%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET668+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:41:35 PM UTC 2026
% Result : Theorem 2.80s 1.29s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 28
% Syntax : Number of formulae : 159 ( 32 unt; 18 def)
% Number of atoms : 548 ( 11 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 679 ( 290 ~; 287 |; 41 &)
% ( 29 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 18 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 130 ( 0 sgn 120 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ( subset(X0,X1)
& subset(X1,X0) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f16,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f32,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p32) ).
fof(f33,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = domain(X1,X0,X2)
& subset(X1,range(X1,X0,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_31) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = domain(X1,X0,X2)
& subset(X1,range(X1,X0,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) )
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) )
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f37]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f43]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f16]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f60]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f74,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( domain(X1,X0,X2) != X1
| ~ subset(X1,range(X1,X0,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f75,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( domain(X1,X0,X2) != X1
| ~ subset(X1,range(X1,X0,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f74]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0)
& ilf_type(sK1(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f80]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f53]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f58]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f93]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f61]) ).
fof(f103,plain,
( ( sK13 != domain(sK13,sK12,sK14)
| ~ subset(sK13,range(sK13,sK12,sK14)) )
& subset(identity_relation_of(sK13),sK14)
& ilf_type(sK14,relation_type(sK13,sK12))
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f75]) ).
fof(f104,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( subset(X2,range(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( subset(X2,domain(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f116,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f117,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f134,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
fof(f139,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f144,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f145,plain,
! [X0,X1] :
( empty(X1)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f95]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f163,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f32]) ).
fof(f164,plain,
ilf_type(sK12,set_type),
inference(cnf_transformation,[],[f103]) ).
fof(f165,plain,
ilf_type(sK13,set_type),
inference(cnf_transformation,[],[f103]) ).
fof(f166,plain,
ilf_type(sK14,relation_type(sK13,sK12)),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
( sK13 != domain(sK13,sK12,sK14)
| ~ subset(sK13,range(sK13,sK12,sK14)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f172,definition,
! [X0,X1] :
( sQ15_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ15_eqProxy])],[equality_proxy_definition]) ).
fof(f173,plain,
! [X0,X1] :
( sQ15_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(equality_proxy_replacement,[],[f104,f172]) ).
fof(f180,plain,
( ~ sQ15_eqProxy(sK13,domain(sK13,sK12,sK14))
| ~ subset(sK13,range(sK13,sK12,sK14)) ),
inference(equality_proxy_replacement,[],[f168,f172]) ).
fof(f182,plain,
! [X0,X1] :
( sQ15_eqProxy(X1,X0)
| ~ sQ15_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f172]) ).
fof(f188,definition,
( spl16_1
<=> subset(sK13,range(sK13,sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f189,plain,
( ~ subset(sK13,range(sK13,sK12,sK14))
| spl16_1 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,definition,
( spl16_2
<=> sQ15_eqProxy(sK13,domain(sK13,sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f192,plain,
( ~ sQ15_eqProxy(sK13,domain(sK13,sK12,sK14))
| spl16_2 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f193,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f180,f191,f188]) ).
fof(f214,definition,
( spl16_3
<=> ilf_type(sK13,set_type) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f215,plain,
( ~ ilf_type(sK13,set_type)
| spl16_3 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f223,plain,
( $false
| spl16_3 ),
inference(resolution,[],[f215,f165]) ).
fof(f226,plain,
spl16_3,
inference(avatar_contradiction_clause,[],[f223]) ).
fof(f264,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(power_set(X1),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f145,f144]) ).
fof(f320,plain,
( ~ sQ15_eqProxy(domain(sK13,sK12,sK14),sK13)
| spl16_2 ),
inference(resolution,[],[f192,f182]) ).
fof(f322,definition,
( spl16_13
<=> ilf_type(domain(sK13,sK12,sK14),set_type) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
fof(f323,plain,
( ~ ilf_type(domain(sK13,sK12,sK14),set_type)
| spl16_13 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f325,definition,
( spl16_14
<=> subset(domain(sK13,sK12,sK14),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
fof(f326,plain,
( ~ subset(domain(sK13,sK12,sK14),sK13)
| spl16_14 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f328,definition,
( spl16_15
<=> subset(sK13,domain(sK13,sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
fof(f329,plain,
( ~ subset(sK13,domain(sK13,sK12,sK14))
| spl16_15 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f334,plain,
( $false
| spl16_13 ),
inference(resolution,[],[f323,f163]) ).
