%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET725+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:41:45 PM UTC 2026
% Result : Theorem 6.56s 2.00s
% Output : Refutation 8.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 17
% Syntax : Number of formulae : 181 ( 29 unt; 10 def)
% Number of atoms : 673 ( 68 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 846 ( 354 ~; 363 |; 87 &)
% ( 17 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-5 aty)
% Number of variables : 358 ( 0 sgn 329 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps) ).
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X5,X2)
& member(X6,X4) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_function) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X4,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injective) ).
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
fof(f19,axiom,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( injective(X0,X1,X2)
& surjective(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) )
=> one_to_one(X0,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII16) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) )
=> one_to_one(X0,X3,X4) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
=> one_to_one(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X4,X5) )
=> X3 = X4 ) )
=> injective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f36,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f44,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X3,X5)
& apply(X0,X4,X5)
& member(X3,X1)
& member(X4,X1)
& member(X5,X2) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f45,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
| ? [X3,X4,X5] :
( X3 != X4
& apply(X0,X3,X5)
& apply(X0,X4,X5)
& member(X3,X1)
& member(X4,X1)
& member(X5,X2) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f47,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f48,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
? [X0,X1,X2,X3,X4] :
( ~ one_to_one(X0,X3,X4)
& maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f52,plain,
? [X0,X1,X2,X3,X4] :
( ~ one_to_one(X0,X3,X4)
& maps(X0,X3,X4)
& maps(X1,X4,X3)
& maps(X2,X4,X3)
& identity(compose_function(X1,X0,X3,X4,X3),X3)
& identity(compose_function(X0,X2,X4,X3,X4),X4) ),
inference(flattening,[],[f51]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK3(X0,X2,X3),X2)
& apply(X0,X3,sK3(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f40]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X7] :
( member(X7,X3)
& apply(X1,X5,X7)
& apply(X0,X7,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(nnf_transformation,[],[f42]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ? [X8] :
( member(X8,X3)
& apply(X1,X5,X8)
& apply(X0,X8,X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ member(X7,X3)
| ~ apply(X1,X5,X7)
| ~ apply(X0,X7,X6) ) )
& ( ( member(sK4(X0,X1,X3,X5,X6),X3)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& apply(X0,sK4(X0,X1,X3,X5,X6),X6) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X8,sK4(X0,X1,X3,X5,X6))],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
& apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
& apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
& member(sK5(X0,X1,X2),X1)
& member(sK6(X0,X1,X2),X1)
& member(sK7(X0,X1,X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5(X0,X1,X2)),skolemize(X4,sK6(X0,X1,X2)),skolemize(X5,sK7(X0,X1,X2))],[f45]) ).
fof(f77,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,sK8(X0,X1,X2)) )
& member(sK8(X0,X1,X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f46]) ).
fof(f93,plain,
( ~ one_to_one(sK13,sK16,sK17)
& maps(sK13,sK16,sK17)
& maps(sK14,sK17,sK16)
& maps(sK15,sK17,sK16)
& identity(compose_function(sK14,sK13,sK16,sK17,sK16),sK16)
& identity(compose_function(sK13,sK15,sK17,sK16,sK17),sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16),skolemize(X4,sK17)],[f52]) ).
fof(f120,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK4(X0,X1,X3,X5,X6),X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X1,X5,sK4(X0,X1,X3,X5,X6))
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f75]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK4(X0,X1,X3,X5,X6),X3)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f75]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f129,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f130,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f131,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f132,plain,
! [X2,X0,X1] :
( apply(X0,sK5(X0,X1,X2),sK7(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f133,plain,
! [X2,X0,X1] :
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f134,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f135,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK8(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f153,plain,
identity(compose_function(sK13,sK15,sK17,sK16,sK17),sK17),
inference(cnf_transformation,[],[f93]) ).
fof(f154,plain,
identity(compose_function(sK14,sK13,sK16,sK17,sK16),sK16),
inference(cnf_transformation,[],[f93]) ).
fof(f156,plain,
maps(sK14,sK17,sK16),
inference(cnf_transformation,[],[f93]) ).
fof(f157,plain,
maps(sK13,sK16,sK17),
inference(cnf_transformation,[],[f93]) ).
fof(f158,plain,
~ one_to_one(sK13,sK16,sK17),
inference(cnf_transformation,[],[f93]) ).
fof(f162,definition,
sF18 = compose_function(sK14,sK13,sK16,sK17,sK16),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f163,plain,
compose_function(sK14,sK13,sK16,sK17,sK16) = sF18,
inference(reorient_equations,[],[f162]) ).
fof(f164,plain,
identity(sF18,sK16),
inference(definition_folding,[],[f154,f163]) ).
fof(f165,definition,
sF19 = compose_function(sK13,sK15,sK17,sK16,sK17),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f166,plain,
compose_function(sK13,sK15,sK17,sK16,sK17) = sF19,
inference(reorient_equations,[],[f165]) ).
fof(f167,plain,
identity(sF19,sK17),
inference(definition_folding,[],[f153,f166]) ).
fof(f168,plain,
! [X0,X1] :
( apply(sK14,sK4(sK14,sK13,sK17,X0,X1),X1)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK16) ),
inference(superposition,[],[f123,f163]) ).
