%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 12:44:22 PM UTC 2026
% Result : Theorem 0.41s 0.47s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 112 ( 20 unt; 2 def)
% Number of atoms : 369 ( 28 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 444 ( 187 ~; 189 |; 17 &)
% ( 13 <=>; 38 =>; 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 : 208 ( 0 sgn 202 !; 6 ?)
% 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(f28,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
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(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
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(f76,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f88,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f89,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f106,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f115,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f117,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f134,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f32]) ).
fof(f135,plain,
( sK13 != range(sK12,sK13,sK14)
| ~ subset(sK13,domain(sK12,sK13,sK14)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f136,plain,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f75]) ).
fof(f137,plain,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f75]) ).
fof(f146,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f147,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X0)
| ~ member(X2,X1)
| member(X0,power_set(X1)) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f156,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| empty(power_set(X0)) ),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f157,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f172,definition,
( spl15_1
<=> subset(sK13,domain(sK12,sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f174,plain,
( ~ subset(sK13,domain(sK12,sK13,sK14))
| spl15_1 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f176,definition,
( spl15_2
<=> sK13 = range(sK12,sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f178,plain,
( sK13 != range(sK12,sK13,sK14)
| spl15_2 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f179,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f135,f176,f172]) ).
fof(f181,plain,
! [X0] : empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f156,f134]) ).
fof(f202,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f146,f134]) ).
fof(f203,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f202,f134]) ).
fof(f204,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f147,f134]) ).
fof(f205,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f204,f134]) ).
fof(f210,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f76,f134]) ).
fof(f211,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f210,f134]) ).
fof(f228,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f106,f134]) ).
fof(f229,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f228,f134]) ).
fof(f240,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ empty(X1)
| ~ member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(forward_subsumption_resolution,[],[f157,f134]) ).
fof(f241,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[],[f240,f134]) ).
fof(f243,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ empty(power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f241,f229]) ).
fof(f245,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f243,f181]) ).
fof(f290,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(forward_subsumption_resolution,[],[f130,f134]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(forward_subsumption_resolution,[],[f290,f134]) ).
fof(f292,plain,
domain(sK12,sK13,sK14) = domain_of(sK14),
inference(resolution,[],[f291,f136]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(forward_subsumption_resolution,[],[f132,f134]) ).
fof(f299,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(forward_subsumption_resolution,[],[f298,f134]) ).
fof(f300,plain,
range(sK12,sK13,sK14) = range_of(sK14),
inference(resolution,[],[f299,f136]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(forward_subsumption_resolution,[],[f133,f134]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(forward_subsumption_resolution,[],[f302,f134]) ).
fof(f307,plain,
ilf_type(range(sK12,sK13,sK14),subset_type(sK13)),
inference(resolution,[],[f303,f136]) ).
fof(f318,plain,
( ~ subset(sK13,domain_of(sK14))
| spl15_1 ),
inference(superposition,[],[f174,f292]) ).
fof(f341,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X0)
| ~ member(X2,X1)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f155,f134]) ).
fof(f342,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,set_type)
| member(X2,X0)
| ~ member(X2,X1)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f341,f134]) ).
fof(f343,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,X0)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f342,f134]) ).
fof(f347,plain,
! [X2,X0,X1] :
( member(sK1(X0,X1),X2)
| member(X2,power_set(X1))
| subset(X0,X1) ),
inference(resolution,[],[f343,f203]) ).
fof(f351,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(forward_subsumption_resolution,[],[f77,f134]) ).
fof(f352,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(forward_subsumption_resolution,[],[f351,f134]) ).
fof(f353,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(forward_subsumption_resolution,[],[f352,f134]) ).
fof(f354,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK14)
| subset(X0,range(sK12,sK13,sK14)) ),
inference(resolution,[],[f353,f136]) ).
fof(f356,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK14)
| subset(X0,range_of(sK14)) ),
inference(forward_demodulation,[],[f354,f300]) ).
