%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET675+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 : n008.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 12:41:37 PM UTC 2026
% Result : Theorem 2.28s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 116 ( 16 unt; 4 def)
% Number of atoms : 317 ( 74 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 348 ( 147 ~; 144 |; 18 &)
% ( 6 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 162 ( 0 sgn 159 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> image(X0,domain_of(X0)) = range_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> inverse2(X0,range_of(X0)) = domain_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( image4(X0,X1,X2,X0) = range(X0,X1,X2)
& inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
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(f12,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',p12) ).
fof(f23,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',p23) ).
fof(f27,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/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f29,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/sandbox/benchmark/theBenchmark.p',p29) ).
fof(f31,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)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(f33,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',p33) ).
fof(f35,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p35) ).
fof(f36,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) = range(X1,X0,X2)
& inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) = domain(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_39) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) = range(X1,X0,X2)
& inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) = domain(X1,X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] :
( image(X0,domain_of(X0)) = range_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0] :
( inverse2(X0,range_of(X0)) = domain_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( image4(X0,X1,X2,X0) = range(X0,X1,X2)
& inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f41,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(f49,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f64,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,[],[f23]) ).
fof(f69,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,[],[f27]) ).
fof(f71,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,[],[f29]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( image4(X0,X1,X2,X3) = image(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,[],[f31]) ).
fof(f75,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,[],[f33]) ).
fof(f77,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( image4(X1,X0,X2,inverse4(X1,X0,X2,X0)) != range(X1,X0,X2)
| inverse4(X1,X0,X2,image4(X1,X0,X2,X1)) != domain(X1,X0,X2) )
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f37]) ).
fof(f81,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f49]) ).
fof(f82,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f81]) ).
fof(f100,plain,
( ( image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) != range(sK11,sK10,sK12)
| inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) != domain(sK11,sK10,sK12) )
& ilf_type(sK12,relation_type(sK11,sK10))
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f77]) ).
fof(f101,plain,
! [X0] :
( image(X0,domain_of(X0)) = range_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f102,plain,
! [X0] :
( domain_of(X0) = inverse2(X0,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f103,plain,
! [X2,X0,X1] :
( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f104,plain,
! [X2,X0,X1] :
( image4(X0,X1,X2,X0) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f105,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,[],[f41]) ).
fof(f118,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f143,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f64]) ).
fof(f149,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f69]) ).
fof(f151,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(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(cnf_transformation,[],[f73]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f75]) ).
fof(f157,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f35]) ).
fof(f160,plain,
ilf_type(sK12,relation_type(sK11,sK10)),
inference(cnf_transformation,[],[f100]) ).
fof(f161,plain,
( image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) != range(sK11,sK10,sK12)
| inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) != domain(sK11,sK10,sK12) ),
inference(cnf_transformation,[],[f100]) ).
fof(f164,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f118]) ).
fof(f168,definition,
( spl13_1
<=> inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) = domain(sK11,sK10,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f170,plain,
( inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) != domain(sK11,sK10,sK12)
| spl13_1 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f172,definition,
( spl13_2
<=> image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) = range(sK11,sK10,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f174,plain,
( image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) != range(sK11,sK10,sK12)
| spl13_2 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f161,f172,f168]) ).
fof(f181,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f164,f157]) ).
fof(f193,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f143,f157]) ).
fof(f194,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f193,f157]) ).
fof(f219,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,[],[f105,f157]) ).
fof(f220,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f219,f157]) ).
fof(f233,plain,
! [X2,X0,X1] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f149,f157]) ).
fof(f234,plain,
! [X2,X0,X1] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f233,f157]) ).
fof(f242,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f151,f157]) ).
fof(f243,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f242,f157]) ).
fof(f254,plain,
! [X2,X0,X1] :
( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f103,f157]) ).
fof(f255,plain,
! [X2,X0,X1] :
( inverse4(X0,X1,X2,X1) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f254,f157]) ).
fof(f258,plain,
! [X2,X0,X1] :
( image4(X0,X1,X2,X0) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f104,f157]) ).
fof(f259,plain,
! [X2,X0,X1] :
( image4(X0,X1,X2,X0) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f258,f157]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f153,f157]) ).
fof(f275,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f274,f157]) ).
fof(f276,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(forward_subsumption_resolution,[],[f275,f157]) ).
fof(f277,plain,
! [X0] : image4(sK11,sK10,sK12,X0) = image(sK12,X0),
inference(resolution,[],[f276,f160]) ).
fof(f280,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f155,f157]) ).
fof(f281,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f280,f157]) ).
fof(f282,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(forward_subsumption_resolution,[],[f281,f157]) ).
fof(f285,plain,
( range(sK11,sK10,sK12) = image(sK12,sK11)
| ~ ilf_type(sK12,relation_type(sK11,sK10)) ),
inference(superposition,[],[f259,f277]) ).