fof(f169,plain,
! [X0,X1] :
( apply(sK13,sK4(sK13,sK15,sK16,X0,X1),X1)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK17) ),
inference(superposition,[],[f123,f166]) ).
fof(f170,plain,
! [X0,X1] :
( apply(sK13,X0,sK4(sK14,sK13,sK17,X0,X1))
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK16) ),
inference(superposition,[],[f124,f163]) ).
fof(f172,plain,
! [X0,X1] :
( member(sK4(sK14,sK13,sK17,X0,X1),sK17)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK16) ),
inference(superposition,[],[f125,f163]) ).
fof(f173,plain,
! [X0,X1] :
( member(sK4(sK13,sK15,sK16,X0,X1),sK16)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK17)
| ~ member(X1,sK17) ),
inference(superposition,[],[f125,f166]) ).
fof(f178,plain,
! [X0] :
( apply(sF19,X0,X0)
| ~ member(X0,sK17) ),
inference(resolution,[],[f127,f167]) ).
fof(f179,plain,
! [X0] :
( apply(sF18,X0,X0)
| ~ member(X0,sK16) ),
inference(resolution,[],[f127,f164]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK13,sK15,sK16,X0,sK8(sK13,X1,X2)),X1)
| surjective(sK13,X1,X2)
| ~ apply(sF19,X0,sK8(sK13,X1,X2))
| ~ member(X0,sK17)
| ~ member(sK8(sK13,X1,X2),sK17) ),
inference(resolution,[],[f135,f169]) ).
fof(f202,plain,
! [X0,X1] :
( surjective(sK13,sK16,X0)
| ~ apply(sF19,X1,sK8(sK13,sK16,X0))
| ~ member(X1,sK17)
| ~ member(sK8(sK13,sK16,X0),sK17)
| ~ apply(sF19,X1,sK8(sK13,sK16,X0))
| ~ member(X1,sK17)
| ~ member(sK8(sK13,sK16,X0),sK17) ),
inference(resolution,[],[f196,f173]) ).
fof(f203,plain,
! [X0,X1] :
( ~ apply(sF19,X1,sK8(sK13,sK16,X0))
| surjective(sK13,sK16,X0)
| ~ member(X1,sK17)
| ~ member(sK8(sK13,sK16,X0),sK17) ),
inference(duplicate_literal_removal,[],[f202]) ).
fof(f204,plain,
! [X0] :
( surjective(sK13,sK16,X0)
| ~ member(sK8(sK13,sK16,X0),sK17)
| ~ member(sK8(sK13,sK16,X0),sK17)
| ~ member(sK8(sK13,sK16,X0),sK17) ),
inference(resolution,[],[f203,f178]) ).
fof(f205,plain,
! [X0] :
( ~ member(sK8(sK13,sK16,X0),sK17)
| surjective(sK13,sK16,X0) ),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f206,plain,
( surjective(sK13,sK16,sK17)
| surjective(sK13,sK16,sK17) ),
inference(resolution,[],[f205,f134]) ).
fof(f207,plain,
surjective(sK13,sK16,sK17),
inference(duplicate_literal_removal,[],[f206]) ).
fof(f208,plain,
( ~ injective(sK13,sK16,sK17)
| one_to_one(sK13,sK16,sK17) ),
inference(resolution,[],[f207,f136]) ).
fof(f209,plain,
~ injective(sK13,sK16,sK17),
inference(forward_subsumption_resolution,[],[f208,f158]) ).
fof(f220,plain,
! [X0] :
( apply(sK13,X0,sK3(sK13,sK17,X0))
| ~ member(X0,sK16) ),
inference(resolution,[],[f121,f157]) ).
fof(f222,plain,
! [X0] :
( apply(sK14,X0,sK3(sK14,sK16,X0))
| ~ member(X0,sK17) ),
inference(resolution,[],[f121,f156]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(sK14,sK16,X0),X3)
| ~ apply(sK14,X0,X1)
| sK3(sK14,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ member(X0,sK17)
| ~ maps(sK14,X2,X3) ),
inference(resolution,[],[f222,f120]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(sK13,sK17,X0),X3)
| ~ apply(sK13,X0,X1)
| sK3(sK13,sK17,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ member(X0,sK16)
| ~ maps(sK13,X2,X3) ),
inference(resolution,[],[f220,f120]) ).
fof(f278,plain,
! [X0] :
( member(sK3(sK13,sK17,X0),sK17)
| ~ member(X0,sK16) ),
inference(resolution,[],[f122,f157]) ).
fof(f280,plain,
! [X0] :
( member(sK3(sK14,sK16,X0),sK16)
| ~ member(X0,sK17) ),
inference(resolution,[],[f122,f156]) ).
fof(f281,plain,
! [X2,X0,X1] :
( ~ member(X0,sK16)
| ~ apply(sK13,X0,X1)
| sK3(sK13,sK17,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK17)
| ~ member(X0,sK16)
| ~ maps(sK13,X2,sK17) ),
inference(resolution,[],[f278,f227]) ).
