%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET712+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:41:43 PM UTC 2026
% Result : Theorem 3.02s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of formulae : 169 ( 15 unt; 9 def)
% Number of atoms : 650 ( 52 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 807 ( 326 ~; 370 |; 73 &)
% ( 20 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 300 ( 0 sgn 274 !; 26 ?)
% 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/sandbox2/benchmark/theBenchmark.p',maps) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X3,X1)
& member(X4,X2) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
& one_to_one(X0,X1,X2) )
=> maps(inverse_function(X0,X1,X2),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII03) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( ( maps(X0,X1,X2)
& one_to_one(X0,X1,X2) )
=> maps(inverse_function(X0,X1,X2),X2,X1) ),
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] :
( one_to_one(X0,X1,X2)
=> ( injective(X0,X1,X2)
& surjective(X0,X1,X2) ) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f33,plain,
! [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 ) ) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f34,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f35,plain,
? [X0,X1,X2] :
( ~ maps(inverse_function(X0,X1,X2),X2,X1)
& maps(X0,X1,X2)
& one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ~ maps(inverse_function(X0,X1,X2),X2,X1)
& maps(X0,X1,X2)
& one_to_one(X0,X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( maps(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) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f38,plain,
! [X0,X1,X2] :
( maps(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) ) ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f42,plain,
! [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) )
| ~ injective(X0,X1,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f43,plain,
! [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) )
| ~ injective(X0,X1,X2) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f45,definition,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f46,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& sP0(X0,X1,X2) ) ),
inference(definition_folding,[],[f38,f45]) ).
fof(f47,plain,
( ~ maps(inverse_function(sK1,sK2,sK3),sK3,sK2)
& maps(sK1,sK2,sK3)
& one_to_one(sK1,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f36]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X5,X6,X7] :
( X6 != X7
& apply(X0,X5,X6)
& apply(X0,X5,X7)
& member(X5,X1)
& member(X6,X2)
& member(X7,X2) ) )
& ( ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3,X4,X5] :
( X4 != X5
& apply(X0,X3,X4)
& apply(X0,X3,X5)
& member(X3,X1)
& member(X4,X2)
& member(X5,X2) ) )
& ( ! [X6,X7,X8] :
( X7 = X8
| ~ apply(X0,X6,X7)
| ~ apply(X0,X6,X8)
| ~ member(X6,X1)
| ~ member(X7,X2)
| ~ member(X8,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
& apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
& apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
& member(sK4(X0,X1,X2),X1)
& member(sK5(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X2) ) )
& ( ! [X6,X7,X8] :
( X7 = X8
| ~ apply(X0,X6,X7)
| ~ apply(X0,X6,X8)
| ~ member(X6,X1)
| ~ member(X7,X2)
| ~ member(X8,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2)),skolemize(X5,sK6(X0,X1,X2))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X2)
| ~ apply(X0,X3,X4) )
& member(X3,X1) )
| ~ sP0(X0,X1,X2) )
& ( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& sP0(X0,X1,X2) )
| ~ maps(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X2)
| ~ apply(X0,X3,X4) )
& member(X3,X1) )
| ~ sP0(X0,X1,X2) )
& ( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& sP0(X0,X1,X2) )
| ~ maps(X0,X1,X2) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X2)
| ~ apply(X0,X3,X4) )
& member(X3,X1) )
| ~ sP0(X0,X1,X2) )
& ( ( ! [X5] :
( ? [X6] :
( member(X6,X2)
& apply(X0,X5,X6) )
| ~ member(X5,X1) )
& sP0(X0,X1,X2) )
| ~ maps(X0,X1,X2) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
| ( ! [X4] :
( ~ member(X4,X2)
| ~ apply(X0,sK7(X0,X1,X2),X4) )
& member(sK7(X0,X1,X2),X1) )
| ~ sP0(X0,X1,X2) )
& ( ( ! [X5] :
( ( member(sK8(X0,X2,X5),X2)
& apply(X0,X5,sK8(X0,X2,X5)) )
| ~ member(X5,X1) )
& sP0(X0,X1,X2) )
| ~ maps(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X2,X5))],[f53]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( ( ( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3) )
& ( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4) ) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(nnf_transformation,[],[f40]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( member(sK9(X0,X1,X3),X1)
& apply(X0,sK9(X0,X1,X3),X3) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X4,sK9(X0,X1,X3))],[f44]) ).