fof(f335,plain,
spl16_13,
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f339,definition,
( spl16_16
<=> member(sK1(domain(sK13,sK12,sK14),sK13),domain(sK13,sK12,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
fof(f340,plain,
( member(sK1(domain(sK13,sK12,sK14),sK13),domain(sK13,sK12,sK14))
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f343,definition,
( spl16_17
<=> member(sK1(domain(sK13,sK12,sK14),sK13),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
fof(f344,plain,
( ~ member(sK1(domain(sK13,sK12,sK14),sK13),sK13)
| spl16_17 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f671,definition,
( spl16_69
<=> ilf_type(sK1(domain(sK13,sK12,sK14),sK13),set_type) ),
introduced(definition,[new_symbols(definition,[spl16_69])],[avatar_definition]) ).
fof(f672,plain,
( ~ ilf_type(sK1(domain(sK13,sK12,sK14),sK13),set_type)
| spl16_69 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f674,definition,
( spl16_70
<=> ! [X0] :
( ~ member(sK1(domain(sK13,sK12,sK14),sK13),X0)
| ~ ilf_type(X0,set_type)
| ~ member(X0,power_set(sK13)) ) ),
introduced(definition,[new_symbols(definition,[spl16_70])],[avatar_definition]) ).
fof(f675,plain,
( ! [X0] :
( ~ member(sK1(domain(sK13,sK12,sK14),sK13),X0)
| ~ ilf_type(X0,set_type)
| ~ member(X0,power_set(sK13)) )
| ~ spl16_70 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f681,plain,
( $false
| spl16_69 ),
inference(resolution,[],[f672,f163]) ).
fof(f682,plain,
spl16_69,
inference(avatar_contradiction_clause,[],[f681]) ).
fof(f711,plain,
( ~ subset(identity_relation_of(sK13),sK14)
| ~ ilf_type(sK14,relation_type(sK13,sK12))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK13,set_type)
| spl16_1 ),
inference(resolution,[],[f105,f189]) ).
fof(f712,plain,
( ~ subset(identity_relation_of(sK13),sK14)
| ~ ilf_type(sK14,relation_type(sK13,sK12))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(sK12,set_type)
| spl16_1 ),
inference(duplicate_literal_removal,[],[f711]) ).
fof(f715,definition,
( spl16_74
<=> ilf_type(sK12,set_type) ),
introduced(definition,[new_symbols(definition,[spl16_74])],[avatar_definition]) ).
fof(f716,plain,
( ~ ilf_type(sK12,set_type)
| spl16_74 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f718,definition,
( spl16_75
<=> ilf_type(sK14,relation_type(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl16_75])],[avatar_definition]) ).
fof(f719,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK12))
| spl16_75 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f721,definition,
( spl16_76
<=> subset(identity_relation_of(sK13),sK14) ),
introduced(definition,[new_symbols(definition,[spl16_76])],[avatar_definition]) ).
fof(f722,plain,
( ~ subset(identity_relation_of(sK13),sK14)
| spl16_76 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f723,plain,
( ~ spl16_74
| ~ spl16_3
| ~ spl16_75
| ~ spl16_76
| spl16_1 ),
inference(avatar_split_clause,[],[f712,f188,f721,f718,f214,f715]) ).
fof(f724,plain,
( $false
| spl16_74 ),
inference(resolution,[],[f716,f164]) ).
fof(f727,plain,
spl16_74,
inference(avatar_contradiction_clause,[],[f724]) ).
fof(f728,plain,
( $false
| spl16_75 ),
inference(resolution,[],[f719,f166]) ).
fof(f729,plain,
spl16_75,
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f730,plain,
( $false
| spl16_76 ),
inference(resolution,[],[f722,f167]) ).
fof(f735,plain,
spl16_76,
inference(avatar_contradiction_clause,[],[f730]) ).
fof(f760,plain,
( ~ subset(domain(sK13,sK12,sK14),sK13)
| ~ subset(sK13,domain(sK13,sK12,sK14))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(domain(sK13,sK12,sK14),set_type)
| spl16_2 ),
inference(resolution,[],[f320,f173]) ).
fof(f762,plain,
( ~ spl16_13
| ~ spl16_3
| ~ spl16_15
| ~ spl16_14
| spl16_2 ),
inference(avatar_split_clause,[],[f760,f191,f325,f328,f214,f322]) ).
