%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET666+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 12:44:22 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 128 ( 23 unt; 13 def)
% Number of atoms : 422 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 519 ( 225 ~; 218 |; 28 &)
% ( 26 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 96 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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',p1) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f12,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',p12) ).
fof(f14,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/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f16,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',p16) ).
fof(f17,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',p17) ).
fof(f18,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',p18) ).
fof(f24,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f25,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_29) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
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,[],[f1]) ).
fof(f29,plain,
! [X0] :
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f37,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,[],[f12]) ).
fof(f39,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,[],[f14]) ).
fof(f40,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,[],[f39]) ).
fof(f42,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,[],[f16]) ).
fof(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f45,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,[],[f18]) ).
fof(f46,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,[],[f45]) ).
fof(f55,plain,
? [X0] :
( ~ ilf_type(identity_relation_of(X0),identity_relation_of_type(X0))
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0)) )
& ( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f64,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,[],[f37]) ).
fof(f66,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,[],[f40]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0)
& ilf_type(sK4(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,[sK4]),skolemize(X2,sK4(X0,X1))],[f67]) ).
fof(f69,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,[],[f43]) ).
fof(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0)
& ilf_type(sK5(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,[sK5]),skolemize(X2,sK5(X0,X1))],[f70]) ).
fof(f72,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,[],[f46]) ).
fof(f80,plain,
( ~ ilf_type(identity_relation_of(sK11),identity_relation_of_type(sK11))
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f55]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f27]) ).
fof(f84,plain,
! [X0] :
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f29]) ).
fof(f90,plain,
! [X0,X1] :
( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f99,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(cnf_transformation,[],[f64]) ).
fof(f101,plain,
! [X3,X0,X1] :
( 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(cnf_transformation,[],[f68]) ).
fof(f108,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f109,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f111,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f113,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(cnf_transformation,[],[f72]) ).
fof(f126,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f24]) ).
fof(f128,plain,
~ ilf_type(identity_relation_of(sK11),identity_relation_of_type(sK11)),
inference(cnf_transformation,[],[f80]) ).
fof(f132,plain,
! [X0] :
( empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f111]) ).
fof(f133,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(consistent_polarity_flipping,[],[f113]) ).
fof(f185,plain,
( ~ ilf_type(identity_relation_of(sK11),relation_type(sK11,sK11))
| ~ ilf_type(identity_relation_of(sK11),set_type)
| ~ ilf_type(sK11,set_type) ),
inference(resolution,[],[f90,f128]) ).
fof(f187,definition,
( spl12_3
<=> ilf_type(sK11,set_type) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f189,plain,
( ~ ilf_type(sK11,set_type)
| spl12_3 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,definition,
( spl12_4
<=> ilf_type(identity_relation_of(sK11),set_type) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f193,plain,
( ~ ilf_type(identity_relation_of(sK11),set_type)
| spl12_4 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f195,definition,
( spl12_5
<=> ilf_type(identity_relation_of(sK11),relation_type(sK11,sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f197,plain,
( ~ ilf_type(identity_relation_of(sK11),relation_type(sK11,sK11))
| spl12_5 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( ~ spl12_3
| ~ spl12_4
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f185,f195,f191,f187]) ).
fof(f199,plain,
( $false
| spl12_3 ),
inference(resolution,[],[f189,f126]) ).
fof(f200,plain,
spl12_3,
inference(avatar_contradiction_clause,[],[f199]) ).
fof(f201,plain,
( $false
| spl12_4 ),
inference(resolution,[],[f193,f126]) ).
fof(f202,plain,
spl12_4,
inference(avatar_contradiction_clause,[],[f201]) ).
fof(f238,plain,
( ~ ilf_type(identity_relation_of(sK11),subset_type(cross_product(sK11,sK11)))
| ~ ilf_type(sK11,set_type)
| ~ ilf_type(sK11,set_type)
| spl12_5 ),
inference(resolution,[],[f82,f197]) ).