fof(f60,plain,
one_to_one(sK1,sK2,sK3),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
maps(sK1,sK2,sK3),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
~ maps(inverse_function(sK1,sK2,sK3),sK3,sK2),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ sP0(X0,X1,X2)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X6,X8)
| ~ member(X6,X1)
| ~ member(X7,X2)
| ~ member(X8,X2)
| X7 = X8 ),
inference(cnf_transformation,[],[f50]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f66,plain,
! [X2,X0,X1] :
( member(sK4(X0,X1,X2),X1)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f67,plain,
! [X2,X0,X1] :
( apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f68,plain,
! [X2,X0,X1] :
( apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f69,plain,
! [X2,X0,X1] :
( sK5(X0,X1,X2) != sK6(X0,X1,X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ maps(X0,X1,X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f71,plain,
! [X2,X0,X1,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X5,X1)
| apply(X0,X5,sK8(X0,X2,X5)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f72,plain,
! [X2,X0,X1,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X5,X1)
| member(sK8(X0,X2,X5),X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| maps(X0,X1,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f74,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,sK7(X0,X1,X2),X4)
| ~ member(X4,X2)
| maps(X0,X1,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4] :
( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ injective(X0,X1,X2)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X2)
| X3 = X4 ),
inference(cnf_transformation,[],[f43]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| apply(X0,sK9(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| member(sK9(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f91,plain,
sP0(sK1,sK2,sK3),
inference(resolution,[],[f70,f61]) ).
fof(f92,plain,
surjective(sK1,sK2,sK3),
inference(resolution,[],[f77,f60]) ).
fof(f93,plain,
injective(sK1,sK2,sK3),
inference(resolution,[],[f78,f60]) ).
fof(f102,plain,
! [X0] :
( member(sK8(sK1,sK3,X0),sK3)
| ~ member(X0,sK2) ),
inference(resolution,[],[f72,f61]) ).
fof(f103,plain,
! [X0] :
( member(sK9(sK1,sK2,X0),sK2)
| ~ member(X0,sK3) ),
inference(resolution,[],[f86,f92]) ).
fof(f104,plain,
! [X0] :
( apply(sK1,X0,sK8(sK1,sK3,X0))
| ~ member(X0,sK2) ),
inference(resolution,[],[f71,f61]) ).
fof(f107,plain,
! [X0] :
( apply(sK1,sK9(sK1,sK2,X0),X0)
| ~ member(X0,sK3) ),
inference(resolution,[],[f85,f92]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK6(inverse_function(X0,X1,X2),X3,X4),sK4(inverse_function(X0,X1,X2),X3,X4))
| ~ member(sK6(inverse_function(X0,X1,X2),X3,X4),X1)
| ~ member(sK4(inverse_function(X0,X1,X2),X3,X4),X2)
| sP0(inverse_function(X0,X1,X2),X3,X4) ),
inference(resolution,[],[f76,f67]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,sK5(inverse_function(X0,X1,X2),X3,X4),sK4(inverse_function(X0,X1,X2),X3,X4))
| ~ member(sK5(inverse_function(X0,X1,X2),X3,X4),X1)
| ~ member(sK4(inverse_function(X0,X1,X2),X3,X4),X2)
| sP0(inverse_function(X0,X1,X2),X3,X4) ),
inference(resolution,[],[f76,f68]) ).
fof(f116,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ apply(X2,X0,sK7(inverse_function(X2,X3,X4),X5,X1))
| maps(inverse_function(X2,X3,X4),X5,X1)
| ~ sP0(inverse_function(X2,X3,X4),X5,X1)
| ~ member(X0,X1)
| ~ member(X0,X3)
| ~ member(sK7(inverse_function(X2,X3,X4),X5,X1),X4) ),
inference(resolution,[],[f74,f75]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ apply(sK1,X0,X2)
| ~ apply(sK1,X0,X1)
| ~ member(X0,sK2)
| ~ member(X1,sK3)
| ~ member(X2,sK3)
| X1 = X2 ),
inference(resolution,[],[f63,f91]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ apply(sK1,X2,X1)
| ~ apply(sK1,X0,X1)
| ~ member(X0,sK2)
| ~ member(X2,sK2)
| ~ member(X1,sK3)
| X0 = X2 ),
inference(resolution,[],[f79,f93]) ).
fof(f127,plain,
! [X0,X1] :
( ~ apply(sK1,sK9(sK1,sK2,X0),X1)
| ~ member(sK9(sK1,sK2,X0),sK2)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| X0 = X1
| ~ member(X0,sK3) ),
inference(resolution,[],[f119,f107]) ).
