%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 12:44:23 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 22 unt; 2 def)
% Number of atoms : 248 ( 70 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 263 ( 109 ~; 106 |; 11 &)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 163 ( 0 sgn 160 !; 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(f78,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| image(X0,domain_of(X0)) = range_of(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f79,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| domain_of(X0) = inverse2(X0,range_of(X0)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X0) = range(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f83,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,[],[f41]) ).
fof(f94,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f49]) ).
fof(f119,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,[],[f64]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f129,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)
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f131,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,[],[f75]) ).
fof(f133,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f35]) ).
fof(f134,plain,
( inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) != domain(sK11,sK10,sK12)
| image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) != range(sK11,sK10,sK12) ),
inference(cnf_transformation,[],[f77]) ).
fof(f135,plain,
ilf_type(sK12,relation_type(sK11,sK10)),
inference(cnf_transformation,[],[f77]) ).
fof(f141,definition,
( spl13_1
<=> image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) = range(sK11,sK10,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f143,plain,
( image4(sK11,sK10,sK12,inverse4(sK11,sK10,sK12,sK10)) != range(sK11,sK10,sK12)
| spl13_1 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f145,definition,
( spl13_2
<=> inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) = domain(sK11,sK10,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f147,plain,
( inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) != domain(sK11,sK10,sK12)
| spl13_2 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f134,f145,f141]) ).
fof(f150,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) ),
inference(forward_subsumption_resolution,[],[f131,f133]) ).
fof(f152,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(forward_subsumption_resolution,[],[f129,f133]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(forward_subsumption_resolution,[],[f127,f133]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(forward_subsumption_resolution,[],[f125,f133]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f119,f133]) ).
fof(f178,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f94,f133]) ).
fof(f182,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))) ),
inference(forward_subsumption_resolution,[],[f83,f133]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f80,f133]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X0) = range(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f81,f133]) ).
fof(f186,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) ),
inference(forward_subsumption_resolution,[],[f150,f133]) ).
fof(f188,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(forward_subsumption_resolution,[],[f152,f133]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(forward_subsumption_resolution,[],[f154,f133]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(forward_subsumption_resolution,[],[f156,f133]) ).
fof(f194,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f160,f133]) ).
fof(f210,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f182,f133]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f183,f133]) ).
fof(f212,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X0) = range(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f184,f133]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(forward_subsumption_resolution,[],[f186,f133]) ).
fof(f216,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(forward_subsumption_resolution,[],[f188,f133]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[],[f194,f178]) ).
fof(f299,plain,
range(sK11,sK10,sK12) = range_of(sK12),
inference(resolution,[],[f190,f135]) ).
fof(f306,plain,
domain(sK11,sK10,sK12) = domain_of(sK12),
inference(resolution,[],[f192,f135]) ).
fof(f322,plain,
! [X0] : inverse4(sK11,sK10,sK12,X0) = inverse2(sK12,X0),
inference(resolution,[],[f214,f135]) ).
fof(f330,plain,
! [X0] : image4(sK11,sK10,sK12,X0) = image(sK12,X0),
inference(resolution,[],[f216,f135]) ).
fof(f334,plain,
domain(sK11,sK10,sK12) = inverse4(sK11,sK10,sK12,sK10),
inference(resolution,[],[f211,f135]) ).
fof(f335,plain,
domain(sK11,sK10,sK12) = inverse2(sK12,sK10),
inference(forward_demodulation,[],[f334,f322]) ).
fof(f339,plain,
domain_of(sK12) = inverse2(sK12,sK10),
inference(forward_demodulation,[],[f335,f306]) ).
fof(f347,plain,
image4(sK11,sK10,sK12,sK11) = range(sK11,sK10,sK12),
inference(resolution,[],[f212,f135]) ).
fof(f348,plain,
image4(sK11,sK10,sK12,sK11) = range_of(sK12),
inference(forward_demodulation,[],[f347,f299]) ).
fof(f352,plain,
range_of(sK12) = image(sK12,sK11),
inference(forward_demodulation,[],[f348,f330]) ).
fof(f356,plain,
( range(sK11,sK10,sK12) != image(sK12,inverse4(sK11,sK10,sK12,sK10))
| spl13_1 ),
inference(superposition,[],[f143,f330]) ).
fof(f359,plain,
( range(sK11,sK10,sK12) != image(sK12,inverse2(sK12,sK10))
| spl13_1 ),
inference(forward_demodulation,[],[f356,f322]) ).
fof(f360,plain,
( range(sK11,sK10,sK12) != image(sK12,domain_of(sK12))
| spl13_1 ),
inference(forward_demodulation,[],[f359,f339]) ).
fof(f361,plain,
( image(sK12,domain_of(sK12)) != range_of(sK12)
| spl13_1 ),
inference(forward_demodulation,[],[f360,f299]) ).
fof(f363,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[],[f231,f210]) ).
fof(f453,plain,
ilf_type(sK12,binary_relation_type),
inference(resolution,[],[f363,f135]) ).
fof(f484,plain,
domain_of(sK12) = inverse2(sK12,range_of(sK12)),
inference(resolution,[],[f453,f79]) ).
fof(f485,plain,
image(sK12,domain_of(sK12)) = range_of(sK12),
inference(resolution,[],[f453,f78]) ).
fof(f486,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f485,f361]) ).
fof(f487,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f486]) ).
fof(f489,plain,
( inverse4(sK11,sK10,sK12,image4(sK11,sK10,sK12,sK11)) != domain_of(sK12)
| spl13_2 ),
inference(forward_demodulation,[],[f147,f306]) ).
fof(f491,plain,
( domain_of(sK12) != inverse2(sK12,image4(sK11,sK10,sK12,sK11))
| spl13_2 ),
inference(forward_demodulation,[],[f489,f322]) ).
fof(f493,plain,
( domain_of(sK12) != inverse2(sK12,image(sK12,sK11))
| spl13_2 ),
inference(forward_demodulation,[],[f491,f330]) ).
fof(f495,plain,
( domain_of(sK12) != inverse2(sK12,range_of(sK12))
| spl13_2 ),
inference(forward_demodulation,[],[f493,f352]) ).
fof(f496,plain,
( $false
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f495,f484]) ).
fof(f497,plain,
spl13_2,
inference(avatar_contradiction_clause,[],[f496]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f148]) ).
cnf(s2,plain,
spl13_1,
inference(sat_conversion,[],[f487]) ).
cnf(s3,plain,
spl13_2,
inference(sat_conversion,[],[f497]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f498,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.39 % Computer : n026.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.40 % WCLimit : 300
% 0.09/0.40 % DateTime : Mon Sep 28 02:32:12 UTC 2026
% 0.09/0.40 % CPUTime :
% 0.09/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.43 Running first-order model finding
% 0.09/0.43 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
% 0.16/0.48 % (3418604)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3418613)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3524181356:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3418610)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3418609)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3680664540_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (3418610)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2037175742:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3418611)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4251834667:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3418612)dis+10_1_sil=32000:sp=arity:random_seed=380909355:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3418614)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4126607837:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3418613) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3418604-3418613"...
% 0.16/0.48 % (3418615)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3080981765:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (3418613)...printing done.
% 0.16/0.48 % (3418613)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3418613)------------------------------
% 0.16/0.48 % (3418613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3418613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3418613)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3418613)Termination reason: Refutation
% 0.16/0.48 % (3418613)Time elapsed: 0.008 s
% 0.16/0.48 % (3418613)Peak memory usage: 12 MB
% 0.16/0.48 % (3418613)Instructions burned: 21 (million)
% 0.16/0.48 % (3418604)Success in time 0.04 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------