fof(f288,plain,
range(sK11,sK10,sK12) = image(sK12,sK11),
inference(forward_subsumption_resolution,[],[f285,f160]) ).
fof(f290,plain,
! [X0] : inverse4(sK11,sK10,sK12,X0) = inverse2(sK12,X0),
inference(resolution,[],[f282,f160]) ).
fof(f295,definition,
( spl13_3
<=> ilf_type(sK12,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f296,plain,
( ilf_type(sK12,binary_relation_type)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( ~ ilf_type(sK12,binary_relation_type)
| spl13_3 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f305,plain,
( domain(sK11,sK10,sK12) != inverse2(sK12,image4(sK11,sK10,sK12,sK11))
| spl13_1 ),
inference(superposition,[],[f170,f290]) ).
fof(f307,plain,
( domain(sK11,sK10,sK12) = inverse2(sK12,sK10)
| ~ ilf_type(sK12,relation_type(sK11,sK10)) ),
inference(superposition,[],[f255,f290]) ).
fof(f310,plain,
domain(sK11,sK10,sK12) = inverse2(sK12,sK10),
inference(forward_subsumption_resolution,[],[f307,f160]) ).
fof(f311,plain,
( domain(sK11,sK10,sK12) != inverse2(sK12,image(sK12,sK11))
| spl13_1 ),
inference(forward_demodulation,[],[f305,f277]) ).
fof(f313,plain,
( ~ relation_like(sK12)
| spl13_3 ),
inference(resolution,[],[f297,f181]) ).
fof(f321,plain,
( ! [X0,X1] : ~ ilf_type(sK12,subset_type(cross_product(X0,X1)))
| spl13_3 ),
inference(resolution,[],[f313,f194]) ).
fof(f339,definition,
( spl13_5
<=> ilf_type(sK12,subset_type(cross_product(sK11,sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f340,plain,
( ilf_type(sK12,subset_type(cross_product(sK11,sK10)))
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f341,plain,
( ~ ilf_type(sK12,subset_type(cross_product(sK11,sK10)))
| spl13_5 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f347,plain,
( ~ ilf_type(sK12,relation_type(sK11,sK10))
| spl13_5 ),
inference(resolution,[],[f341,f220]) ).
fof(f349,plain,
( $false
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f347,f160]) ).
fof(f350,plain,
spl13_5,
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f364,plain,
( range_of(sK12) = image(sK12,sK11)
| ~ ilf_type(sK12,relation_type(sK11,sK10)) ),
inference(superposition,[],[f243,f288]) ).
fof(f365,plain,
range_of(sK12) = image(sK12,sK11),
inference(forward_subsumption_resolution,[],[f364,f160]) ).
fof(f373,plain,
( domain_of(sK12) = inverse2(sK12,sK10)
| ~ ilf_type(sK12,relation_type(sK11,sK10)) ),
inference(superposition,[],[f234,f310]) ).
fof(f374,plain,
domain_of(sK12) = inverse2(sK12,sK10),
inference(forward_subsumption_resolution,[],[f373,f160]) ).
fof(f377,plain,
( domain(sK11,sK10,sK12) != inverse2(sK12,range_of(sK12))
| spl13_1 ),
inference(forward_demodulation,[],[f311,f365]) ).
fof(f378,plain,
( inverse2(sK12,sK10) != inverse2(sK12,range_of(sK12))
| spl13_1 ),
inference(forward_demodulation,[],[f377,f310]) ).
fof(f379,plain,
( domain_of(sK12) != inverse2(sK12,range_of(sK12))
| spl13_1 ),
inference(forward_demodulation,[],[f378,f374]) ).
fof(f380,plain,
( domain_of(sK12) != domain_of(sK12)
| ~ ilf_type(sK12,binary_relation_type)
| spl13_1 ),
inference(superposition,[],[f379,f102]) ).
fof(f381,plain,
( ~ ilf_type(sK12,binary_relation_type)
| spl13_1 ),
inference(trivial_inequality_removal,[],[f380]) ).
fof(f385,plain,
( $false
| spl13_3
| ~ spl13_5 ),
inference(resolution,[],[f321,f340]) ).
fof(f388,plain,
( spl13_3
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f389,plain,
( ~ spl13_3
| spl13_1 ),
inference(avatar_split_clause,[],[f381,f168,f295]) ).
fof(f391,plain,
( image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) != image(sK12,sK11)
| spl13_2 ),
inference(forward_demodulation,[],[f174,f288]) ).
fof(f393,plain,
( image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) != range_of(sK12)
| spl13_2 ),
inference(forward_demodulation,[],[f391,f365]) ).
fof(f395,plain,
( range_of(sK12) != image(sK12,inverse4(sK11,sK10,sK12,sK10))
| spl13_2 ),
inference(forward_demodulation,[],[f393,f277]) ).
fof(f397,plain,
( range_of(sK12) != image(sK12,inverse2(sK12,sK10))
| spl13_2 ),
inference(forward_demodulation,[],[f395,f290]) ).