fof(f130,plain,
! [X0,X1] :
( ~ apply(sK1,sK9(sK1,sK2,X0),X1)
| ~ member(sK9(sK1,sK2,X0),sK2)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f127]) ).
fof(f132,plain,
! [X0,X1] :
( ~ apply(sK1,sK9(sK1,sK2,X0),X1)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f130,f103]) ).
fof(f136,plain,
! [X0] :
( ~ member(sK8(sK1,sK3,sK9(sK1,sK2,X0)),sK3)
| ~ member(X0,sK3)
| sK8(sK1,sK3,sK9(sK1,sK2,X0)) = X0
| ~ member(sK9(sK1,sK2,X0),sK2) ),
inference(resolution,[],[f132,f104]) ).
fof(f138,plain,
! [X0] :
( ~ member(X0,sK3)
| sK8(sK1,sK3,sK9(sK1,sK2,X0)) = X0
| ~ member(sK9(sK1,sK2,X0),sK2) ),
inference(forward_subsumption_resolution,[],[f136,f102]) ).
fof(f139,plain,
! [X0] :
( ~ member(X0,sK3)
| sK8(sK1,sK3,sK9(sK1,sK2,X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f138,f103]) ).
fof(f142,plain,
! [X0,X1] :
( sP0(X0,sK3,X1)
| sK4(X0,sK3,X1) = sK8(sK1,sK3,sK9(sK1,sK2,sK4(X0,sK3,X1))) ),
inference(resolution,[],[f139,f66]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,X0,X1),X2,X3)),X3)
| ~ sP0(inverse_function(sK1,X0,X1),X2,X3)
| maps(inverse_function(sK1,X0,X1),X2,X3)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,X0,X1),X2,X3)),X0)
| ~ member(sK7(inverse_function(sK1,X0,X1),X2,X3),X1)
| ~ member(sK7(inverse_function(sK1,X0,X1),X2,X3),sK3) ),
inference(resolution,[],[f116,f107]) ).
fof(f184,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK1,X0,sK4(inverse_function(sK1,X1,X2),X3,X4))
| ~ member(X0,sK2)
| ~ member(sK6(inverse_function(sK1,X1,X2),X3,X4),sK2)
| ~ member(sK4(inverse_function(sK1,X1,X2),X3,X4),sK3)
| sK6(inverse_function(sK1,X1,X2),X3,X4) = X0
| ~ member(sK6(inverse_function(sK1,X1,X2),X3,X4),X1)
| ~ member(sK4(inverse_function(sK1,X1,X2),X3,X4),X2)
| sP0(inverse_function(sK1,X1,X2),X3,X4) ),
inference(resolution,[],[f125,f109]) ).
fof(f185,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK1,X0,sK4(inverse_function(sK1,X1,X2),X3,X4))
| ~ member(X0,sK2)
| ~ member(sK5(inverse_function(sK1,X1,X2),X3,X4),sK2)
| ~ member(sK4(inverse_function(sK1,X1,X2),X3,X4),sK3)
| sK5(inverse_function(sK1,X1,X2),X3,X4) = X0
| ~ member(sK5(inverse_function(sK1,X1,X2),X3,X4),X1)
| ~ member(sK4(inverse_function(sK1,X1,X2),X3,X4),X2)
| sP0(inverse_function(sK1,X1,X2),X3,X4) ),
inference(resolution,[],[f125,f110]) ).
fof(f586,definition,
( spl10_1
<=> sK4(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK8(sK1,sK3,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f587,plain,
( sK4(inverse_function(sK1,sK2,sK3),sK3,sK2) != sK8(sK1,sK3,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)))
| spl10_1 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f588,plain,
( sK4(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK8(sK1,sK3,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)))
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f606,definition,
( spl10_3
<=> member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f607,plain,
( member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f608,plain,
( ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| spl10_3 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f610,definition,
( spl10_4
<=> member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f611,plain,
( ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| spl10_4 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f612,plain,
( member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f640,plain,
( ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| spl10_3 ),
inference(resolution,[],[f608,f103]) ).
fof(f641,plain,
( ~ spl10_4
| spl10_3 ),
inference(avatar_split_clause,[],[f640,f606,f610]) ).
fof(f651,plain,
( maps(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4 ),
inference(resolution,[],[f611,f73]) ).
fof(f652,plain,
( ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4 ),
inference(forward_subsumption_resolution,[],[f651,f62]) ).