fof(f243,plain,
( ~ ilf_type(identity_relation_of(sK11),subset_type(cross_product(sK11,sK11)))
| ~ ilf_type(sK11,set_type)
| spl12_5 ),
inference(duplicate_literal_removal,[],[f238]) ).
fof(f245,definition,
( spl12_6
<=> ilf_type(identity_relation_of(sK11),subset_type(cross_product(sK11,sK11))) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f247,plain,
( ~ ilf_type(identity_relation_of(sK11),subset_type(cross_product(sK11,sK11)))
| spl12_6 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,plain,
( ~ spl12_3
| ~ spl12_6
| spl12_5 ),
inference(avatar_split_clause,[],[f243,f195,f245,f187]) ).
fof(f250,plain,
( ~ ilf_type(identity_relation_of(sK11),member_type(power_set(cross_product(sK11,sK11))))
| ~ ilf_type(identity_relation_of(sK11),set_type)
| ~ ilf_type(cross_product(sK11,sK11),set_type)
| spl12_6 ),
inference(resolution,[],[f247,f99]) ).
fof(f253,definition,
( spl12_7
<=> ilf_type(cross_product(sK11,sK11),set_type) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f255,plain,
( ~ ilf_type(cross_product(sK11,sK11),set_type)
| spl12_7 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f257,definition,
( spl12_8
<=> ilf_type(identity_relation_of(sK11),member_type(power_set(cross_product(sK11,sK11)))) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f259,plain,
( ~ ilf_type(identity_relation_of(sK11),member_type(power_set(cross_product(sK11,sK11))))
| spl12_8 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
( ~ spl12_7
| ~ spl12_4
| ~ spl12_8
| spl12_6 ),
inference(avatar_split_clause,[],[f250,f245,f257,f191,f253]) ).
fof(f261,plain,
( $false
| spl12_7 ),
inference(resolution,[],[f255,f126]) ).
fof(f262,plain,
spl12_7,
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f264,plain,
( ~ member(identity_relation_of(sK11),power_set(cross_product(sK11,sK11)))
| ~ empty(power_set(cross_product(sK11,sK11)))
| ~ ilf_type(power_set(cross_product(sK11,sK11)),set_type)
| ~ ilf_type(identity_relation_of(sK11),set_type)
| spl12_8 ),
inference(resolution,[],[f259,f133]) ).
fof(f266,definition,
( spl12_9
<=> ilf_type(power_set(cross_product(sK11,sK11)),set_type) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f268,plain,
( ~ ilf_type(power_set(cross_product(sK11,sK11)),set_type)
| spl12_9 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f270,definition,
( spl12_10
<=> empty(power_set(cross_product(sK11,sK11))) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f272,plain,
( ~ empty(power_set(cross_product(sK11,sK11)))
| spl12_10 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f274,definition,
( spl12_11
<=> member(identity_relation_of(sK11),power_set(cross_product(sK11,sK11))) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f276,plain,
( ~ member(identity_relation_of(sK11),power_set(cross_product(sK11,sK11)))
| spl12_11 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f277,plain,
( ~ spl12_4
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| spl12_8 ),
inference(avatar_split_clause,[],[f264,f257,f274,f270,f266,f191]) ).
fof(f278,plain,
( ~ ilf_type(cross_product(sK11,sK11),set_type)
| spl12_10 ),
inference(resolution,[],[f272,f132]) ).
fof(f281,plain,
( ~ spl12_7
| spl12_10 ),
inference(avatar_split_clause,[],[f278,f270,f253]) ).
fof(f282,plain,
( $false
| spl12_9 ),
inference(resolution,[],[f268,f126]) ).
fof(f283,plain,
spl12_9,
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f284,plain,
( ~ member(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),cross_product(sK11,sK11))
| ~ ilf_type(cross_product(sK11,sK11),set_type)
| ~ ilf_type(identity_relation_of(sK11),set_type)
| spl12_11 ),
inference(resolution,[],[f276,f109]) ).