fof(f798,plain,
( member(sK1(domain(sK13,sK12,sK14),sK13),domain(sK13,sK12,sK14))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(domain(sK13,sK12,sK14),set_type)
| spl16_14 ),
inference(resolution,[],[f326,f116]) ).
fof(f799,plain,
( ~ spl16_13
| ~ spl16_3
| spl16_16
| spl16_14 ),
inference(avatar_split_clause,[],[f798,f325,f339,f214,f322]) ).
fof(f878,plain,
( ~ ilf_type(domain(sK13,sK12,sK14),set_type)
| ~ member(domain(sK13,sK12,sK14),power_set(sK13))
| ~ spl16_16
| ~ spl16_70 ),
inference(resolution,[],[f675,f340]) ).
fof(f898,definition,
( spl16_100
<=> member(domain(sK13,sK12,sK14),power_set(sK13)) ),
introduced(definition,[new_symbols(definition,[spl16_100])],[avatar_definition]) ).
fof(f899,plain,
( ~ member(domain(sK13,sK12,sK14),power_set(sK13))
| spl16_100 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f931,plain,
( ~ subset(identity_relation_of(sK13),sK14)
| ~ ilf_type(sK14,relation_type(sK13,sK12))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK13,set_type)
| spl16_15 ),
inference(resolution,[],[f106,f329]) ).
fof(f932,plain,
( ~ subset(identity_relation_of(sK13),sK14)
| ~ ilf_type(sK14,relation_type(sK13,sK12))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(sK12,set_type)
| spl16_15 ),
inference(duplicate_literal_removal,[],[f931]) ).
fof(f934,plain,
( ~ spl16_74
| ~ spl16_3
| ~ spl16_75
| ~ spl16_76
| spl16_15 ),
inference(avatar_split_clause,[],[f932,f328,f721,f718,f214,f715]) ).
fof(f935,plain,
( ~ spl16_100
| ~ spl16_13
| ~ spl16_16
| ~ spl16_70 ),
inference(avatar_split_clause,[],[f878,f674,f339,f322,f898]) ).
fof(f938,plain,
( ~ member(sK1(domain(sK13,sK12,sK14),sK13),sK13)
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(domain(sK13,sK12,sK14),set_type)
| spl16_14 ),
inference(resolution,[],[f326,f117]) ).
fof(f940,plain,
( ~ spl16_13
| ~ spl16_3
| ~ spl16_17
| spl16_14 ),
inference(avatar_split_clause,[],[f938,f325,f343,f214,f322]) ).
fof(f950,definition,
( spl16_107
<=> ilf_type(power_set(sK13),set_type) ),
introduced(definition,[new_symbols(definition,[spl16_107])],[avatar_definition]) ).
fof(f951,plain,
( ~ ilf_type(power_set(sK13),set_type)
| spl16_107 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f957,plain,
( ! [X0] :
( ~ member(sK1(domain(sK13,sK12,sK14),sK13),X0)
| ~ ilf_type(sK1(domain(sK13,sK12,sK14),sK13),set_type)
| ~ member(X0,power_set(sK13))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(X0,set_type) )
| spl16_17 ),
inference(resolution,[],[f344,f139]) ).
fof(f959,plain,
( ~ spl16_3
| ~ spl16_69
| spl16_70
| spl16_17 ),
inference(avatar_split_clause,[],[f957,f343,f674,f671,f214]) ).
fof(f960,plain,
( $false
| spl16_107 ),
inference(resolution,[],[f951,f163]) ).
fof(f961,plain,
spl16_107,
inference(avatar_contradiction_clause,[],[f960]) ).
fof(f965,definition,
( spl16_109
<=> ilf_type(domain(sK13,sK12,sK14),member_type(power_set(sK13))) ),
introduced(definition,[new_symbols(definition,[spl16_109])],[avatar_definition]) ).
fof(f966,plain,
( ~ ilf_type(domain(sK13,sK12,sK14),member_type(power_set(sK13)))
| spl16_109 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f972,plain,
( ~ ilf_type(domain(sK13,sK12,sK14),subset_type(sK13))
| ~ ilf_type(domain(sK13,sK12,sK14),set_type)
| ~ ilf_type(sK13,set_type)
| spl16_109 ),
inference(resolution,[],[f966,f134]) ).
fof(f974,definition,
( spl16_111
<=> ilf_type(domain(sK13,sK12,sK14),subset_type(sK13)) ),
introduced(definition,[new_symbols(definition,[spl16_111])],[avatar_definition]) ).