fof(f664,plain,
( sK4(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK8(sK1,sK3,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)))
| spl10_4 ),
inference(resolution,[],[f652,f142]) ).
fof(f673,plain,
( spl10_1
| spl10_4 ),
inference(avatar_split_clause,[],[f664,f610,f586]) ).
fof(f685,plain,
( apply(sK1,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ spl10_1 ),
inference(superposition,[],[f104,f588]) ).
fof(f688,definition,
( spl10_10
<=> member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f689,plain,
( member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f690,plain,
( ~ member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| spl10_10 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f692,definition,
( spl10_11
<=> member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f693,plain,
( ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| spl10_11 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f697,definition,
( spl10_12
<=> apply(sK1,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
fof(f699,plain,
( apply(sK1,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f700,plain,
( ~ spl10_10
| spl10_12
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f685,f586,f697,f688]) ).
fof(f724,plain,
( ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| spl10_10 ),
inference(resolution,[],[f690,f103]) ).
fof(f725,plain,
( ~ spl10_11
| spl10_10 ),
inference(avatar_split_clause,[],[f724,f688,f692]) ).
fof(f733,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_11 ),
inference(resolution,[],[f693,f66]) ).
fof(f734,plain,
( $false
| spl10_4
| spl10_11 ),
inference(forward_subsumption_resolution,[],[f733,f652]) ).
fof(f735,plain,
( spl10_4
| spl10_11 ),
inference(avatar_contradiction_clause,[],[f734]) ).
fof(f768,plain,
( ~ member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12 ),
inference(resolution,[],[f699,f184]) ).
fof(f786,plain,
( ~ member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12 ),
inference(duplicate_literal_removal,[],[f768]) ).
fof(f788,plain,
( ~ member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f786,f64]) ).
fof(f790,plain,
( ~ member(sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f788,f66]) ).
fof(f792,plain,
( sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f790,f689]) ).
fof(f794,plain,
( sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f792,f652]) ).
fof(f804,plain,
( apply(sK1,sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(superposition,[],[f699,f794]) ).
fof(f835,plain,
( ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(resolution,[],[f804,f185]) ).
fof(f849,plain,
( ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(duplicate_literal_removal,[],[f835]) ).
fof(f851,plain,
( ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f849,f64]) ).
fof(f853,plain,
( ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f851,f65]) ).
fof(f854,plain,
( sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f853,f66]) ).
fof(f855,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f854,f69]) ).
fof(f856,plain,
( $false
| spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_subsumption_resolution,[],[f855,f652]) ).
fof(f857,plain,
( spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(avatar_contradiction_clause,[],[f856]) ).
fof(f864,definition,
( spl10_17
<=> sP0(inverse_function(sK1,sK2,sK3),sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl10_17])],[avatar_definition]) ).
fof(f865,plain,
( ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| spl10_17 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f866,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_17 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f868,definition,
( spl10_18
<=> sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl10_18])],[avatar_definition]) ).
fof(f870,plain,
( sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)) = sK6(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_18 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f871,plain,
( spl10_17
| spl10_18
| ~ spl10_10
| ~ spl10_12 ),
inference(avatar_split_clause,[],[f792,f697,f688,f868,f864]) ).
fof(f906,plain,
( ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| maps(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ spl10_3 ),
inference(resolution,[],[f607,f165]) ).
fof(f911,plain,
( ~ sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| maps(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ spl10_3 ),
inference(duplicate_literal_removal,[],[f906]) ).
fof(f915,plain,
( maps(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ spl10_3
| ~ spl10_17 ),
inference(forward_subsumption_resolution,[],[f911,f866]) ).
fof(f917,plain,
( ~ member(sK9(sK1,sK2,sK7(inverse_function(sK1,sK2,sK3),sK3,sK2)),sK2)
| ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ spl10_3
| ~ spl10_17 ),
inference(forward_subsumption_resolution,[],[f915,f62]) ).
fof(f918,plain,
( ~ member(sK7(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| ~ spl10_3
| ~ spl10_17 ),
inference(forward_subsumption_resolution,[],[f917,f103]) ).
fof(f919,plain,
( $false
| ~ spl10_3
| ~ spl10_4
| ~ spl10_17 ),
inference(forward_subsumption_resolution,[],[f918,f612]) ).
fof(f920,plain,
( ~ spl10_3
| ~ spl10_4
| ~ spl10_17 ),
inference(avatar_contradiction_clause,[],[f919]) ).
