%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:47:33 PM UTC 2026
% Result : Theorem 9.87s 2.25s
% Output : Refutation 10.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 96 ( 8 unt; 5 def)
% Number of atoms : 366 ( 8 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 442 ( 172 ~; 166 |; 85 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 128 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f8,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)],[f7]) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f11,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,[],[f8]) ).
fof(f12,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,[],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
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(ennf_transformation,[],[f11]) ).
fof(f16,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,[],[f15]) ).
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(ennf_transformation,[],[f12]) ).
fof(f18,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,[],[f17]) ).
fof(f19,definition,
! [X1] :
( ? [X5] :
( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) )
| ~ sP0(X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f20,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) )
| sP0(X1) ),
inference(definition_folding,[],[f16,f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( subset(sK1(X0,X1),X0)
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f25]) ).
fof(f29,plain,
! [X1] :
( ? [X5] :
( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( subset(X1,X0)
& ~ are_equipotent(X1,X0)
& ~ in(X1,X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ( subset(sK5(X0),X0)
& ~ are_equipotent(sK5(X0),X0)
& ~ in(sK5(X0),X0) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f30]) ).
fof(f32,plain,
! [X1] :
( ~ in(sK6,X1)
| ( ~ in(sK8(X1),X1)
& in(sK7(X1),X1)
& subset(sK8(X1),sK7(X1)) )
| ( ~ in(powerset(sK9(X1)),X1)
& in(sK9(X1),X1) )
| sP0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X2,sK7(X1)),skolemize(X3,sK8(X1)),skolemize(X4,sK9(X1))],[f20]) ).
fof(f33,plain,
! [X0] :
( in(X0,sK10(X0))
& ! [X2,X3] :
( in(X3,sK10(X0))
| ~ in(X2,sK10(X0))
| ~ subset(X3,X2) )
& ! [X4] :
( ~ in(X4,sK10(X0))
| ( in(sK11(X0,X4),sK10(X0))
& ! [X6] :
( in(X6,sK11(X0,X4))
| ~ subset(X6,X4) ) ) )
& ! [X7] :
( ~ subset(X7,sK10(X0))
| are_equipotent(X7,sK10(X0))
| in(X7,sK10(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X1,sK10(X0)),skolemize(X5,sK11(X0,X4))],[f18]) ).
fof(f35,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X0] :
( ~ sP0(X0)
| ~ in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
! [X0] :
( ~ sP0(X0)
| ~ are_equipotent(sK5(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0] :
( ~ sP0(X0)
| subset(sK5(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X1] :
( ~ in(sK6,X1)
| subset(sK8(X1),sK7(X1))
| in(sK9(X1),X1)
| sP0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X1] :
( ~ in(sK6,X1)
| subset(sK8(X1),sK7(X1))
| ~ in(powerset(sK9(X1)),X1)
| sP0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X1] :
( in(sK7(X1),X1)
| ~ in(sK6,X1)
| in(sK9(X1),X1)
| sP0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X1] :
( ~ in(sK6,X1)
| in(sK7(X1),X1)
| ~ in(powerset(sK9(X1)),X1)
| sP0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X1] :
( ~ in(sK8(X1),X1)
| ~ in(sK6,X1)
| in(sK9(X1),X1)
| sP0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f53,plain,
! [X1] :
( ~ in(sK8(X1),X1)
| ~ in(sK6,X1)
| ~ in(powerset(sK9(X1)),X1)
| sP0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f54,plain,
! [X0,X7] :
( ~ subset(X7,sK10(X0))
| are_equipotent(X7,sK10(X0))
| in(X7,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X6,X4] :
( ~ subset(X6,X4)
| in(X6,sK11(X0,X4))
| ~ in(X4,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X4] :
( in(sK11(X0,X4),sK10(X0))
| ~ in(X4,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK10(X0))
| in(X3,sK10(X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f58,plain,
! [X0] : in(X0,sK10(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f35]) ).
fof(f63,plain,
! [X0,X1] :
( subset(sK2(powerset(X0),X1),X0)
| subset(powerset(X0),X1) ),
inference(resolution,[],[f60,f40]) ).