fof(f282,plain,
! [X2,X0,X1] :
( ~ apply(sK13,X0,X1)
| ~ member(X0,sK16)
| sK3(sK13,sK17,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK17)
| ~ maps(sK13,X2,sK17) ),
inference(duplicate_literal_removal,[],[f281]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ member(X0,sK17)
| ~ apply(sK14,X0,X1)
| sK3(sK14,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK16)
| ~ member(X0,sK17)
| ~ maps(sK14,X2,sK16) ),
inference(resolution,[],[f280,f223]) ).
fof(f286,plain,
! [X2,X0,X1] :
( ~ apply(sK14,X0,X1)
| ~ member(X0,sK17)
| sK3(sK14,sK16,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK16)
| ~ maps(sK14,X2,sK16) ),
inference(duplicate_literal_removal,[],[f285]) ).
fof(f295,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK13,sK17,X0,X1),sK17)
| sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X1)) = X1
| ~ member(sK4(sK14,sK13,sK17,X0,X1),X2)
| ~ member(X1,sK16)
| ~ maps(sK14,X2,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK16) ),
inference(resolution,[],[f286,f168]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK13,sK17,X0,X1),sK17)
| sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X1)) = X1
| ~ member(sK4(sK14,sK13,sK17,X0,X1),X2)
| ~ member(X1,sK16)
| ~ maps(sK14,X2,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16) ),
inference(duplicate_literal_removal,[],[f295]) ).
fof(f300,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK14,sK13,sK17,X0,X1),X2)
| sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X1)) = X1
| ~ member(X1,sK16)
| ~ maps(sK14,X2,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f298,f172]) ).
fof(f301,plain,
! [X2,X0,X1] :
( ~ member(X0,sK16)
| sK4(sK14,sK13,sK17,X0,X1) = sK3(sK13,sK17,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK14,sK13,sK17,X0,X1),sK17)
| ~ maps(sK13,X2,sK17)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK16) ),
inference(resolution,[],[f282,f170]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ member(sK7(sK13,X0,X1),sK17)
| sK3(sK13,sK17,sK5(sK13,X0,X1)) = sK7(sK13,X0,X1)
| ~ member(sK5(sK13,X0,X1),X2)
| ~ member(sK5(sK13,X0,X1),sK16)
| ~ maps(sK13,X2,sK17)
| injective(sK13,X0,X1) ),
inference(resolution,[],[f282,f132]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ member(sK7(sK13,X0,X1),sK17)
| sK7(sK13,X0,X1) = sK3(sK13,sK17,sK6(sK13,X0,X1))
| ~ member(sK6(sK13,X0,X1),X2)
| ~ member(sK6(sK13,X0,X1),sK16)
| ~ maps(sK13,X2,sK17)
| injective(sK13,X0,X1) ),
inference(resolution,[],[f282,f131]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ member(X0,sK16)
| sK4(sK14,sK13,sK17,X0,X1) = sK3(sK13,sK17,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK14,sK13,sK17,X0,X1),sK17)
| ~ maps(sK13,X2,sK17)
| ~ apply(sF18,X0,X1)
| ~ member(X1,sK16) ),
inference(duplicate_literal_removal,[],[f301]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ apply(sF18,X0,X1)
| sK4(sK14,sK13,sK17,X0,X1) = sK3(sK13,sK17,X0)
| ~ member(X0,X2)
| ~ maps(sK13,X2,sK17)
| ~ member(X0,sK16)
| ~ member(X1,sK16) ),
inference(forward_subsumption_resolution,[],[f308,f172]) ).
fof(f315,plain,
! [X0,X1] :
( sK3(sK13,sK17,X0) = sK4(sK14,sK13,sK17,X0,X0)
| ~ member(X0,X1)
| ~ maps(sK13,X1,sK17)
| ~ member(X0,sK16)
| ~ member(X0,sK16)
| ~ member(X0,sK16) ),
inference(resolution,[],[f310,f179]) ).
fof(f318,plain,
! [X0,X1] :
( ~ maps(sK13,X1,sK17)
| ~ member(X0,X1)
| sK3(sK13,sK17,X0) = sK4(sK14,sK13,sK17,X0,X0)
| ~ member(X0,sK16) ),
inference(duplicate_literal_removal,[],[f315]) ).
fof(f319,plain,
! [X0,X1] :
( sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X1)) = X1
| ~ member(X1,sK16)
| ~ maps(sK14,sK17,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16)
| ~ member(X1,sK16) ),
inference(resolution,[],[f300,f172]) ).
fof(f320,plain,
! [X0,X1] :
( sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X1)) = X1
| ~ member(X1,sK16)
| ~ maps(sK14,sK17,sK16)
| ~ apply(sF18,X0,X1)
| ~ member(X0,sK16) ),
inference(duplicate_literal_removal,[],[f319]) ).
fof(f321,plain,
! [X0,X1] :
( ~ apply(sF18,X0,X1)
| ~ member(X1,sK16)
| sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X1)) = X1
| ~ member(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f320,f156]) ).
fof(f322,plain,
! [X0] :
( ~ member(X0,sK16)
| sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X0)) = X0
| ~ member(X0,sK16)
| ~ member(X0,sK16) ),
inference(resolution,[],[f321,f179]) ).