fof(f357,plain,
ilf_type(range_of(sK14),subset_type(sK13)),
inference(forward_demodulation,[],[f307,f300]) ).
fof(f358,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(forward_subsumption_resolution,[],[f78,f134]) ).
fof(f359,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(forward_subsumption_resolution,[],[f358,f134]) ).
fof(f360,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(forward_subsumption_resolution,[],[f359,f134]) ).
fof(f361,plain,
~ member(range_of(sK14),power_set(sK13)),
inference(resolution,[],[f357,f245]) ).
fof(f364,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK14)
| subset(X0,domain(sK12,sK13,sK14)) ),
inference(resolution,[],[f360,f136]) ).
fof(f366,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK14)
| subset(X0,domain_of(sK14)) ),
inference(forward_demodulation,[],[f364,f292]) ).
fof(f388,plain,
subset(sK13,range_of(sK14)),
inference(resolution,[],[f356,f137]) ).
fof(f390,plain,
subset(sK13,domain_of(sK14)),
inference(resolution,[],[f366,f137]) ).
fof(f392,plain,
( $false
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f390,f318]) ).
fof(f393,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f392]) ).
fof(f409,plain,
( sK13 != range_of(sK14)
| spl15_2 ),
inference(superposition,[],[f178,f300]) ).
fof(f543,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| subset(X0,X1)
| subset(X0,X1) ),
inference(resolution,[],[f347,f205]) ).
fof(f549,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f543]) ).
fof(f787,plain,
subset(range_of(sK14),sK13),
inference(resolution,[],[f549,f361]) ).
fof(f990,plain,
( ~ subset(sK13,range_of(sK14))
| sK13 = range_of(sK14) ),
inference(resolution,[],[f787,f211]) ).
fof(f991,plain,
sK13 = range_of(sK14),
inference(forward_subsumption_resolution,[],[f990,f388]) ).
fof(f992,plain,
( $false
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f991,f409]) ).
fof(f993,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f992]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(sat_conversion,[],[f179]) ).
cnf(s7,plain,
spl15_1,
inference(sat_conversion,[],[f393]) ).
cnf(s52,plain,
spl15_2,
inference(sat_conversion,[],[f993]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s1,s52,s7]) ).
fof(f994,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET669+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n001.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 02:35:02 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.47 % (4160247)Will run a generic schedule for satisfiability detection.
% 0.41/0.47 % (4160257)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1603816506:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.41/0.47 % (4160253)% WARNING: option uhcvi not known.
% 0.41/0.47 % (4160256)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1779421444:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.41/0.47 % (4160252)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2810263831_2999 on theBenchmark for (2999ds/0Mi)
% 0.41/0.47 % (4160254)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1107991698:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.41/0.47 % (4160255)dis+10_1_sil=32000:sp=arity:random_seed=3719935581:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.41/0.47 % (4160258)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3387203626:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.41/0.47 % (4160253)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2061246935:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.41/0.47 % TRYING [1]
% 0.41/0.47 % TRYING [2]
% 0.41/0.47 % TRYING [3]
% 0.41/0.47 % (4160253) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4160247-4160253"...
% 0.41/0.47 % (4160253)...printing done.
% 0.41/0.47 % (4160253)Refutation found. Thanks to Tanya!
% 0.41/0.47 % SZS status Theorem for theBenchmark
% 0.41/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.41/0.47 % (4160253)------------------------------
% 0.41/0.47 % (4160253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.47 % (4160253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.47 % (4160253)CaDiCaL version: 2.1.3
% 0.41/0.47 % (4160253)Termination reason: Refutation
% 0.41/0.47 % (4160253)Time elapsed: 0.026 s
% 0.41/0.47 % (4160253)Peak memory usage: 13 MB
% 0.41/0.47 % (4160253)Instructions burned: 31 (million)
% 0.41/0.47 % (4160247)Success in time 0.06 s
% 0.41/0.47 % Vampire exiting
%------------------------------------------------------------------------------