fof(f929,plain,
( sK4(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK8(sK1,sK3,sK9(sK1,sK2,sK4(inverse_function(sK1,sK2,sK3),sK3,sK2)))
| spl10_17 ),
inference(resolution,[],[f865,f142]) ).
fof(f946,plain,
( apply(sK1,sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK4(inverse_function(sK1,sK2,sK3),sK3,sK2))
| ~ spl10_12
| ~ spl10_18 ),
inference(superposition,[],[f699,f870]) ).
fof(f981,plain,
( ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12
| ~ spl10_18 ),
inference(resolution,[],[f946,f185]) ).
fof(f995,plain,
( ~ member(sK6(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12
| ~ spl10_18 ),
inference(duplicate_literal_removal,[],[f981]) ).
fof(f997,plain,
( ~ member(sK5(inverse_function(sK1,sK2,sK3),sK3,sK2),sK2)
| ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12
| ~ spl10_18 ),
inference(forward_subsumption_resolution,[],[f995,f64]) ).
fof(f999,plain,
( ~ member(sK4(inverse_function(sK1,sK2,sK3),sK3,sK2),sK3)
| sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12
| ~ spl10_18 ),
inference(forward_subsumption_resolution,[],[f997,f65]) ).
fof(f1000,plain,
( sK6(inverse_function(sK1,sK2,sK3),sK3,sK2) = sK5(inverse_function(sK1,sK2,sK3),sK3,sK2)
| sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12
| ~ spl10_18 ),
inference(forward_subsumption_resolution,[],[f999,f66]) ).
fof(f1001,plain,
( sP0(inverse_function(sK1,sK2,sK3),sK3,sK2)
| ~ spl10_12
| ~ spl10_18 ),
inference(forward_subsumption_resolution,[],[f1000,f69]) ).
fof(f1002,plain,
( $false
| ~ spl10_12
| spl10_17
| ~ spl10_18 ),
inference(forward_subsumption_resolution,[],[f1001,f865]) ).
fof(f1003,plain,
( ~ spl10_12
| spl10_17
| ~ spl10_18 ),
inference(avatar_contradiction_clause,[],[f1002]) ).
fof(f1005,plain,
( $false
| spl10_11
| spl10_17 ),
inference(forward_subsumption_resolution,[],[f733,f865]) ).
fof(f1006,plain,
( spl10_11
| spl10_17 ),
inference(avatar_contradiction_clause,[],[f1005]) ).
fof(f1018,plain,
( $false
| spl10_1
| spl10_17 ),
inference(forward_subsumption_resolution,[],[f929,f587]) ).
fof(f1019,plain,
( spl10_1
| spl10_17 ),
inference(avatar_contradiction_clause,[],[f1018]) ).
cnf(s8,plain,
( spl10_3
| ~ spl10_4 ),
inference(sat_conversion,[],[f641]) ).
cnf(s9,plain,
( spl10_1
| spl10_4 ),
inference(sat_conversion,[],[f673]) ).
cnf(s11,plain,
( ~ spl10_1
| ~ spl10_10
| spl10_12 ),
inference(sat_conversion,[],[f700]) ).
cnf(s16,plain,
( spl10_10
| ~ spl10_11 ),
inference(sat_conversion,[],[f725]) ).
cnf(s17,plain,
( spl10_4
| spl10_11 ),
inference(sat_conversion,[],[f735]) ).
cnf(s18,plain,
( spl10_4
| ~ spl10_10
| ~ spl10_12 ),
inference(sat_conversion,[],[f857]) ).
cnf(s19,plain,
( ~ spl10_10
| ~ spl10_12
| spl10_17
| spl10_18 ),
inference(sat_conversion,[],[f871]) ).
cnf(s21,plain,
( ~ spl10_3
| ~ spl10_4
| ~ spl10_17 ),
inference(sat_conversion,[],[f920]) ).
cnf(s22,plain,
( ~ spl10_12
| spl10_17
| ~ spl10_18 ),
inference(sat_conversion,[],[f1003]) ).
cnf(s24,plain,
( spl10_11
| spl10_17 ),
inference(sat_conversion,[],[f1006]) ).
cnf(s26,plain,
( spl10_1
| spl10_17 ),
inference(sat_conversion,[],[f1019]) ).
cnf(s27,plain,
( ~ spl10_17
| ~ spl10_4 ),
inference(rat,[],[s8,s21]) ).
cnf(s28,plain,
spl10_1,
inference(rat,[],[s27,s9,s26]) ).
cnf(s29,plain,
spl10_4,
inference(rat,[],[s18,s11,s16,s17,s28]) ).