fof(f325,plain,
! [X0] :
( ~ member(X0,sK16)
| sK3(sK14,sK16,sK4(sK14,sK13,sK17,X0,X0)) = X0 ),
inference(duplicate_literal_removal,[],[f322]) ).
fof(f348,plain,
! [X0,X1] :
( sK7(sK13,X0,sK17) = sK3(sK13,sK17,sK6(sK13,X0,sK17))
| ~ member(sK6(sK13,X0,sK17),X1)
| ~ member(sK6(sK13,X0,sK17),sK16)
| ~ maps(sK13,X1,sK17)
| injective(sK13,X0,sK17)
| injective(sK13,X0,sK17) ),
inference(resolution,[],[f305,f128]) ).
fof(f349,plain,
! [X0,X1] :
( ~ member(sK6(sK13,X0,sK17),sK16)
| ~ member(sK6(sK13,X0,sK17),X1)
| sK7(sK13,X0,sK17) = sK3(sK13,sK17,sK6(sK13,X0,sK17))
| ~ maps(sK13,X1,sK17)
| injective(sK13,X0,sK17) ),
inference(duplicate_literal_removal,[],[f348]) ).
fof(f350,plain,
! [X0] :
( ~ member(sK6(sK13,sK16,sK17),X0)
| sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK6(sK13,sK16,sK17))
| ~ maps(sK13,X0,sK17)
| injective(sK13,sK16,sK17)
| injective(sK13,sK16,sK17) ),
inference(resolution,[],[f349,f129]) ).
fof(f351,plain,
! [X0] :
( ~ member(sK6(sK13,sK16,sK17),X0)
| sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK6(sK13,sK16,sK17))
| ~ maps(sK13,X0,sK17)
| injective(sK13,sK16,sK17) ),
inference(duplicate_literal_removal,[],[f350]) ).
fof(f352,plain,
! [X0] :
( ~ member(sK6(sK13,sK16,sK17),X0)
| sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK6(sK13,sK16,sK17))
| ~ maps(sK13,X0,sK17) ),
inference(forward_subsumption_resolution,[],[f351,f209]) ).
fof(f354,definition,
( spl20_1
<=> sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK6(sK13,sK16,sK17)) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f356,plain,
( sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK6(sK13,sK16,sK17))
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f358,definition,
( spl20_2
<=> ! [X0] :
( ~ member(sK6(sK13,sK16,sK17),X0)
| ~ maps(sK13,X0,sK17) ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f359,plain,
( ! [X0] :
( ~ member(sK6(sK13,sK16,sK17),X0)
| ~ maps(sK13,X0,sK17) )
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f360,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f352,f358,f354]) ).
fof(f361,plain,
( ~ maps(sK13,sK16,sK17)
| injective(sK13,sK16,sK17)
| ~ spl20_2 ),
inference(resolution,[],[f359,f129]) ).
fof(f362,plain,
( injective(sK13,sK16,sK17)
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f361,f157]) ).
fof(f363,plain,
( $false
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f362,f209]) ).
fof(f364,plain,
~ spl20_2,
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f369,definition,
( spl20_3
<=> member(sK6(sK13,sK16,sK17),sK16) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f370,plain,
( member(sK6(sK13,sK16,sK17),sK16)
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f371,plain,
( ~ member(sK6(sK13,sK16,sK17),sK16)
| spl20_3 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f386,plain,
( injective(sK13,sK16,sK17)
| spl20_3 ),
inference(resolution,[],[f371,f129]) ).
fof(f387,plain,
( $false
| spl20_3 ),
inference(forward_subsumption_resolution,[],[f386,f209]) ).
fof(f388,plain,
spl20_3,
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f390,plain,
( sK6(sK13,sK16,sK17) = sK3(sK14,sK16,sK4(sK14,sK13,sK17,sK6(sK13,sK16,sK17),sK6(sK13,sK16,sK17)))
| ~ spl20_3 ),
inference(resolution,[],[f370,f325]) ).
fof(f476,plain,
! [X0] :
( ~ member(X0,sK16)
| sK3(sK13,sK17,X0) = sK4(sK14,sK13,sK17,X0,X0)
| ~ member(X0,sK16) ),
inference(resolution,[],[f318,f157]) ).
fof(f477,plain,
! [X0] :
( ~ member(X0,sK16)
| sK3(sK13,sK17,X0) = sK4(sK14,sK13,sK17,X0,X0) ),
inference(duplicate_literal_removal,[],[f476]) ).
fof(f484,plain,
( sK3(sK13,sK17,sK6(sK13,sK16,sK17)) = sK4(sK14,sK13,sK17,sK6(sK13,sK16,sK17),sK6(sK13,sK16,sK17))
| ~ spl20_3 ),
inference(resolution,[],[f477,f370]) ).
fof(f488,plain,
( sK7(sK13,sK16,sK17) = sK4(sK14,sK13,sK17,sK6(sK13,sK16,sK17),sK6(sK13,sK16,sK17))
| ~ spl20_1
| ~ spl20_3 ),
inference(forward_demodulation,[],[f484,f356]) ).