fof(f65,plain,
( subset(sK8(sK10(sK6)),sK7(sK10(sK6)))
| in(sK9(sK10(sK6)),sK10(sK6))
| sP0(sK10(sK6)) ),
inference(resolution,[],[f58,f48]) ).
fof(f66,plain,
( subset(sK8(sK10(sK6)),sK7(sK10(sK6)))
| ~ in(powerset(sK9(sK10(sK6))),sK10(sK6))
| sP0(sK10(sK6)) ),
inference(resolution,[],[f58,f49]) ).
fof(f69,definition,
( spl12_1
<=> sP0(sK10(sK6)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f70,plain,
( sP0(sK10(sK6))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl12_2
<=> in(powerset(sK9(sK10(sK6))),sK10(sK6)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f73,plain,
( ~ in(powerset(sK9(sK10(sK6))),sK10(sK6))
| spl12_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f79,definition,
( spl12_4
<=> subset(sK8(sK10(sK6)),sK7(sK10(sK6))) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f80,plain,
( subset(sK8(sK10(sK6)),sK7(sK10(sK6)))
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( spl12_1
| ~ spl12_2
| spl12_4 ),
inference(avatar_split_clause,[],[f66,f79,f72,f69]) ).
fof(f83,definition,
( spl12_5
<=> in(sK9(sK10(sK6)),sK10(sK6)) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f84,plain,
( in(sK9(sK10(sK6)),sK10(sK6))
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( spl12_1
| spl12_5
| spl12_4 ),
inference(avatar_split_clause,[],[f65,f79,f83,f69]) ).
fof(f88,plain,
( ! [X0] :
( in(sK8(sK10(sK6)),sK10(X0))
| ~ in(sK7(sK10(sK6)),sK10(X0)) )
| ~ spl12_4 ),
inference(resolution,[],[f80,f57]) ).
fof(f93,plain,
! [X2,X0,X1] :
( in(sK2(powerset(X0),X1),sK11(X2,X0))
| subset(powerset(X0),X1)
| ~ in(X0,sK10(X2)) ),
inference(resolution,[],[f63,f55]) ).
fof(f126,plain,
( ~ in(sK7(sK10(sK6)),sK10(sK6))
| ~ in(sK6,sK10(sK6))
| in(sK9(sK10(sK6)),sK10(sK6))
| sP0(sK10(sK6))
| ~ spl12_4 ),
inference(resolution,[],[f88,f52]) ).
fof(f127,plain,
( ~ in(sK7(sK10(sK6)),sK10(sK6))
| ~ in(sK6,sK10(sK6))
| ~ in(powerset(sK9(sK10(sK6))),sK10(sK6))
| sP0(sK10(sK6))
| ~ spl12_4 ),
inference(resolution,[],[f88,f53]) ).
fof(f128,plain,
( ~ in(sK6,sK10(sK6))
| in(sK9(sK10(sK6)),sK10(sK6))
| sP0(sK10(sK6))
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f126,f50]) ).
fof(f129,plain,
( in(sK9(sK10(sK6)),sK10(sK6))
| sP0(sK10(sK6))
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f128,f58]) ).
fof(f130,plain,
( spl12_1
| spl12_5
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f129,f79,f83,f69]) ).
fof(f134,plain,
! [X0,X1] :
( subset(powerset(X0),sK11(X1,X0))
| ~ in(X0,sK10(X1))
| subset(powerset(X0),sK11(X1,X0)) ),
inference(resolution,[],[f93,f41]) ).
fof(f135,plain,
! [X0,X1] :
( subset(powerset(X0),sK11(X1,X0))
| ~ in(X0,sK10(X1)) ),
inference(duplicate_literal_removal,[],[f134]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ in(sK11(X1,X0),sK10(X2))
| ~ in(X0,sK10(X1))
| in(powerset(X0),sK10(X2)) ),
inference(resolution,[],[f135,f57]) ).
fof(f140,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1))
| in(powerset(X0),sK10(X1))
| ~ in(X0,sK10(X1)) ),
inference(resolution,[],[f139,f56]) ).
