) ).
cnf(s161,plain,
spl9_228,
inference(rat,[],[s154,s156,s160]) ).
cnf(s164,plain,
~ spl9_21,
inference(rat,[],[s8,s156,s160]) ).
cnf(s165,plain,
~ spl9_20,
inference(rat,[],[s7,s156,s160]) ).
cnf(s167,plain,
$false,
inference(rat,[],[s115,s161,s165,s164]) ).
fof(f2907,plain,
$false,
inference(avatar_sat_refutation,[],[s167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU168+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:58:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.41/0.67 % (756)Will run a generic schedule for satisfiability detection.
% 1.41/0.67 % (765)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2704999386:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.41/0.67 % (762)% WARNING: option uhcvi not known.
% 1.41/0.67 % (761)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4095302589_2999 on theBenchmark for (2999ds/0Mi)
% 1.41/0.67 % (762)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1831034607:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.41/0.67 % (763)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3725052432:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.41/0.67 % (764)dis+10_1_sil=32000:sp=arity:random_seed=3442296386:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.41/0.67 % (767)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3306960220:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.41/0.67 % (766)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3197373481:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.41/0.67 % TRYING [1]
% 1.41/0.67 % TRYING [2]
% 1.41/0.67 % TRYING [3]
% 1.41/0.67 % TRYING [4]
% 1.41/0.67 % TRYING [5]
% 1.41/0.67 % TRYING [6]
% 1.41/0.67 % (765)Instruction limit reached!
% 1.41/0.67 % (765)------------------------------
% 1.41/0.67 % (765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.67 % (765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.67 % (765)CaDiCaL version: 2.1.3
% 1.41/0.67 % (765)Termination reason: Instruction limit
% 1.41/0.67 % (765)Termination phase: Saturation
% 1.41/0.67 % (765)Time elapsed: 0.034 s
% 1.41/0.67 % (765)Peak memory usage: 12 MB
% 1.41/0.67 % (765)Instructions burned: 117 (million)
% 1.41/0.67 % TRYING [7]
% 1.41/0.67 % (775)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1842819102:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.41/0.67 % TRYING [1]
% 1.41/0.67 % TRYING [2]
% 1.41/0.67 % TRYING [3]
% 1.41/0.67 % TRYING [4]
% 1.41/0.67 % TRYING [5]
% 1.41/0.67 % TRYING [6]
% 1.41/0.67 % (764)Instruction limit reached!
% 1.41/0.67 % (764)------------------------------
% 1.41/0.67 % (764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.67 % (764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.67 % (764)CaDiCaL version: 2.1.3
% 1.41/0.67 % (764)Termination reason: Instruction limit
% 1.41/0.67 % (764)Termination phase: Saturation
% 1.41/0.67 % (764)Time elapsed: 0.062 s
% 1.41/0.67 % (764)Peak memory usage: 12 MB
% 1.41/0.67 % (764)Instructions burned: 103 (million)
% 1.41/0.67 % TRYING [8]
% 1.41/0.67 % TRYING [7]
% 1.41/0.67 % (777)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1194424905:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.41/0.67 % (766)Instruction limit reached!
% 1.41/0.67 % (766)------------------------------
% 1.41/0.67 % (766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.67 % (766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.67 % (766)CaDiCaL version: 2.1.3
% 1.41/0.67 % (766)Termination reason: Instruction limit
% 1.41/0.67 % (766)Termination phase: Saturation
% 1.41/0.67 % (766)Time elapsed: 0.083 s
% 1.41/0.67 % (766)Peak memory usage: 12 MB
% 1.41/0.67 % (766)Instructions burned: 132 (million)
% 1.41/0.67 % (779)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=127547404:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.41/0.67 % (767)Instruction limit reached!
% 1.41/0.67 % (767)------------------------------
% 1.41/0.67 % (767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.67 % (767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.67 % (767)CaDiCaL version: 2.1.3
% 1.41/0.67 % (767)Termination reason: Instruction limit
% 1.41/0.67 % (767)Termination phase: Saturation
% 1.41/0.67 % (767)Time elapsed: 0.109 s
% 1.41/0.67 % (767)Peak memory usage: 15 MB
% 1.41/0.67 % (767)Instructions burned: 160 (million)
% 1.41/0.67 % (781)ott-21_1_sil=16000:fs=off:random_seed=2272023123:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.41/0.67 % (777)Instruction limit reached!
% 1.41/0.67 % (777)------------------------------
% 1.41/0.67 % (777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.67 % (777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.67 % (777)CaDiCaL version: 2.1.3
% 1.41/0.67 % (777)Termination reason: Instruction limit
% 1.41/0.67 % (777)Termination phase: Saturation
% 1.41/0.67 % (777)Time elapsed: 0.084 s
% 1.41/0.67 % (777)Peak memory usage: 13 MB
% 1.41/0.67 % (777)Instructions burned: 132 (million)
% 1.41/0.67 % (783)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2248889703:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.41/0.67 % TRYING [9]
% 1.41/0.67 % (779) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-756-779"...
% 1.41/0.67 % (779)...printing done.
% 1.41/0.67 % (779)Refutation found. Thanks to Tanya!
% 1.41/0.67 % SZS status Theorem for theBenchmark
% 1.41/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.67 % (779)------------------------------
% 1.41/0.67 % (779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.67 % (779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.67 % (779)CaDiCaL version: 2.1.3
% 1.41/0.67 % (779)Termination reason: Refutation
% 1.41/0.67 % (779)Time elapsed: 0.096 s
% 1.41/0.67 % (779)Peak memory usage: 14 MB
% 1.41/0.67 % (779)Instructions burned: 149 (million)
% 1.41/0.67 % (756)Success in time 0.244 s
% 1.41/0.67 % Vampire exiting
%------------------------------------------------------------------------------