fof(f490,plain,
( sK6(sK13,sK16,sK17) = sK3(sK14,sK16,sK7(sK13,sK16,sK17))
| ~ spl20_1
| ~ spl20_3 ),
inference(superposition,[],[f390,f488]) ).
fof(f521,plain,
! [X0,X1] :
( sK7(sK13,X0,sK17) = sK3(sK13,sK17,sK5(sK13,X0,sK17))
| ~ member(sK5(sK13,X0,sK17),X1)
| ~ member(sK5(sK13,X0,sK17),sK16)
| ~ maps(sK13,X1,sK17)
| injective(sK13,X0,sK17)
| injective(sK13,X0,sK17) ),
inference(resolution,[],[f304,f128]) ).
fof(f522,plain,
! [X0,X1] :
( ~ member(sK5(sK13,X0,sK17),sK16)
| ~ member(sK5(sK13,X0,sK17),X1)
| sK7(sK13,X0,sK17) = sK3(sK13,sK17,sK5(sK13,X0,sK17))
| ~ maps(sK13,X1,sK17)
| injective(sK13,X0,sK17) ),
inference(duplicate_literal_removal,[],[f521]) ).
fof(f523,plain,
! [X0] :
( ~ member(sK5(sK13,sK16,sK17),X0)
| sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK5(sK13,sK16,sK17))
| ~ maps(sK13,X0,sK17)
| injective(sK13,sK16,sK17)
| injective(sK13,sK16,sK17) ),
inference(resolution,[],[f522,f130]) ).
fof(f524,plain,
! [X0] :
( ~ member(sK5(sK13,sK16,sK17),X0)
| sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK5(sK13,sK16,sK17))
| ~ maps(sK13,X0,sK17)
| injective(sK13,sK16,sK17) ),
inference(duplicate_literal_removal,[],[f523]) ).
fof(f525,plain,
! [X0] :
( ~ member(sK5(sK13,sK16,sK17),X0)
| sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK5(sK13,sK16,sK17))
| ~ maps(sK13,X0,sK17) ),
inference(forward_subsumption_resolution,[],[f524,f209]) ).
fof(f527,definition,
( spl20_14
<=> sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK5(sK13,sK16,sK17)) ),
introduced(definition,[new_symbols(definition,[spl20_14])],[avatar_definition]) ).
fof(f529,plain,
( sK7(sK13,sK16,sK17) = sK3(sK13,sK17,sK5(sK13,sK16,sK17))
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f531,definition,
( spl20_15
<=> ! [X0] :
( ~ member(sK5(sK13,sK16,sK17),X0)
| ~ maps(sK13,X0,sK17) ) ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
fof(f532,plain,
( ! [X0] :
( ~ member(sK5(sK13,sK16,sK17),X0)
| ~ maps(sK13,X0,sK17) )
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f533,plain,
( spl20_14
| spl20_15 ),
inference(avatar_split_clause,[],[f525,f531,f527]) ).
fof(f538,definition,
( spl20_16
<=> member(sK5(sK13,sK16,sK17),sK16) ),
introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition]) ).
fof(f539,plain,
( member(sK5(sK13,sK16,sK17),sK16)
| ~ spl20_16 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f540,plain,
( ~ member(sK5(sK13,sK16,sK17),sK16)
| spl20_16 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f550,plain,
( injective(sK13,sK16,sK17)
| spl20_16 ),
inference(resolution,[],[f540,f130]) ).
fof(f551,plain,
( $false
| spl20_16 ),
inference(forward_subsumption_resolution,[],[f550,f209]) ).
fof(f552,plain,
spl20_16,
inference(avatar_contradiction_clause,[],[f551]) ).
fof(f553,plain,
( ~ maps(sK13,sK16,sK17)
| injective(sK13,sK16,sK17)
| ~ spl20_15 ),
inference(resolution,[],[f532,f130]) ).
fof(f554,plain,
( injective(sK13,sK16,sK17)
| ~ spl20_15 ),
inference(forward_subsumption_resolution,[],[f553,f157]) ).
fof(f555,plain,
( $false
| ~ spl20_15 ),
inference(forward_subsumption_resolution,[],[f554,f209]) ).
fof(f556,plain,
~ spl20_15,
inference(avatar_contradiction_clause,[],[f555]) ).
fof(f561,plain,
( sK3(sK13,sK17,sK5(sK13,sK16,sK17)) = sK4(sK14,sK13,sK17,sK5(sK13,sK16,sK17),sK5(sK13,sK16,sK17))
| ~ spl20_16 ),
inference(resolution,[],[f539,f477]) ).
fof(f563,plain,
( sK7(sK13,sK16,sK17) = sK4(sK14,sK13,sK17,sK5(sK13,sK16,sK17),sK5(sK13,sK16,sK17))
| ~ spl20_14
| ~ spl20_16 ),
inference(forward_demodulation,[],[f561,f529]) ).