fof(f142,plain,
! [X0,X1] :
( in(powerset(X0),sK10(X1))
| ~ in(X0,sK10(X1)) ),
inference(duplicate_literal_removal,[],[f140]) ).
fof(f144,plain,
( ~ in(sK9(sK10(sK6)),sK10(sK6))
| spl12_2 ),
inference(resolution,[],[f142,f73]) ).
fof(f146,plain,
( $false
| spl12_2
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f144,f84]) ).
fof(f147,plain,
( spl12_2
| ~ spl12_5 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f148,plain,
( ~ in(sK6,sK10(sK6))
| ~ in(powerset(sK9(sK10(sK6))),sK10(sK6))
| sP0(sK10(sK6))
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f127,f51]) ).
fof(f149,plain,
( ~ in(powerset(sK9(sK10(sK6))),sK10(sK6))
| sP0(sK10(sK6))
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f148,f58]) ).
fof(f150,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f149,f79,f72,f69]) ).
fof(f151,plain,
( ~ are_equipotent(sK5(sK10(sK6)),sK10(sK6))
| ~ spl12_1 ),
inference(resolution,[],[f70,f46]) ).
fof(f152,plain,
( subset(sK5(sK10(sK6)),sK10(sK6))
| ~ spl12_1 ),
inference(resolution,[],[f70,f47]) ).
fof(f153,plain,
( ~ in(sK5(sK10(sK6)),sK10(sK6))
| ~ spl12_1 ),
inference(resolution,[],[f70,f45]) ).
fof(f154,plain,
( are_equipotent(sK5(sK10(sK6)),sK10(sK6))
| in(sK5(sK10(sK6)),sK10(sK6))
| ~ spl12_1 ),
inference(resolution,[],[f152,f54]) ).
fof(f159,plain,
( in(sK5(sK10(sK6)),sK10(sK6))
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f154,f151]) ).
fof(f160,plain,
( $false
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f159,f153]) ).
fof(f161,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f160]) ).
cnf(s2,plain,
( spl12_1
| ~ spl12_2
| spl12_4 ),
inference(sat_conversion,[],[f81]) ).
cnf(s3,plain,
( spl12_1
| spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f85]) ).
cnf(s7,plain,
( spl12_1
| ~ spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s9,plain,
( spl12_2
| ~ spl12_5 ),
inference(sat_conversion,[],[f147]) ).
cnf(s10,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_4 ),
inference(sat_conversion,[],[f150]) ).
cnf(s11,plain,
~ spl12_1,
inference(sat_conversion,[],[f161]) ).
cnf(s12,plain,
( ~ spl12_2
| ~ spl12_4 ),
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
( ~ spl12_4
| spl12_5 ),
inference(rat,[],[s7,s11]) ).
cnf(s14,plain,
( spl12_4
| spl12_5 ),
inference(rat,[],[s3,s11]) ).
cnf(s15,plain,
( ~ spl12_2
| spl12_4 ),
inference(rat,[],[s2,s11]) ).
cnf(s17,plain,
spl12_5,
inference(rat,[],[s14,s13]) ).
cnf(s18,plain,
spl12_2,
inference(rat,[],[s9,s17]) ).
cnf(s19,plain,
~ spl12_4,
inference(rat,[],[s12,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s15,s19,s18]) ).
fof(f162,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:54:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.87/2.24 % (4131881)Detected formulas, will run a generic FOF schedule.
% 9.87/2.24 % (4131921)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2275687600:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.87/2.24 % (4131921)Instruction limit reached!
% 9.87/2.24 % (4131921)------------------------------
% 9.87/2.24 % (4131921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.24 % (4131921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.24 % (4131921)CaDiCaL version: 2.1.3
% 9.87/2.24 % (4131921)Termination reason: Instruction limit
% 9.87/2.24 % (4131921)Termination phase: Saturation
% 9.87/2.24 % (4131921)Time elapsed: 0.025 s
% 9.87/2.24 % (4131921)Peak memory usage: 88 MB
% 9.87/2.24 % (4131921)Instructions burned: 113 (million)
% 9.87/2.24 % (4131919)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=3701070956:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.87/2.24 % (4131920)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=989119379:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.87/2.25 % (4131918)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=1633188925:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.87/2.25 % (4131924)dis-21_1_sil=8000:lcm=predicate:random_seed=2527615540: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)
% 9.87/2.25 % (4131923)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2184127223:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.87/2.25 % (4131922)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1639710735:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.87/2.25 % (4131924)Instruction limit reached!
