%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET669+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 : n019.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 2.77s 1.30s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 108 ( 14 unt; 2 def)
% Number of atoms : 412 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 519 ( 215 ~; 215 |; 41 &)
% ( 13 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 216 ( 0 sgn 206 !; 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(f30,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p30) ).
fof(f31,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
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(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( subset(X1,domain(X0,X1,X2))
& X1 = range(X0,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_32) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( subset(X1,domain(X0,X1,X2))
& X1 = range(X0,X1,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(f72,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f30]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f31]) ).
fof(f74,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ subset(X1,domain(X0,X1,X2))
| range(X0,X1,X2) != X1 )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f75,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ subset(X1,domain(X0,X1,X2))
| range(X0,X1,X2) != X1 )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& 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,
( ( ~ subset(sK13,domain(sK12,sK13,sK14))
| sK13 != range(sK12,sK13,sK14) )
& subset(identity_relation_of(sK13),sK14)
& ilf_type(sK14,relation_type(sK12,sK13))
& 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] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f95]) ).
fof(f161,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f163,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f32]) ).
fof(f166,plain,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
( ~ subset(sK13,domain(sK12,sK13,sK14))
| sK13 != range(sK12,sK13,sK14) ),
inference(cnf_transformation,[],[f103]) ).
fof(f177,definition,
( spl15_1
<=> sK13 = range(sK12,sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f179,plain,
( sK13 != range(sK12,sK13,sK14)
| spl15_1 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f181,definition,
( spl15_2
<=> subset(sK13,domain(sK12,sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f184,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f168,f181,f177]) ).
fof(f186,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f144,f163]) ).
fof(f199,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f116,f163]) ).
fof(f200,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f199,f163]) ).
fof(f201,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f117,f163]) ).
fof(f202,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f201,f163]) ).
fof(f205,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f104,f163]) ).
fof(f206,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(forward_subsumption_resolution,[],[f205,f163]) ).
fof(f221,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f134,f163]) ).
fof(f222,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f221,f163]) ).
fof(f231,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f145,f163]) ).
fof(f232,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f231,f163]) ).
fof(f234,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f232,f222]) ).
fof(f236,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[],[f234,f186]) ).
fof(f293,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f161,f163]) ).
fof(f294,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f293,f163]) ).
fof(f295,plain,
( sK13 != range_of(sK14)
| ~ ilf_type(sK14,relation_type(sK12,sK13))
| spl15_1 ),
inference(superposition,[],[f179,f294]) ).
fof(f296,plain,
( sK13 != range_of(sK14)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f295,f166]) ).
fof(f297,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f162,f163]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f297,f163]) ).
fof(f299,plain,
! [X2,X0,X1] :
( ilf_type(range_of(X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(superposition,[],[f298,f294]) ).
fof(f300,plain,
! [X2,X0,X1] :
( ilf_type(range_of(X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(duplicate_literal_removal,[],[f299]) ).
fof(f301,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f139,f163]) ).
fof(f302,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f301,f163]) ).
fof(f303,plain,
! [X3,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ member(X3,X0)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f302,f163]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,subset_type(X2))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[],[f303,f236]) ).
fof(f314,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(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f105,f163]) ).
fof(f315,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(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f314,f163]) ).
fof(f316,plain,
! [X2,X3,X0,X1] :
( ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f315,f163]) ).
fof(f322,plain,
! [X0,X1] :
( ~ ilf_type(sK14,relation_type(X0,X1))
| subset(sK13,range(X0,X1,sK14)) ),
inference(resolution,[],[f316,f167]) ).
fof(f325,plain,
subset(sK13,range(sK12,sK13,sK14)),
inference(resolution,[],[f322,f166]) ).
fof(f327,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(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f106,f163]) ).
fof(f328,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(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f327,f163]) ).
fof(f329,plain,
! [X2,X3,X0,X1] :
( ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f328,f163]) ).
fof(f332,plain,
( subset(sK13,range_of(sK14))
| ~ ilf_type(sK14,relation_type(sK12,sK13)) ),
inference(superposition,[],[f325,f294]) ).
fof(f333,plain,
subset(sK13,range_of(sK14)),
inference(forward_subsumption_resolution,[],[f332,f166]) ).
fof(f335,plain,
! [X0,X1] :
( ~ ilf_type(sK14,relation_type(X0,X1))
| subset(sK13,domain(X0,X1,sK14)) ),
inference(resolution,[],[f329,f167]) ).
