%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET686+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:44:25 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 144 ( 13 unt; 9 def)
% Number of atoms : 575 ( 8 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 703 ( 272 ~; 332 |; 42 &)
% ( 20 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 250 ( 0 sgn 234 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) ) ) ) ) ),
file('/export/starexec/sandbox/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,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',p2) ).
fof(f5,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',p5) ).
fof(f7,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',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f25,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_53) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,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,[],[f2]) ).
fof(f32,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,[],[f31]) ).
fof(f35,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,[],[f5]) ).
fof(f37,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,[],[f7]) ).
fof(f38,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,[],[f37]) ).
fof(f41,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f47,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f61,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(sK0(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| member(ordered_pair(X1,sK0(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type)
| member(X1,inverse2(X2,X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f73,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[],[f35]) ).
fof(f75,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,[],[f38]) ).
fof(f78,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f87,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f113,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f114,plain,
! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(sK15,X5),sK14)
| ~ ilf_type(X5,member_type(sK13))
| ~ member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f115,plain,
( member(sK16,sK12)
| member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f116,plain,
( member(ordered_pair(sK15,sK16),sK14)
| member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f119,plain,
ilf_type(sK14,relation_type(sK11,sK13)),
inference(cnf_transformation,[],[f62]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,binary_relation_type)
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ilf_type(X3,set_type)
| member(X1,inverse2(X2,X0)) ),
inference(consistent_polarity_flipping,[],[f66]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,binary_relation_type)
| member(ordered_pair(X1,sK0(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0)) ),
inference(consistent_polarity_flipping,[],[f64]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,binary_relation_type)
| member(sK0(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0)) ),
inference(consistent_polarity_flipping,[],[f63]) ).
fof(f135,plain,
! [X2,X3,X0,X1,X4] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,set_type)
| ilf_type(X3,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) ),
inference(consistent_polarity_flipping,[],[f67]) ).
fof(f139,plain,
! [X3,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f73]) ).
fof(f143,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,[],[f75]) ).
fof(f147,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ~ member(X1,X0)
| ~ empty(X0) ),
inference(consistent_polarity_flipping,[],[f78]) ).
fof(f153,plain,
! [X0] :
( ilf_type(X0,set_type)
| relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(consistent_polarity_flipping,[],[f87]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ relation_like(X2) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,relation_type(X0,X1))
| ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(consistent_polarity_flipping,[],[f111]) ).
fof(f180,plain,
! [X0] : ~ ilf_type(X0,set_type),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f184,plain,
~ ilf_type(sK14,relation_type(sK11,sK13)),
inference(consistent_polarity_flipping,[],[f119]) ).
fof(f187,plain,
! [X5] :
( ~ member(X5,sK12)
| ~ member(ordered_pair(sK15,X5),sK14)
| ilf_type(X5,member_type(sK13))
| ~ member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f191,definition,
( spl17_1
<=> member(sK15,inverse4(sK11,sK13,sK14,sK12)) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f192,plain,
( member(sK15,inverse4(sK11,sK13,sK14,sK12))
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f193,plain,
( ~ member(sK15,inverse4(sK11,sK13,sK14,sK12))
| spl17_1 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f195,definition,
( spl17_2
<=> ! [X5] :
( ~ member(X5,sK12)
| ilf_type(X5,member_type(sK13))
| ~ member(ordered_pair(sK15,X5),sK14) ) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f196,plain,
( ! [X5] :
( ~ member(ordered_pair(sK15,X5),sK14)
| ilf_type(X5,member_type(sK13))
| ~ member(X5,sK12) )
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f197,plain,
( ~ spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f187,f195,f191]) ).
fof(f199,definition,
( spl17_3
<=> member(sK16,sK12) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f202,plain,
( spl17_1
| spl17_3 ),
inference(avatar_split_clause,[],[f115,f199,f191]) ).
fof(f204,definition,
( spl17_4
<=> member(ordered_pair(sK15,sK16),sK14) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f206,plain,
( member(ordered_pair(sK15,sK16),sK14)
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
( spl17_1
| spl17_4 ),
inference(avatar_split_clause,[],[f116,f204,f191]) ).
fof(f214,definition,
( spl17_6
<=> ! [X1] : ~ ilf_type(X1,set_type) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
fof(f215,plain,
( ! [X1] : ~ ilf_type(X1,set_type)
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f228,plain,
spl17_6,
inference(avatar_split_clause,[],[f180,f214]) ).