fof(f567,plain,
( ! [X0] :
( ~ member(sK7(sK13,sK16,sK17),X0)
| sK3(sK14,sK16,sK7(sK13,sK16,sK17)) = sK5(sK13,sK16,sK17)
| ~ member(sK5(sK13,sK16,sK17),sK16)
| ~ maps(sK14,X0,sK16)
| ~ apply(sF18,sK5(sK13,sK16,sK17),sK5(sK13,sK16,sK17))
| ~ member(sK5(sK13,sK16,sK17),sK16) )
| ~ spl20_14
| ~ spl20_16 ),
inference(superposition,[],[f300,f563]) ).
fof(f574,plain,
( ! [X0] :
( ~ member(sK7(sK13,sK16,sK17),X0)
| sK3(sK14,sK16,sK7(sK13,sK16,sK17)) = sK5(sK13,sK16,sK17)
| ~ member(sK5(sK13,sK16,sK17),sK16)
| ~ maps(sK14,X0,sK16)
| ~ apply(sF18,sK5(sK13,sK16,sK17),sK5(sK13,sK16,sK17)) )
| ~ spl20_14
| ~ spl20_16 ),
inference(duplicate_literal_removal,[],[f567]) ).
fof(f576,plain,
( ! [X0] :
( ~ member(sK7(sK13,sK16,sK17),X0)
| sK3(sK14,sK16,sK7(sK13,sK16,sK17)) = sK5(sK13,sK16,sK17)
| ~ member(sK5(sK13,sK16,sK17),sK16)
| ~ maps(sK14,X0,sK16) )
| ~ spl20_14
| ~ spl20_16 ),
inference(forward_subsumption_resolution,[],[f574,f179]) ).
fof(f578,plain,
( ! [X0] :
( ~ member(sK7(sK13,sK16,sK17),X0)
| sK3(sK14,sK16,sK7(sK13,sK16,sK17)) = sK5(sK13,sK16,sK17)
| ~ maps(sK14,X0,sK16) )
| ~ spl20_14
| ~ spl20_16 ),
inference(forward_subsumption_resolution,[],[f576,f539]) ).
fof(f579,plain,
( ! [X0] :
( sK6(sK13,sK16,sK17) = sK5(sK13,sK16,sK17)
| ~ member(sK7(sK13,sK16,sK17),X0)
| ~ maps(sK14,X0,sK16) )
| ~ spl20_1
| ~ spl20_3
| ~ spl20_14
| ~ spl20_16 ),
inference(forward_demodulation,[],[f578,f490]) ).
fof(f581,definition,
( spl20_19
<=> ! [X0] :
( ~ member(sK7(sK13,sK16,sK17),X0)
| ~ maps(sK14,X0,sK16) ) ),
introduced(definition,[new_symbols(definition,[spl20_19])],[avatar_definition]) ).
fof(f582,plain,
( ! [X0] :
( ~ member(sK7(sK13,sK16,sK17),X0)
| ~ maps(sK14,X0,sK16) )
| ~ spl20_19 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f584,definition,
( spl20_20
<=> sK6(sK13,sK16,sK17) = sK5(sK13,sK16,sK17) ),
introduced(definition,[new_symbols(definition,[spl20_20])],[avatar_definition]) ).
fof(f586,plain,
( sK6(sK13,sK16,sK17) = sK5(sK13,sK16,sK17)
| ~ spl20_20 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f587,plain,
( spl20_19
| spl20_20
| ~ spl20_1
| ~ spl20_3
| ~ spl20_14
| ~ spl20_16 ),
inference(avatar_split_clause,[],[f579,f538,f527,f369,f354,f584,f581]) ).
fof(f591,plain,
( ~ maps(sK14,sK17,sK16)
| injective(sK13,sK16,sK17)
| ~ spl20_19 ),
inference(resolution,[],[f582,f128]) ).
fof(f595,plain,
( injective(sK13,sK16,sK17)
| ~ spl20_19 ),
inference(forward_subsumption_resolution,[],[f591,f156]) ).
fof(f596,plain,
( $false
| ~ spl20_19 ),
inference(forward_subsumption_resolution,[],[f595,f209]) ).
fof(f597,plain,
~ spl20_19,
inference(avatar_contradiction_clause,[],[f596]) ).
fof(f611,plain,
( sK5(sK13,sK16,sK17) != sK5(sK13,sK16,sK17)
| injective(sK13,sK16,sK17)
| ~ spl20_20 ),
inference(superposition,[],[f133,f586]) ).
fof(f612,plain,
( injective(sK13,sK16,sK17)
| ~ spl20_20 ),
inference(trivial_inequality_removal,[],[f611]) ).
fof(f613,plain,
( $false
| ~ spl20_20 ),
inference(forward_subsumption_resolution,[],[f612,f209]) ).
fof(f614,plain,
~ spl20_20,
inference(avatar_contradiction_clause,[],[f613]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f360]) ).
cnf(s2,plain,
~ spl20_2,
inference(sat_conversion,[],[f364]) ).
cnf(s6,plain,
spl20_3,
inference(sat_conversion,[],[f388]) ).
cnf(s15,plain,
( spl20_14
| spl20_15 ),
inference(sat_conversion,[],[f533]) ).
cnf(s18,plain,
spl20_16,
inference(sat_conversion,[],[f552]) ).
cnf(s19,plain,
~ spl20_15,
inference(sat_conversion,[],[f556]) ).