fof(f339,plain,
( sK13 = range_of(sK14)
| ~ subset(range_of(sK14),sK13) ),
inference(resolution,[],[f333,f206]) ).
fof(f340,plain,
( ~ subset(range_of(sK14),sK13)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f339,f296]) ).
fof(f341,plain,
( ~ member(sK1(range_of(sK14),sK13),sK13)
| spl15_1 ),
inference(resolution,[],[f340,f202]) ).
fof(f342,plain,
subset(sK13,domain(sK12,sK13,sK14)),
inference(resolution,[],[f335,f166]) ).
fof(f344,plain,
spl15_2,
inference(avatar_split_clause,[],[f342,f181]) ).
fof(f490,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X3,X1))
| ~ member(X0,range_of(X2))
| member(X0,X1) ),
inference(resolution,[],[f304,f300]) ).
fof(f736,plain,
! [X0] :
( member(X0,sK13)
| ~ member(X0,range_of(sK14)) ),
inference(resolution,[],[f490,f166]) ).
fof(f750,plain,
( ~ member(sK1(range_of(sK14),sK13),range_of(sK14))
| spl15_1 ),
inference(resolution,[],[f736,f341]) ).
fof(f771,plain,
( subset(range_of(sK14),sK13)
| spl15_1 ),
inference(resolution,[],[f750,f200]) ).
fof(f772,plain,
( $false
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f771,f340]) ).
fof(f773,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f772]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f184]) ).
cnf(s3,plain,
spl15_2,
inference(sat_conversion,[],[f344]) ).
cnf(s6,plain,
spl15_1,
inference(sat_conversion,[],[f773]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s3,s6]) ).
fof(f774,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET669+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n019.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 02:29:18 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
% 2.77/1.30 % (3606267)Detected formulas, will run a generic FOF schedule.
% 2.77/1.30 % (3606274)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=654433658:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.30 % (3606275)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1909424978:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.30 % (3606272)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=3832250434:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.30 % (3606276)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3963954114:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.30 % (3606278)dis-21_1_sil=8000:lcm=predicate:random_seed=2228528166: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)
% 2.77/1.30 % (3606273)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=867805343:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.30 % (3606277)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=447958577:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.30 % (3606275)Refutation not found, incomplete strategy
% 2.77/1.30 % (3606275)------------------------------
% 2.77/1.30 % (3606275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.30 % (3606275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.30 % (3606275)CaDiCaL version: 2.1.3
% 2.77/1.30 % (3606275)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.30 % (3606275)Time elapsed: 0.003 s
% 2.77/1.30 % (3606275)Peak memory usage: 88 MB
% 2.77/1.30 % (3606275)Instructions burned: 2 (million)
% 2.77/1.30 % (3606278)Also succeeded, but the first one will report.
% 2.77/1.30 % (3606277)First to succeed.
% 2.77/1.30 % (3606277)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3606267"
% 2.77/1.30 % (3606276)Instruction limit reached!
% 2.77/1.30 % (3606276)------------------------------
% 2.77/1.30 % (3606276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.30 % (3606276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.30 % (3606276)CaDiCaL version: 2.1.3
% 2.77/1.30 % (3606276)Termination reason: Instruction limit
% 2.77/1.30 % (3606276)Termination phase: Saturation
% 2.77/1.30 % (3606276)Time elapsed: 0.069 s
% 2.77/1.30 % (3606276)Peak memory usage: 88 MB
% 2.77/1.30 % (3606276)Instructions burned: 119 (million)
% 2.77/1.30 % (3606286)lrs+10_1_sil=8000:sp=occurrence:random_seed=49721168:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.77/1.30 % (3606275)------------------------------
% 2.77/1.30 % (3606275)------------------------------
% 2.77/1.30 % (3606277)Refutation found. Thanks to Tanya!
% 2.77/1.30 % SZS status Theorem for theBenchmark
% 2.77/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (3606277)------------------------------
% 0.16/1.50 % (3606277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (3606277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (3606277)CaDiCaL version: 2.1.3
% 0.16/1.50 % (3606277)Termination reason: Refutation
% 0.16/1.50 % (3606277)Time elapsed: 0.031 s
% 0.16/1.50 % (3606277)Peak memory usage: 90 MB
% 0.16/1.50 % (3606277)Instructions burned: 39 (million)
% 0.16/1.50 % (3606277)------------------------------
% 0.16/1.50 % (3606277)------------------------------
% 0.16/1.50 % (3606267)Success in time 0.456 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------