fof(f239,plain,
( ! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f153,f215]) ).
fof(f248,plain,
( ! [X0,X1] :
( ilf_type(X1,set_type)
| ~ member(X1,X0)
| ~ empty(X0) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f147,f215]) ).
fof(f249,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ member(X1,X0) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f248,f215]) ).
fof(f252,plain,
( ! [X2,X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ relation_like(X2) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f177,f215]) ).
fof(f253,plain,
( ! [X2,X0,X1] :
( ~ relation_like(X2)
| ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f252,f215]) ).
fof(f262,plain,
( ! [X0,X1] :
( ilf_type(X1,set_type)
| empty(X1)
| ~ member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f143,f215]) ).
fof(f263,plain,
( ! [X0,X1] :
( empty(X1)
| ~ member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f262,f215]) ).
fof(f264,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f263,f249]) ).
fof(f282,plain,
( ! [X3,X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f139,f215]) ).
fof(f283,plain,
( ! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f282,f215]) ).
fof(f330,definition,
( spl17_15
<=> relation_like(sK14) ),
introduced(definition,[new_symbols(definition,[spl17_15])],[avatar_definition]) ).
fof(f331,plain,
( ~ relation_like(sK14)
| spl17_15 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f332,plain,
( relation_like(sK14)
| ~ spl17_15 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f338,plain,
( ! [X0,X1] : ilf_type(sK14,subset_type(cross_product(X0,X1)))
| ~ spl17_6
| ~ spl17_15 ),
inference(resolution,[],[f332,f253]) ).
fof(f344,plain,
( ! [X0,X1] : ilf_type(sK14,relation_type(X0,X1))
| ~ spl17_6
| ~ spl17_15 ),
inference(resolution,[],[f338,f283]) ).
fof(f347,plain,
( $false
| ~ spl17_6
| ~ spl17_15 ),
inference(backward_subsumption_resolution,[],[f184,f344]) ).
fof(f349,plain,
( ~ spl17_6
| ~ spl17_15 ),
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f375,plain,
( ! [X2,X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X2,binary_relation_type)
| member(sK0(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f133,f215]) ).
fof(f376,plain,
( ! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X0)
| ilf_type(X2,binary_relation_type)
| ~ member(X1,inverse2(X2,X0)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f375,f215]) ).
fof(f382,plain,
( ! [X2,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X2,binary_relation_type)
| member(ordered_pair(X1,sK0(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f132,f215]) ).
fof(f383,plain,
( ! [X2,X0,X1] :
( member(ordered_pair(X1,sK0(X0,X1,X2)),X2)
| ilf_type(X2,binary_relation_type)
| ~ member(X1,inverse2(X2,X0)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f382,f215]) ).
fof(f396,plain,
( ! [X2,X3,X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X2,relation_type(X0,X1))
| ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f178,f215]) ).
fof(f397,plain,
( ! [X2,X3,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f396,f215]) ).
fof(f398,plain,
( ! [X2,X3,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f397,f215]) ).
fof(f401,plain,
( ! [X0] : inverse4(sK11,sK13,sK14,X0) = inverse2(sK14,X0)
| ~ spl17_6 ),
inference(resolution,[],[f398,f184]) ).
fof(f402,plain,
( ! [X2,X3,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,binary_relation_type)
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| member(X1,inverse2(X2,X0)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f130,f215]) ).
fof(f403,plain,
( ! [X2,X3,X0,X1] :
( ilf_type(X0,set_type)
| ilf_type(X2,binary_relation_type)
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| member(X1,inverse2(X2,X0)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f402,f215]) ).
fof(f404,plain,
( ! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0)
| ilf_type(X2,binary_relation_type)
| member(X1,inverse2(X2,X0)) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f403,f215]) ).
fof(f405,plain,
( ! [X0] :
( ~ member(sK16,X0)
| ilf_type(sK14,binary_relation_type)
| member(sK15,inverse2(sK14,X0)) )
| ~ spl17_4
| ~ spl17_6 ),
inference(resolution,[],[f404,f206]) ).
fof(f414,definition,
( spl17_17
<=> ilf_type(sK14,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl17_17])],[avatar_definition]) ).
