%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:41:31 PM UTC 2026
% Result : Theorem 3.10s 1.33s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 82 ( 12 unt; 2 def)
% Number of atoms : 322 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 400 ( 160 ~; 157 |; 42 &)
% ( 12 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 184 ( 0 sgn 172 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f10,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/sandbox/benchmark/theBenchmark.p',p10) ).
fof(f13,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/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f15,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/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f21,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f22,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_7) ).
fof(f23,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,X3) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f33,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,[],[f10]) ).
fof(f36,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,[],[f13]) ).
fof(f37,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,[],[f36]) ).
fof(f38,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f39,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,[],[f15]) ).
fof(f40,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,[],[f39]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X2,X0)
| ~ member(X3,X1) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(X0,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X2,X0)
| ~ member(X3,X1) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(X0,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f24]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f51]) ).
fof(f55,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,[],[f33]) ).
fof(f61,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,[],[f37]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0)
& ilf_type(sK3(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,[sK3]),skolemize(X2,sK3(X0,X1))],[f62]) ).
fof(f64,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,[],[f40]) ).
fof(f72,plain,
( ( ~ member(sK11,sK9)
| ~ member(sK12,sK10) )
& member(ordered_pair(sK11,sK12),sK13)
& ilf_type(sK13,relation_type(sK9,sK10))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK9,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12),skolemize(X4,sK13)],[f50]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f79,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f27]) ).
fof(f86,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,[],[f55]) ).
fof(f94,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,[],[f63]) ).
fof(f99,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f100,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,[],[f64]) ).
fof(f114,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f21]) ).
fof(f119,plain,
ilf_type(sK13,relation_type(sK9,sK10)),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
member(ordered_pair(sK11,sK12),sK13),
inference(cnf_transformation,[],[f72]) ).
fof(f121,plain,
( ~ member(sK11,sK9)
| ~ member(sK12,sK10) ),
inference(cnf_transformation,[],[f72]) ).
fof(f129,definition,
( spl14_1
<=> member(sK12,sK10) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f133,definition,
( spl14_2
<=> member(sK11,sK9) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f135,plain,
( ~ member(sK11,sK9)
| spl14_2 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f121,f133,f129]) ).
fof(f156,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f99,f114]) ).
fof(f185,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,[],[f86,f114]) ).
fof(f186,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f185,f114]) ).
fof(f193,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f100,f114]) ).
fof(f194,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f193,f114]) ).
fof(f218,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f79,f114]) ).
fof(f219,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f218,f114]) ).
fof(f249,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,[],[f94,f114]) ).
fof(f250,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f249,f114]) ).
fof(f251,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f250,f114]) ).
fof(f254,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f73,f114]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f254,f114]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f255,f114]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(forward_subsumption_resolution,[],[f256,f114]) ).
fof(f261,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X0),X3)
| member(X0,X1)
| ~ member(X3,power_set(cross_product(X4,X1))) ),
inference(resolution,[],[f257,f251]) ).
fof(f268,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f74,f114]) ).
fof(f269,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f268,f114]) ).
fof(f270,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type) ),
inference(forward_subsumption_resolution,[],[f269,f114]) ).
fof(f271,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(forward_subsumption_resolution,[],[f270,f114]) ).
fof(f275,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,X2),X3)
| member(X0,X1)
| ~ member(X3,power_set(cross_product(X1,X4))) ),
inference(resolution,[],[f271,f251]) ).
fof(f302,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X1,X0)))
| member(sK12,X0) ),
inference(resolution,[],[f261,f120]) ).
fof(f323,plain,
! [X0,X1] :
( member(sK11,X0)
| ~ member(sK13,power_set(cross_product(X0,X1))) ),
inference(resolution,[],[f275,f120]) ).
fof(f353,plain,
! [X0,X1] :
( member(sK12,X0)
| ~ ilf_type(sK13,member_type(power_set(cross_product(X1,X0))))
| empty(power_set(cross_product(X1,X0))) ),
inference(resolution,[],[f302,f194]) ).
fof(f354,plain,
! [X0,X1] :
( ~ ilf_type(sK13,member_type(power_set(cross_product(X1,X0))))
| member(sK12,X0) ),
inference(forward_subsumption_resolution,[],[f353,f156]) ).
fof(f369,plain,
! [X0,X1] :
( ~ ilf_type(sK13,subset_type(cross_product(X1,X0)))
| member(sK12,X0) ),
inference(resolution,[],[f354,f186]) ).
fof(f374,plain,
! [X0,X1] :
( ~ ilf_type(sK13,relation_type(X1,X0))
| member(sK12,X0) ),
inference(resolution,[],[f369,f219]) ).
fof(f380,plain,
member(sK12,sK10),
inference(resolution,[],[f374,f119]) ).
fof(f385,plain,
spl14_1,
inference(avatar_split_clause,[],[f380,f129]) ).
fof(f386,plain,
( ! [X0] : ~ member(sK13,power_set(cross_product(sK9,X0)))
| spl14_2 ),
inference(resolution,[],[f135,f323]) ).