fof(f287,definition,
( spl12_12
<=> member(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),cross_product(sK11,sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f289,plain,
( ~ member(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),cross_product(sK11,sK11))
| spl12_12 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f290,plain,
( ~ spl12_4
| ~ spl12_7
| ~ spl12_12
| spl12_11 ),
inference(avatar_split_clause,[],[f284,f274,f287,f253,f191]) ).
fof(f293,definition,
( spl12_13
<=> ilf_type(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),set_type) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
fof(f295,plain,
( ~ ilf_type(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),set_type)
| spl12_13 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f322,plain,
( $false
| spl12_13 ),
inference(resolution,[],[f295,f126]) ).
fof(f323,plain,
spl12_13,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f387,plain,
( ! [X0] :
( ~ member(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),X0)
| ~ ilf_type(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),set_type)
| ~ subset(X0,cross_product(sK11,sK11))
| ~ ilf_type(cross_product(sK11,sK11),set_type)
| ~ ilf_type(X0,set_type) )
| spl12_12 ),
inference(resolution,[],[f101,f289]) ).
fof(f390,definition,
( spl12_19
<=> ! [X0] :
( ~ member(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),X0)
| ~ ilf_type(X0,set_type)
| ~ subset(X0,cross_product(sK11,sK11)) ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
fof(f391,plain,
( ! [X0] :
( ~ member(sK5(identity_relation_of(sK11),cross_product(sK11,sK11)),X0)
| ~ ilf_type(X0,set_type)
| ~ subset(X0,cross_product(sK11,sK11)) )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f392,plain,
( ~ spl12_7
| ~ spl12_13
| spl12_19
| spl12_12 ),
inference(avatar_split_clause,[],[f387,f287,f390,f293,f253]) ).
fof(f414,plain,
( ~ ilf_type(identity_relation_of(sK11),set_type)
| ~ subset(identity_relation_of(sK11),cross_product(sK11,sK11))
| member(identity_relation_of(sK11),power_set(cross_product(sK11,sK11)))
| ~ ilf_type(cross_product(sK11,sK11),set_type)
| ~ ilf_type(identity_relation_of(sK11),set_type)
| ~ spl12_19 ),
inference(resolution,[],[f391,f108]) ).
fof(f420,plain,
( ~ ilf_type(identity_relation_of(sK11),set_type)
| ~ subset(identity_relation_of(sK11),cross_product(sK11,sK11))
| member(identity_relation_of(sK11),power_set(cross_product(sK11,sK11)))
| ~ ilf_type(cross_product(sK11,sK11),set_type)
| ~ spl12_19 ),
inference(duplicate_literal_removal,[],[f414]) ).
fof(f434,definition,
( spl12_27
<=> subset(identity_relation_of(sK11),cross_product(sK11,sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_27])],[avatar_definition]) ).
fof(f436,plain,
( ~ subset(identity_relation_of(sK11),cross_product(sK11,sK11))
| spl12_27 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f437,plain,
( ~ spl12_7
| spl12_11
| ~ spl12_27
| ~ spl12_4
| ~ spl12_19 ),
inference(avatar_split_clause,[],[f420,f390,f191,f434,f274,f253]) ).
fof(f438,plain,
( ~ ilf_type(sK11,set_type)
| spl12_27 ),
inference(resolution,[],[f436,f84]) ).
fof(f439,plain,
( ~ spl12_3
| spl12_27 ),
inference(avatar_split_clause,[],[f438,f434,f187]) ).
cnf(s3,plain,
( ~ spl12_3
| ~ spl12_4
| ~ spl12_5 ),
inference(sat_conversion,[],[f198]) ).
cnf(s4,plain,
spl12_3,
inference(sat_conversion,[],[f200]) ).