fof(f415,plain,
( ~ ilf_type(sK14,binary_relation_type)
| spl17_17 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f416,plain,
( ilf_type(sK14,binary_relation_type)
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f418,definition,
( spl17_18
<=> ! [X0] :
( ~ member(sK16,X0)
| member(sK15,inverse2(sK14,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
fof(f419,plain,
( ! [X0] :
( member(sK15,inverse2(sK14,X0))
| ~ member(sK16,X0) )
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f432,plain,
( relation_like(sK14)
| ~ spl17_6
| ~ spl17_17 ),
inference(resolution,[],[f416,f239]) ).
fof(f433,plain,
( $false
| ~ spl17_6
| spl17_15
| ~ spl17_17 ),
inference(forward_subsumption_resolution,[],[f432,f331]) ).
fof(f434,plain,
( ~ spl17_6
| spl17_15
| ~ spl17_17 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f435,plain,
( ! [X2,X3,X0,X1,X4] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X2,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f135,f215]) ).
fof(f436,plain,
( ! [X2,X3,X0,X1,X4] :
( ilf_type(X0,set_type)
| ilf_type(X1,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f435,f215]) ).
fof(f437,plain,
( ! [X2,X3,X0,X1,X4] :
( ilf_type(X0,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f436,f215]) ).
fof(f438,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| ilf_type(X4,relation_type(X0,X1))
| member(X3,X1) )
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f437,f215]) ).
fof(f440,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X4,inverse2(X0,X3))
| member(sK0(X3,X4,X0),X2)
| ilf_type(X0,binary_relation_type)
| ilf_type(X0,relation_type(X1,X2)) )
| ~ spl17_6 ),
inference(resolution,[],[f438,f383]) ).
fof(f518,plain,
( member(sK15,inverse2(sK14,sK12))
| ~ spl17_1
| ~ spl17_6 ),
inference(forward_demodulation,[],[f192,f401]) ).
fof(f530,plain,
( ! [X0] :
( ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ilf_type(sK14,binary_relation_type)
| ~ member(sK15,inverse2(sK14,X0)) )
| ~ spl17_2
| ~ spl17_6 ),
inference(resolution,[],[f196,f383]) ).
fof(f531,plain,
( ! [X0] :
( ~ member(sK0(X0,sK15,sK14),sK12)
| ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK15,inverse2(sK14,X0)) )
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(forward_subsumption_resolution,[],[f530,f415]) ).
fof(f532,plain,
( ilf_type(sK0(sK12,sK15,sK14),member_type(sK13))
| ~ member(sK15,inverse2(sK14,sK12))
| ilf_type(sK14,binary_relation_type)
| ~ member(sK15,inverse2(sK14,sK12))
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(resolution,[],[f531,f376]) ).
fof(f533,plain,
( ilf_type(sK0(sK12,sK15,sK14),member_type(sK13))
| ~ member(sK15,inverse2(sK14,sK12))
| ilf_type(sK14,binary_relation_type)
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(duplicate_literal_removal,[],[f532]) ).
fof(f534,plain,
( ilf_type(sK0(sK12,sK15,sK14),member_type(sK13))
| ilf_type(sK14,binary_relation_type)
| ~ spl17_1
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(forward_subsumption_resolution,[],[f533,f518]) ).
fof(f535,plain,
( ilf_type(sK0(sK12,sK15,sK14),member_type(sK13))
| ~ spl17_1
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(forward_subsumption_resolution,[],[f534,f415]) ).
fof(f604,plain,
( ! [X0,X1] :
( member(sK0(sK12,sK15,sK14),X0)
| ilf_type(sK14,binary_relation_type)
| ilf_type(sK14,relation_type(X1,X0)) )
| ~ spl17_1
| ~ spl17_6 ),
inference(resolution,[],[f440,f518]) ).
fof(f605,plain,
( ! [X0,X1] :
( member(sK0(sK12,sK15,sK14),X0)
| ilf_type(sK14,relation_type(X1,X0)) )
| ~ spl17_1
| ~ spl17_6
| spl17_17 ),
inference(forward_subsumption_resolution,[],[f604,f415]) ).
fof(f640,plain,
( ~ member(sK0(sK12,sK15,sK14),sK13)
| ~ spl17_1
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(resolution,[],[f535,f264]) ).
fof(f675,plain,
( ~ member(sK15,inverse2(sK14,sK12))
| spl17_1
| ~ spl17_6 ),
inference(forward_demodulation,[],[f193,f401]) ).