fof(f975,plain,
( ~ ilf_type(domain(sK13,sK12,sK14),subset_type(sK13))
| spl16_111 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f976,plain,
( ~ spl16_3
| ~ spl16_13
| ~ spl16_111
| spl16_109 ),
inference(avatar_split_clause,[],[f972,f965,f974,f322,f214]) ).
fof(f988,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK12))
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK13,set_type)
| spl16_111 ),
inference(resolution,[],[f975,f160]) ).
fof(f989,plain,
( ~ spl16_3
| ~ spl16_74
| ~ spl16_75
| spl16_111 ),
inference(avatar_split_clause,[],[f988,f974,f718,f715,f214]) ).
fof(f1578,plain,
( ~ ilf_type(domain(sK13,sK12,sK14),member_type(power_set(sK13)))
| ~ ilf_type(power_set(sK13),set_type)
| ~ ilf_type(domain(sK13,sK12,sK14),set_type)
| ~ ilf_type(sK13,set_type)
| spl16_100 ),
inference(resolution,[],[f264,f899]) ).
fof(f1622,plain,
( ~ spl16_3
| ~ spl16_13
| ~ spl16_107
| ~ spl16_109
| spl16_100 ),
inference(avatar_split_clause,[],[f1578,f898,f965,f950,f322,f214]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f193]) ).
cnf(s4,plain,
spl16_3,
inference(sat_conversion,[],[f226]) ).
cnf(s13,plain,
spl16_13,
inference(sat_conversion,[],[f335]) ).
cnf(s68,plain,
spl16_69,
inference(sat_conversion,[],[f682]) ).
cnf(s76,plain,
( spl16_1
| ~ spl16_3
| ~ spl16_74
| ~ spl16_75
| ~ spl16_76 ),
inference(sat_conversion,[],[f723]) ).
cnf(s78,plain,
spl16_74,
inference(sat_conversion,[],[f727]) ).
cnf(s79,plain,
spl16_75,
inference(sat_conversion,[],[f729]) ).
cnf(s80,plain,
spl16_76,
inference(sat_conversion,[],[f735]) ).
cnf(s87,plain,
( spl16_2
| ~ spl16_3
| ~ spl16_13
| ~ spl16_14
| ~ spl16_15 ),
inference(sat_conversion,[],[f762]) ).
cnf(s97,plain,
( ~ spl16_3
| ~ spl16_13
| spl16_14
| spl16_16 ),
inference(sat_conversion,[],[f799]) ).
cnf(s124,plain,
( ~ spl16_3
| spl16_15
| ~ spl16_74
| ~ spl16_75
| ~ spl16_76 ),
inference(sat_conversion,[],[f934]) ).
cnf(s125,plain,
( ~ spl16_13
| ~ spl16_16
| ~ spl16_70
| ~ spl16_100 ),
inference(sat_conversion,[],[f935]) ).
cnf(s126,plain,
( ~ spl16_3
| ~ spl16_13
| spl16_14
| ~ spl16_17 ),
inference(sat_conversion,[],[f940]) ).
cnf(s129,plain,
( ~ spl16_3
| spl16_17
| ~ spl16_69
| spl16_70 ),
inference(sat_conversion,[],[f959]) ).
cnf(s130,plain,
spl16_107,
inference(sat_conversion,[],[f961]) ).
cnf(s133,plain,
( ~ spl16_3
| ~ spl16_13
| spl16_109
| ~ spl16_111 ),
inference(sat_conversion,[],[f976]) ).
cnf(s138,plain,
( ~ spl16_3
| ~ spl16_74
| ~ spl16_75
| spl16_111 ),
inference(sat_conversion,[],[f989]) ).
cnf(s242,plain,
( ~ spl16_3
| ~ spl16_13
| spl16_100
| ~ spl16_107
| ~ spl16_109 ),
inference(sat_conversion,[],[f1622]) ).
cnf(s264,plain,
( spl16_1
| ~ spl16_3 ),
inference(rat,[],[s76,s80,s79,s78]) ).
cnf(s293,plain,
spl16_111,
inference(rat,[],[s138,s78,s79,s4]) ).
cnf(s294,plain,
spl16_109,
inference(rat,[],[s133,s293,s13,s4]) ).
cnf(s295,plain,
spl16_15,
inference(rat,[],[s124,s80,s79,s78,s4]) ).
cnf(s296,plain,
spl16_1,
inference(rat,[],[s264,s4]) ).