cnf(s5,plain,
spl12_4,
inference(sat_conversion,[],[f202]) ).
cnf(s6,plain,
( ~ spl12_3
| spl12_5
| ~ spl12_6 ),
inference(sat_conversion,[],[f248]) ).
cnf(s7,plain,
( ~ spl12_4
| spl12_6
| ~ spl12_7
| ~ spl12_8 ),
inference(sat_conversion,[],[f260]) ).
cnf(s8,plain,
spl12_7,
inference(sat_conversion,[],[f262]) ).
cnf(s9,plain,
( ~ spl12_4
| spl12_8
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11 ),
inference(sat_conversion,[],[f277]) ).
cnf(s10,plain,
( ~ spl12_7
| spl12_10 ),
inference(sat_conversion,[],[f281]) ).
cnf(s11,plain,
spl12_9,
inference(sat_conversion,[],[f283]) ).
cnf(s12,plain,
( ~ spl12_4
| ~ spl12_7
| spl12_11
| ~ spl12_12 ),
inference(sat_conversion,[],[f290]) ).
cnf(s17,plain,
spl12_13,
inference(sat_conversion,[],[f323]) ).
cnf(s18,plain,
( ~ spl12_7
| spl12_12
| ~ spl12_13
| spl12_19 ),
inference(sat_conversion,[],[f392]) ).
cnf(s26,plain,
( ~ spl12_4
| ~ spl12_7
| spl12_11
| ~ spl12_19
| ~ spl12_27 ),
inference(sat_conversion,[],[f437]) ).
cnf(s27,plain,
( ~ spl12_3
| spl12_27 ),
inference(sat_conversion,[],[f439]) ).
cnf(s29,plain,
( ~ spl12_4
| spl12_8
| ~ spl12_10
| ~ spl12_11 ),
inference(rat,[],[s9,s11]) ).
cnf(s30,plain,
spl12_10,
inference(rat,[],[s10,s8]) ).
cnf(s31,plain,
( ~ spl12_4
| spl12_6
| ~ spl12_8 ),
inference(rat,[],[s7,s8]) ).
cnf(s32,plain,
spl12_27,
inference(rat,[],[s27,s4]) ).
cnf(s33,plain,
~ spl12_5,
inference(rat,[],[s3,s5,s4]) ).
cnf(s34,plain,
~ spl12_6,
inference(rat,[],[s6,s4,s33]) ).
cnf(s35,plain,
~ spl12_8,
inference(rat,[],[s31,s5,s34]) ).
cnf(s36,plain,
~ spl12_11,
inference(rat,[],[s29,s5,s30,s35]) ).
cnf(s38,plain,
~ spl12_19,
inference(rat,[],[s26,s32,s5,s8,s36]) ).
cnf(s39,plain,
~ spl12_12,
inference(rat,[],[s12,s5,s8,s36]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s18,s8,s17,s38,s39]) ).
fof(f440,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET666+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:31:26 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.18/0.48 % (3416436)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (3416456)dis+10_1_sil=32000:sp=arity:random_seed=2539612924:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (3416453)% WARNING: option uhcvi not known.
% 0.18/0.48 % (3416454)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1755850993:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (3416452)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1184642617_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (3416453)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2912943804:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (3416457)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3251149207:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (3416458)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2575959899:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (3416459)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=277139227:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % (3416459) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3416436-3416459"...
% 0.18/0.48 % (3416459)...printing done.
% 0.18/0.48 % (3416459)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (3416459)------------------------------
% 0.18/0.48 % (3416459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3416459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3416459)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3416459)Termination reason: Refutation
% 0.18/0.48 % (3416459)Time elapsed: 0.010 s
% 0.18/0.48 % (3416459)Peak memory usage: 12 MB
% 0.18/0.48 % (3416459)Instructions burned: 13 (million)
% 0.18/0.48 % (3416436)Success in time 0.051 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------