fof(f405,plain,
( ! [X0] :
( ~ ilf_type(sK13,member_type(power_set(cross_product(sK9,X0))))
| empty(power_set(cross_product(sK9,X0))) )
| spl14_2 ),
inference(resolution,[],[f386,f194]) ).
fof(f406,plain,
( ! [X0] : ~ ilf_type(sK13,member_type(power_set(cross_product(sK9,X0))))
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f405,f156]) ).
fof(f411,plain,
( ! [X0] : ~ ilf_type(sK13,subset_type(cross_product(sK9,X0)))
| spl14_2 ),
inference(resolution,[],[f406,f186]) ).
fof(f416,plain,
( ! [X0] : ~ ilf_type(sK13,relation_type(sK9,X0))
| spl14_2 ),
inference(resolution,[],[f411,f219]) ).
fof(f441,plain,
( $false
| spl14_2 ),
inference(resolution,[],[f416,f119]) ).
fof(f443,plain,
spl14_2,
inference(avatar_contradiction_clause,[],[f441]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f136]) ).
cnf(s12,plain,
spl14_1,
inference(sat_conversion,[],[f385]) ).
cnf(s15,plain,
spl14_2,
inference(sat_conversion,[],[f443]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s15,s12]) ).
fof(f444,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 02:28:56 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.10/1.33 % (3977451)Detected formulas, will run a generic FOF schedule.
% 3.10/1.33 % (3977460)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3722399367:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.10/1.33 % (3977460)Refutation not found, incomplete strategy
% 3.10/1.33 % (3977460)------------------------------
% 3.10/1.33 % (3977460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.33 % (3977460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.33 % (3977460)CaDiCaL version: 2.1.3
% 3.10/1.33 % (3977460)Termination reason: Refutation not found, incomplete strategy
% 3.10/1.33 % (3977460)Time elapsed: 0.001 s
% 3.10/1.33 % (3977460)Peak memory usage: 88 MB
% 3.10/1.33 % (3977460)Instructions burned: 1 (million)
% 3.10/1.33 % (3977459)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1643546885:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.10/1.33 % (3977462)dis-21_1_sil=8000:lcm=predicate:random_seed=3421672466: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)
% 3.10/1.33 % (3977456)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=3566980664:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.10/1.33 % (3977461)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1442841638:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.10/1.33 % (3977457)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=3711531321:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.10/1.33 % (3977458)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=3500973238:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.10/1.33 % (3977459)Refutation not found, incomplete strategy
% 3.10/1.33 % (3977459)------------------------------
% 3.10/1.33 % (3977459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.33 % (3977459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.33 % (3977459)CaDiCaL version: 2.1.3
% 3.10/1.33 % (3977459)Termination reason: Refutation not found, incomplete strategy
% 3.10/1.33 % (3977459)Time elapsed: 0.001 s
% 3.10/1.33 % (3977459)Peak memory usage: 87 MB
% 3.10/1.33 % (3977461)First to succeed.
% 3.10/1.33 % (3977461)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3977451"
% 3.10/1.33 % (3977462)Instruction limit reached!
% 3.10/1.33 % (3977462)------------------------------
% 3.10/1.33 % (3977462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.33 % (3977462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.33 % (3977462)CaDiCaL version: 2.1.3
% 3.10/1.33 % (3977462)Termination reason: Instruction limit
% 3.10/1.33 % (3977462)Termination phase: Saturation
% 3.10/1.33 % (3977462)Time elapsed: 0.079 s
% 3.10/1.33 % (3977462)Peak memory usage: 90 MB
% 3.10/1.33 % (3977462)Instructions burned: 129 (million)
% 3.10/1.33 % (3977460)------------------------------
% 3.10/1.33 % (3977460)------------------------------
% 3.10/1.33 % (3977459)------------------------------
% 3.10/1.33 % (3977459)------------------------------
% 3.10/1.33 % (3977470)lrs+10_1_sil=8000:sp=occurrence:random_seed=968336751:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.10/1.33 % (3977471)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3364828097:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.10/1.33 % (3977461)Refutation found. Thanks to Tanya!
% 3.10/1.33 % SZS status Theorem for theBenchmark
% 3.10/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.53 % (3977461)------------------------------
% 3.79/1.53 % (3977461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.53 % (3977461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.53 % (3977461)CaDiCaL version: 2.1.3
% 3.79/1.53 % (3977461)Termination reason: Refutation
% 3.79/1.53 % (3977461)Time elapsed: 0.014 s
% 3.79/1.53 % (3977461)Peak memory usage: 90 MB
% 3.79/1.53 % (3977461)Instructions burned: 17 (million)
% 3.79/1.53 % (3977461)------------------------------
% 3.79/1.53 % (3977461)------------------------------
% 3.79/1.53 % (3977451)Success in time 0.448 s
% 3.79/1.53 % Vampire exiting
%------------------------------------------------------------------------------