fof(f399,plain,
( range_of(sK12) != image(sK12,domain_of(sK12))
| spl13_2 ),
inference(forward_demodulation,[],[f397,f374]) ).
fof(f401,plain,
( range_of(sK12) != range_of(sK12)
| ~ ilf_type(sK12,binary_relation_type)
| spl13_2 ),
inference(superposition,[],[f399,f101]) ).
fof(f402,plain,
( ~ ilf_type(sK12,binary_relation_type)
| spl13_2 ),
inference(trivial_inequality_removal,[],[f401]) ).
fof(f403,plain,
( $false
| spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f402,f296]) ).
fof(f404,plain,
( spl13_2
| ~ spl13_3 ),
inference(avatar_contradiction_clause,[],[f403]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f175]) ).
cnf(s4,plain,
spl13_5,
inference(sat_conversion,[],[f350]) ).
cnf(s7,plain,
( spl13_3
| ~ spl13_5 ),
inference(sat_conversion,[],[f388]) ).
cnf(s8,plain,
( spl13_1
| ~ spl13_3 ),
inference(sat_conversion,[],[f389]) ).
cnf(s9,plain,
( spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f404]) ).
cnf(s10,plain,
spl13_3,
inference(rat,[],[s7,s4]) ).
cnf(s11,plain,
spl13_2,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
spl13_1,
inference(rat,[],[s8,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s11,s12]) ).
fof(f405,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:30:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.28/1.31 % (1812513)Detected formulas, will run a generic FOF schedule.
% 2.28/1.31 % (1812519)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=1401104509:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.28/1.31 % (1812520)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=2964482541:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.28/1.31 % (1812524)dis-21_1_sil=8000:lcm=predicate:random_seed=634016848:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.28/1.31 % (1812518)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=2855454657:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.28/1.31 % (1812521)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3379557719:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.28/1.31 % (1812523)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=498229185:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.28/1.31 % (1812522)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=977380347:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.28/1.31 % (1812521)Refutation not found, incomplete strategy
% 2.28/1.31 % (1812521)------------------------------
% 2.28/1.31 % (1812521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.31 % (1812521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.31 % (1812521)CaDiCaL version: 2.1.3
% 2.28/1.31 % (1812521)Termination reason: Refutation not found, incomplete strategy
% 2.28/1.31 % (1812521)Time elapsed: 0.002 s
% 2.28/1.31 % (1812521)Peak memory usage: 88 MB
% 2.28/1.31 % (1812521)Instructions burned: 2 (million)
% 2.28/1.31 % (1812522)Refutation not found, incomplete strategy
% 2.28/1.31 % (1812522)------------------------------
% 2.28/1.31 % (1812522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.31 % (1812522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.31 % (1812522)CaDiCaL version: 2.1.3
% 2.28/1.31 % (1812522)Termination reason: Refutation not found, incomplete strategy
% 2.28/1.31 % (1812522)Time elapsed: 0.003 s
% 2.28/1.31 % (1812522)Peak memory usage: 88 MB
% 2.28/1.31 % (1812522)Instructions burned: 2 (million)
% 2.28/1.31 % (1812523)First to succeed.
% 2.28/1.31 % (1812523)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1812513"
% 2.28/1.31 % (1812524)Instruction limit reached!
% 2.28/1.31 % (1812524)------------------------------
% 2.28/1.31 % (1812524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/1.31 % (1812524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/1.31 % (1812524)CaDiCaL version: 2.1.3
% 2.28/1.31 % (1812524)Termination reason: Instruction limit
% 2.28/1.31 % (1812524)Termination phase: Saturation
% 2.28/1.31 % (1812524)Time elapsed: 0.079 s
% 2.28/1.31 % (1812524)Peak memory usage: 90 MB
% 2.28/1.31 % (1812524)Instructions burned: 130 (million)
% 2.28/1.31 % (1812521)------------------------------
% 2.28/1.31 % (1812521)------------------------------
% 2.28/1.31 % (1812522)------------------------------
% 2.28/1.31 % (1812522)------------------------------
% 2.28/1.31 % (1812532)lrs+10_1_sil=8000:sp=occurrence:random_seed=1345133516:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.28/1.31 % (1812523)Refutation found. Thanks to Tanya!
% 2.28/1.31 % SZS status Theorem for theBenchmark
% 2.28/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (1812523)------------------------------
% 0.17/1.50 % (1812523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1812523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1812523)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1812523)Termination reason: Refutation
% 0.17/1.50 % (1812523)Time elapsed: 0.012 s
% 0.17/1.50 % (1812523)Peak memory usage: 90 MB
% 0.17/1.50 % (1812523)Instructions burned: 16 (million)
% 0.17/1.50 % (1812523)------------------------------
% 0.17/1.50 % (1812523)------------------------------
% 0.17/1.50 % (1812513)Success in time 0.443 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------