cnf(s20,plain,
( ~ spl20_1
| ~ spl20_3
| ~ spl20_14
| ~ spl20_16
| spl20_19
| spl20_20 ),
inference(sat_conversion,[],[f587]) ).
cnf(s22,plain,
~ spl20_19,
inference(sat_conversion,[],[f597]) ).
cnf(s23,plain,
~ spl20_20,
inference(sat_conversion,[],[f614]) ).
cnf(s24,plain,
( ~ spl20_1
| ~ spl20_3
| ~ spl20_14
| ~ spl20_16 ),
inference(rat,[],[s20,s23,s22]) ).
cnf(s27,plain,
spl20_14,
inference(rat,[],[s15,s19]) ).
cnf(s30,plain,
~ spl20_1,
inference(rat,[],[s24,s18,s27,s6]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s2,s30]) ).
fof(f615,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET725+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n004.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 02:39:22 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 6.56/2.00 % (4096581)Detected formulas, will run a generic FOF schedule.
% 6.56/2.00 % (4096589)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1762367825:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.56/2.00 % (4096589)Refutation not found, incomplete strategy
% 6.56/2.00 % (4096589)------------------------------
% 6.56/2.00 % (4096589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096589)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096589)Termination reason: Refutation not found, incomplete strategy
% 6.56/2.00 % (4096589)Time elapsed: 0.003 s
% 6.56/2.00 % (4096589)Peak memory usage: 88 MB
% 6.56/2.00 % (4096589)Instructions burned: 6 (million)
% 6.56/2.00 % (4096591)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3773151831:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.56/2.00 % (4096590)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=705767395:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.56/2.00 % (4096587)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=406889381:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.56/2.00 % (4096592)dis-21_1_sil=8000:lcm=predicate:random_seed=1303572302: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)
% 6.56/2.00 % (4096586)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=870097075:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.56/2.00 % (4096588)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=1741997412:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.56/2.00 % (4096590)Instruction limit reached!
% 6.56/2.00 % (4096590)------------------------------
% 6.56/2.00 % (4096590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096590)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096590)Termination reason: Instruction limit
% 6.56/2.00 % (4096590)Termination phase: Saturation
% 6.56/2.00 % (4096590)Time elapsed: 0.066 s
% 6.56/2.00 % (4096590)Peak memory usage: 88 MB
% 6.56/2.00 % (4096590)Instructions burned: 120 (million)
% 6.56/2.00 % (4096592)Instruction limit reached!
% 6.56/2.00 % (4096592)------------------------------
% 6.56/2.00 % (4096592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096592)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096592)Termination reason: Instruction limit
% 6.56/2.00 % (4096592)Termination phase: Saturation
% 6.56/2.00 % (4096592)Time elapsed: 0.074 s
% 6.56/2.00 % (4096592)Peak memory usage: 89 MB
% 6.56/2.00 % (4096592)Instructions burned: 129 (million)
% 6.56/2.00 % (4096591)Instruction limit reached!
% 6.56/2.00 % (4096591)------------------------------
% 6.56/2.00 % (4096591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096591)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096591)Termination reason: Instruction limit
% 6.56/2.00 % (4096591)Termination phase: Saturation
% 6.56/2.00 % (4096591)Time elapsed: 0.094 s
% 6.56/2.00 % (4096591)Peak memory usage: 89 MB
% 6.56/2.00 % (4096591)Instructions burned: 139 (million)
% 6.56/2.00 % (4096589)------------------------------
% 6.56/2.00 % (4096589)------------------------------
% 6.56/2.00 % (4096600)lrs+10_1_sil=8000:sp=occurrence:random_seed=1474040818:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.56/2.00 % (4096601)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4102629660:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.56/2.00 % (4096601)Refutation not found, incomplete strategy
% 6.56/2.00 % (4096601)------------------------------
% 6.56/2.00 % (4096601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096601)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096601)Termination reason: Refutation not found, incomplete strategy
% 6.56/2.00 % (4096601)Time elapsed: 0.002 s
% 6.56/2.00 % (4096601)Peak memory usage: 88 MB
% 6.56/2.00 % (4096601)Instructions burned: 1 (million)
% 6.56/2.00 % (4096603)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=4243488689:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.56/2.00 % (4096602)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2057169159:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.56/2.00 % (4096602)Refutation not found, incomplete strategy
% 6.56/2.00 % (4096602)------------------------------
% 6.56/2.00 % (4096602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096602)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096602)Termination reason: Refutation not found, incomplete strategy
% 6.56/2.00 % (4096602)Time elapsed: 0.002 s
% 6.56/2.00 % (4096602)Peak memory usage: 88 MB
% 6.56/2.00 % (4096602)Instructions burned: 1 (million)
% 6.56/2.00 % (4096603)Instruction limit reached!
% 6.56/2.00 % (4096603)------------------------------
% 6.56/2.00 % (4096603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096603)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096603)Termination reason: Instruction limit
% 6.56/2.00 % (4096603)Termination phase: Saturation
% 6.56/2.00 % (4096603)Time elapsed: 0.069 s
% 6.56/2.00 % (4096603)Peak memory usage: 92 MB
% 6.56/2.00 % (4096603)Instructions burned: 248 (million)
% 6.56/2.00 % (4096600)Instruction limit reached!