% 9.87/2.25 % (4131924)------------------------------
% 9.87/2.25 % (4131924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131924)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131924)Termination reason: Instruction limit
% 9.87/2.25 % (4131924)Termination phase: Saturation
% 9.87/2.25 % (4131924)Time elapsed: 0.071 s
% 9.87/2.25 % (4131924)Peak memory usage: 88 MB
% 9.87/2.25 % (4131924)Instructions burned: 130 (million)
% 9.87/2.25 % (4131929)lrs+10_1_sil=8000:sp=occurrence:random_seed=4271544651:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.87/2.25 % (4131923)Instruction limit reached!
% 9.87/2.25 % (4131923)------------------------------
% 9.87/2.25 % (4131923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131923)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131923)Termination reason: Instruction limit
% 9.87/2.25 % (4131923)Termination phase: Saturation
% 9.87/2.25 % (4131923)Time elapsed: 0.103 s
% 9.87/2.25 % (4131923)Peak memory usage: 90 MB
% 9.87/2.25 % (4131923)Instructions burned: 139 (million)
% 9.87/2.25 % (4131922)Instruction limit reached!
% 9.87/2.25 % (4131922)------------------------------
% 9.87/2.25 % (4131922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131922)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131922)Termination reason: Instruction limit
% 9.87/2.25 % (4131922)Termination phase: Saturation
% 9.87/2.25 % (4131922)Time elapsed: 0.117 s
% 9.87/2.25 % (4131922)Peak memory usage: 88 MB
% 9.87/2.25 % (4131922)Instructions burned: 119 (million)
% 9.87/2.25 % (4131929)Instruction limit reached!
% 9.87/2.25 % (4131929)------------------------------
% 9.87/2.25 % (4131929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131929)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131929)Termination reason: Instruction limit
% 9.87/2.25 % (4131929)Termination phase: Saturation
% 9.87/2.25 % (4131929)Time elapsed: 0.088 s
% 9.87/2.25 % (4131929)Peak memory usage: 91 MB
% 9.87/2.25 % (4131929)Instructions burned: 287 (million)
% 9.87/2.25 % (4131933)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3308073927:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.87/2.25 % (4131935)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3170002336:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.87/2.25 % (4131936)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=1067957627:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 9.87/2.25 % (4131937)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=213147027:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 9.87/2.25 % (4131933)Instruction limit reached!
% 9.87/2.25 % (4131933)------------------------------
% 9.87/2.25 % (4131933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131933)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131933)Termination reason: Instruction limit
% 9.87/2.25 % (4131933)Termination phase: Saturation
% 9.87/2.25 % (4131933)Time elapsed: 0.123 s
% 9.87/2.25 % (4131933)Peak memory usage: 90 MB
% 9.87/2.25 % (4131933)Instructions burned: 158 (million)
% 9.87/2.25 % (4131937)Instruction limit reached!
% 9.87/2.25 % (4131937)------------------------------
% 9.87/2.25 % (4131937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131937)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131937)Termination reason: Instruction limit
% 9.87/2.25 % (4131937)Termination phase: Saturation
% 9.87/2.25 % (4131937)Time elapsed: 0.104 s
% 9.87/2.25 % (4131937)Peak memory usage: 88 MB
% 9.87/2.25 % (4131937)Instructions burned: 294 (million)
% 9.87/2.25 % (4131936)Instruction limit reached!