cnf(s299,plain,
spl16_100,
inference(rat,[],[s242,s4,s130,s13,s294]) ).
cnf(s301,plain,
~ spl16_2,
inference(rat,[],[s1,s296]) ).
cnf(s303,plain,
~ spl16_14,
inference(rat,[],[s87,s295,s4,s13,s301]) ).
cnf(s306,plain,
~ spl16_17,
inference(rat,[],[s126,s4,s13,s303]) ).
cnf(s307,plain,
spl16_16,
inference(rat,[],[s97,s4,s13,s303]) ).
cnf(s313,plain,
spl16_70,
inference(rat,[],[s129,s4,s68,s306]) ).
cnf(s314,plain,
$false,
inference(rat,[],[s125,s299,s13,s313,s307]) ).
fof(f1623,plain,
$false,
inference(avatar_sat_refutation,[],[s314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET668+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 02:32:31 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 2.80/1.29 % (2207812)Detected formulas, will run a generic FOF schedule.
% 2.80/1.29 % (2207908)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=3023256315:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.29 % (2207910)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=486418544:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.29 % (2207911)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2995561900:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.29 % (2207914)dis-21_1_sil=8000:lcm=predicate:random_seed=582250732: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)
% 2.80/1.29 % (2207913)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2397357107:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.29 % (2207909)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=3075039858:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.29 % (2207912)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3080882260:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.29 % (2207911)Refutation not found, incomplete strategy
% 2.80/1.29 % (2207911)------------------------------
% 2.80/1.29 % (2207911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.29 % (2207911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.29 % (2207911)CaDiCaL version: 2.1.3
% 2.80/1.29 % (2207911)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.29 % (2207911)Time elapsed: 0.003 s
% 2.80/1.29 % (2207911)Peak memory usage: 88 MB
% 2.80/1.29 % (2207911)Instructions burned: 2 (million)
% 2.80/1.29 % (2207914)First to succeed.
% 2.80/1.29 % (2207914)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2207812"
% 2.80/1.29 % (2207912)Instruction limit reached!
% 2.80/1.29 % (2207912)------------------------------
% 2.80/1.29 % (2207912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.29 % (2207912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.29 % (2207912)CaDiCaL version: 2.1.3
% 2.80/1.29 % (2207912)Termination reason: Instruction limit
% 2.80/1.29 % (2207912)Termination phase: Saturation
% 2.80/1.29 % (2207912)Time elapsed: 0.070 s
% 2.80/1.29 % (2207912)Peak memory usage: 88 MB
% 2.80/1.29 % (2207912)Instructions burned: 120 (million)
% 2.80/1.29 % (2207913)Instruction limit reached!
% 2.80/1.29 % (2207913)------------------------------
% 2.80/1.29 % (2207913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.29 % (2207913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.29 % (2207913)CaDiCaL version: 2.1.3
% 2.80/1.29 % (2207913)Termination reason: Instruction limit
% 2.80/1.29 % (2207913)Termination phase: Saturation
% 2.80/1.29 % (2207913)Time elapsed: 0.105 s
% 2.80/1.29 % (2207913)Peak memory usage: 90 MB
% 2.80/1.29 % (2207913)Instructions burned: 140 (million)
% 2.80/1.29 % (2207936)lrs+10_1_sil=8000:sp=occurrence:random_seed=3390326337:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.80/1.29 % (2207911)------------------------------
% 2.80/1.29 % (2207911)------------------------------
% 2.80/1.29 % (2207937)lrs+10_1_sil=32000:urr=on:br=off:random_seed=416884667:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.80/1.29 % (2207914)Refutation found. Thanks to Tanya!
% 2.80/1.29 % SZS status Theorem for theBenchmark
% 2.80/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.39 % (2207914)------------------------------
% 3.67/1.39 % (2207914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.39 % (2207914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.39 % (2207914)CaDiCaL version: 2.1.3
% 3.67/1.39 % (2207914)Termination reason: Refutation
% 3.67/1.39 % (2207914)Time elapsed: 0.027 s
% 3.67/1.39 % (2207914)Peak memory usage: 90 MB
% 3.67/1.39 % (2207914)Instructions burned: 36 (million)
% 3.67/1.39 % (2207914)------------------------------
% 3.67/1.39 % (2207914)------------------------------
% 3.67/1.39 % (2207812)Success in time 0.448 s
% 3.67/1.39 % Vampire exiting
%------------------------------------------------------------------------------