% 6.56/2.00 % (4096600)------------------------------
% 6.56/2.00 % (4096600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096600)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096600)Termination reason: Instruction limit
% 6.56/2.00 % (4096600)Termination phase: Saturation
% 6.56/2.00 % (4096600)Time elapsed: 0.166 s
% 6.56/2.00 % (4096600)Peak memory usage: 92 MB
% 6.56/2.00 % (4096600)Instructions burned: 287 (million)
% 6.56/2.00 % (4096608)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4273255151:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.56/2.00 % (4096608)Refutation not found, incomplete strategy
% 6.56/2.00 % (4096608)------------------------------
% 6.56/2.00 % (4096608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096608)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096608)Termination reason: Refutation not found, incomplete strategy
% 6.56/2.00 % (4096608)Time elapsed: 0.001 s
% 6.56/2.00 % (4096608)Peak memory usage: 88 MB
% 6.56/2.00 % (4096608)Instructions burned: 1 (million)
% 6.56/2.00 % (4096601)------------------------------
% 6.56/2.00 % (4096601)------------------------------
% 6.56/2.00 % (4096602)------------------------------
% 6.56/2.00 % (4096602)------------------------------
% 6.56/2.00 % (4096609)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2281835408:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.56/2.00 % (4096608)------------------------------
% 6.56/2.00 % (4096608)------------------------------
% 6.56/2.00 % (4096611)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=391737506:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.56/2.00 % (4096612)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3013325790:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.56/2.00 % (4096614)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2482957111:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.56/2.00 % (4096614)Instruction limit reached!
% 6.56/2.00 % (4096614)------------------------------
% 6.56/2.00 % (4096614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096614)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096614)Termination reason: Instruction limit
% 6.56/2.00 % (4096614)Termination phase: Saturation
% 6.56/2.00 % (4096614)Time elapsed: 0.037 s
% 6.56/2.00 % (4096614)Peak memory usage: 89 MB
% 6.56/2.00 % (4096614)Instructions burned: 116 (million)
% 6.56/2.00 % (4096612)Instruction limit reached!
% 6.56/2.00 % (4096612)------------------------------
% 6.56/2.00 % (4096612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096612)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096612)Termination reason: Instruction limit
% 6.56/2.00 % (4096612)Termination phase: Saturation
% 6.56/2.00 % (4096612)Time elapsed: 0.069 s
% 6.56/2.00 % (4096612)Peak memory usage: 89 MB
% 6.56/2.00 % (4096612)Instructions burned: 128 (million)
% 6.56/2.00 % (4096611)Instruction limit reached!
% 6.56/2.00 % (4096611)------------------------------
% 6.56/2.00 % (4096611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096611)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096611)Termination reason: Instruction limit
% 6.56/2.00 % (4096611)Termination phase: Saturation
% 6.56/2.00 % (4096611)Time elapsed: 0.077 s
% 6.56/2.00 % (4096611)Peak memory usage: 90 MB
% 6.56/2.00 % (4096611)Instructions burned: 113 (million)
% 6.56/2.00 % (4096586)First to succeed.
% 6.56/2.00 % (4096586)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4096581"
% 6.56/2.00 % (4096618)lrs+10_1_sil=8000:sp=occurrence:random_seed=1302541042:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.56/2.00 % (4096619)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3474436656:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.56/2.00 % (4096619)Refutation not found, incomplete strategy
% 6.56/2.00 % (4096619)------------------------------
% 6.56/2.00 % (4096619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/2.00 % (4096619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/2.00 % (4096619)CaDiCaL version: 2.1.3
% 6.56/2.00 % (4096619)Termination reason: Refutation not found, incomplete strategy
% 6.56/2.00 % (4096619)Time elapsed: 0.002 s
% 6.56/2.00 % (4096619)Peak memory usage: 88 MB
% 6.56/2.00 % (4096619)Instructions burned: 1 (million)
% 6.56/2.00 % (4096620)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3351653640:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.56/2.00 % (4096618)Also succeeded, but the first one will report.
% 6.56/2.00 % (4096587)Also succeeded, but the first one will report.
% 6.56/2.00 % (4096586)Refutation found. Thanks to Tanya!
% 6.56/2.00 % SZS status Theorem for theBenchmark
% 6.56/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 8.72/2.20 % (4096586)------------------------------
% 8.72/2.20 % (4096586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/2.20 % (4096586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/2.20 % (4096586)CaDiCaL version: 2.1.3
% 8.72/2.20 % (4096586)Termination reason: Refutation
% 8.72/2.20 % (4096586)Time elapsed: 0.731 s
% 8.72/2.20 % (4096586)Peak memory usage: 129 MB
% 8.72/2.20 % (4096586)Instructions burned: 1075 (million)
% 8.72/2.20 % (4096586)------------------------------
% 8.72/2.20 % (4096586)------------------------------
% 8.72/2.20 % (4096581)Success in time 1.139 s
% 8.72/2.20 % Vampire exiting
%------------------------------------------------------------------------------