% 9.87/2.25 % (4131936)------------------------------
% 9.87/2.25 % (4131936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131936)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131936)Termination reason: Instruction limit
% 9.87/2.25 % (4131936)Termination phase: Saturation
% 9.87/2.25 % (4131936)Time elapsed: 0.207 s
% 9.87/2.25 % (4131936)Peak memory usage: 91 MB
% 9.87/2.25 % (4131936)Instructions burned: 248 (million)
% 9.87/2.25 % (4131935)Instruction limit reached!
% 9.87/2.25 % (4131935)------------------------------
% 9.87/2.25 % (4131935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131935)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131935)Termination reason: Instruction limit
% 9.87/2.25 % (4131935)Termination phase: Saturation
% 9.87/2.25 % (4131935)Time elapsed: 0.333 s
% 9.87/2.25 % (4131935)Peak memory usage: 92 MB
% 9.87/2.25 % (4131935)Instructions burned: 326 (million)
% 9.87/2.25 % (4131950)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=172975403:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.87/2.25 % (4131952)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3414460505:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.87/2.25 % (4131952)Instruction limit reached!
% 9.87/2.25 % (4131952)------------------------------
% 9.87/2.25 % (4131952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131952)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131952)Termination reason: Instruction limit
% 9.87/2.25 % (4131952)Termination phase: Saturation
% 9.87/2.25 % (4131952)Time elapsed: 0.066 s
% 9.87/2.25 % (4131952)Peak memory usage: 88 MB
% 9.87/2.25 % (4131952)Instructions burned: 114 (million)
% 9.87/2.25 % (4131959)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1197416702:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 9.87/2.25 % (4131963)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=424565356:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.87/2.25 % (4131919)First to succeed.
% 9.87/2.25 % (4131919)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4131881"
% 9.87/2.25 % (4131918)Also succeeded, but the first one will report.
% 9.87/2.25 % (4131963)Instruction limit reached!
% 9.87/2.25 % (4131963)------------------------------
% 9.87/2.25 % (4131963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131963)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131963)Termination reason: Instruction limit
% 9.87/2.25 % (4131963)Termination phase: Saturation
% 9.87/2.25 % (4131963)Time elapsed: 0.062 s
% 9.87/2.25 % (4131963)Peak memory usage: 89 MB
% 9.87/2.25 % (4131963)Instructions burned: 115 (million)
% 9.87/2.25 % (4131959)Instruction limit reached!
% 9.87/2.25 % (4131959)------------------------------
% 9.87/2.25 % (4131959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.87/2.25 % (4131959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.87/2.25 % (4131959)CaDiCaL version: 2.1.3
% 9.87/2.25 % (4131959)Termination reason: Instruction limit
% 9.87/2.25 % (4131959)Termination phase: Saturation
% 9.87/2.25 % (4131959)Time elapsed: 0.116 s
% 9.87/2.25 % (4131959)Peak memory usage: 88 MB
% 9.87/2.25 % (4131959)Instructions burned: 128 (million)
% 9.87/2.25 % (4131967)lrs+10_1_sil=8000:sp=occurrence:random_seed=96433289:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.87/2.25 % (4131973)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1425733420:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 9.87/2.25 % (4131975)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3680027039:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 9.87/2.25 % (4131967)Also succeeded, but the first one will report.
% 9.87/2.25 % (4131919)Refutation found. Thanks to Tanya!
% 9.87/2.25 % SZS status Theorem for theBenchmark
% 9.87/2.25 % SZS output start Proof for theBenchmark
% See solution above
% 10.51/2.54 % (4131919)------------------------------
% 10.51/2.54 % (4131919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.51/2.54 % (4131919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.51/2.54 % (4131919)CaDiCaL version: 2.1.3
% 10.51/2.54 % (4131919)Termination reason: Refutation
% 10.51/2.54 % (4131919)Time elapsed: 0.820 s
% 10.51/2.54 % (4131919)Peak memory usage: 128 MB
% 10.51/2.54 % (4131919)Instructions burned: 927 (million)
% 10.51/2.54 % (4131919)------------------------------
% 10.51/2.54 % (4131919)------------------------------
% 10.51/2.54 % (4131881)Success in time 1.393 s
% 10.51/2.54 % Vampire exiting
%------------------------------------------------------------------------------