fof(f676,plain,
( ! [X0] :
( ~ member(sK16,X0)
| member(sK15,inverse2(sK14,X0)) )
| ~ spl17_4
| ~ spl17_6
| spl17_17 ),
inference(forward_subsumption_resolution,[],[f405,f415]) ).
fof(f681,plain,
( spl17_18
| ~ spl17_4
| ~ spl17_6
| spl17_17 ),
inference(avatar_split_clause,[],[f676,f414,f214,f204,f418]) ).
fof(f684,definition,
( spl17_29
<=> member(sK15,inverse2(sK14,sK12)) ),
introduced(definition,[new_symbols(definition,[spl17_29])],[avatar_definition]) ).
fof(f686,plain,
( ~ member(sK15,inverse2(sK14,sK12))
| spl17_29 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f701,plain,
( ~ spl17_29
| spl17_1
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f675,f214,f191,f684]) ).
fof(f734,plain,
( ~ member(sK16,sK12)
| ~ spl17_18
| spl17_29 ),
inference(resolution,[],[f686,f419]) ).
fof(f748,plain,
( ~ spl17_3
| ~ spl17_18
| spl17_29 ),
inference(avatar_split_clause,[],[f734,f684,f418,f199]) ).
fof(f785,plain,
( ! [X0] : ilf_type(sK14,relation_type(X0,sK13))
| ~ spl17_1
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(resolution,[],[f605,f640]) ).
fof(f807,plain,
( $false
| ~ spl17_1
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(backward_subsumption_resolution,[],[f184,f785]) ).
fof(f809,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(avatar_contradiction_clause,[],[f807]) ).
cnf(s1,plain,
( ~ spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f197]) ).
cnf(s2,plain,
( spl17_1
| spl17_3 ),
inference(sat_conversion,[],[f202]) ).
cnf(s3,plain,
( spl17_1
| spl17_4 ),
inference(sat_conversion,[],[f207]) ).
cnf(s10,plain,
spl17_6,
inference(sat_conversion,[],[f228]) ).
cnf(s16,plain,
( ~ spl17_6
| ~ spl17_15 ),
inference(sat_conversion,[],[f349]) ).
cnf(s18,plain,
( ~ spl17_6
| spl17_15
| ~ spl17_17 ),
inference(sat_conversion,[],[f434]) ).
cnf(s29,plain,
( ~ spl17_4
| ~ spl17_6
| spl17_17
| spl17_18 ),
inference(sat_conversion,[],[f681]) ).
cnf(s35,plain,
( spl17_1
| ~ spl17_6
| ~ spl17_29 ),
inference(sat_conversion,[],[f701]) ).
cnf(s47,plain,
( ~ spl17_3
| ~ spl17_18
| spl17_29 ),
inference(sat_conversion,[],[f748]) ).
cnf(s58,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_6
| spl17_17 ),
inference(sat_conversion,[],[f809]) ).
cnf(s60,plain,
~ spl17_15,
inference(rat,[],[s16,s10]) ).
cnf(s62,plain,
~ spl17_17,
inference(rat,[],[s18,s10,s60]) ).
cnf(s65,plain,
spl17_1,
inference(rat,[],[s47,s29,s2,s3,s35,s10,s62]) ).
cnf(s66,plain,
~ spl17_2,
inference(rat,[],[s58,s62,s10,s65]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s1,s66,s65]) ).
fof(f810,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET686+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:34:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % (3419831)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (3419838)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1098129847:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.46 % (3419839)dis+10_1_sil=32000:sp=arity:random_seed=1151460316:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (3419836)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2700044653_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % (3419841)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1838581985:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.46 % (3419837)% WARNING: option uhcvi not known.
% 0.10/0.46 % (3419840)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=195135249:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.46 % (3419842)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=917624900:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.46 % (3419837)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=130844429:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % (3419837) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3419831-3419837"...
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (3419837)...printing done.
% 0.10/0.46 % (3419837)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (3419837)------------------------------
% 0.10/0.46 % (3419837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (3419837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (3419837)CaDiCaL version: 2.1.3
% 0.10/0.46 % (3419837)Termination reason: Refutation
% 0.10/0.46 % (3419837)Time elapsed: 0.014 s
% 0.10/0.46 % (3419837)Peak memory usage: 13 MB
% 0.10/0.46 % (3419837)Instructions burned: 33 (million)
% 0.10/0.46 % (3419831)Success in time 0.05 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------