cnf(s31,plain,
~ spl10_17,
inference(rat,[],[s27,s29]) ).
cnf(s32,plain,
spl10_11,
inference(rat,[],[s24,s31]) ).
cnf(s33,plain,
spl10_10,
inference(rat,[],[s16,s32]) ).
cnf(s38,plain,
spl10_12,
inference(rat,[],[s11,s28,s33]) ).
cnf(s39,plain,
~ spl10_18,
inference(rat,[],[s22,s31,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s19,s33,s31,s38,s39]) ).
fof(f1020,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET712+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 02:38:32 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.02/1.31 % (2942005)Detected formulas, will run a generic FOF schedule.
% 3.02/1.31 % (2942014)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4241437556:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.02/1.31 % (2942014)Instruction limit reached!
% 3.02/1.31 % (2942014)------------------------------
% 3.02/1.31 % (2942014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.31 % (2942014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.31 % (2942014)CaDiCaL version: 2.1.3
% 3.02/1.31 % (2942014)Termination reason: Instruction limit
% 3.02/1.31 % (2942014)Termination phase: Saturation
% 3.02/1.31 % (2942014)Time elapsed: 0.038 s
% 3.02/1.31 % (2942014)Peak memory usage: 88 MB
% 3.02/1.31 % (2942014)Instructions burned: 119 (million)
% 3.02/1.31 % (2942016)dis-21_1_sil=8000:lcm=predicate:random_seed=236903508: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)
% 3.02/1.31 % (2942010)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=3667776467:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.02/1.31 % (2942011)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=3816034866:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.02/1.31 % (2942013)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4094511015:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.02/1.31 % (2942012)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=328257729:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.02/1.31 % (2942015)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2863164685:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.02/1.31 % (2942013)Refutation not found, incomplete strategy
% 3.02/1.31 % (2942013)------------------------------
% 3.02/1.31 % (2942013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.31 % (2942013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.31 % (2942013)CaDiCaL version: 2.1.3
% 3.02/1.31 % (2942013)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.31 % (2942013)Time elapsed: 0.004 s
% 3.02/1.31 % (2942013)Peak memory usage: 88 MB
% 3.02/1.31 % (2942013)Instructions burned: 4 (million)
% 3.02/1.31 % (2942016)Instruction limit reached!
% 3.02/1.31 % (2942016)------------------------------
% 3.02/1.31 % (2942016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.31 % (2942016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.31 % (2942016)CaDiCaL version: 2.1.3
% 3.02/1.31 % (2942016)Termination reason: Instruction limit
% 3.02/1.31 % (2942016)Termination phase: Saturation
% 3.02/1.31 % (2942016)Time elapsed: 0.078 s
% 3.02/1.31 % (2942016)Peak memory usage: 88 MB
% 3.02/1.31 % (2942016)Instructions burned: 130 (million)
% 3.02/1.31 % (2942015)Instruction limit reached!
% 3.02/1.31 % (2942015)------------------------------
% 3.02/1.31 % (2942015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.31 % (2942015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.31 % (2942015)CaDiCaL version: 2.1.3
% 3.02/1.31 % (2942015)Termination reason: Instruction limit
% 3.02/1.31 % (2942015)Termination phase: Saturation
% 3.02/1.31 % (2942015)Time elapsed: 0.096 s
% 3.02/1.31 % (2942015)Peak memory usage: 89 MB
% 3.02/1.31 % (2942015)Instructions burned: 140 (million)
% 3.02/1.31 % (2942024)lrs+10_1_sil=8000:sp=occurrence:random_seed=1733758222:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.02/1.31 % (2942024)First to succeed.
% 3.02/1.31 % (2942024)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2942005"
% 3.02/1.31 % (2942025)lrs+10_1_sil=32000:urr=on:br=off:random_seed=659364357:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.02/1.31 % (2942025)Refutation not found, incomplete strategy
% 3.02/1.31 % (2942025)------------------------------
% 3.02/1.31 % (2942025)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.31 % (2942025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.31 % (2942025)CaDiCaL version: 2.1.3
% 3.02/1.31 % (2942025)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.31 % (2942025)Time elapsed: 0.002 s
% 3.02/1.31 % (2942025)Peak memory usage: 88 MB
% 3.02/1.31 % (2942025)Instructions burned: 1 (million)
% 3.02/1.31 % (2942013)------------------------------
% 3.02/1.31 % (2942013)------------------------------
% 3.02/1.31 % (2942026)lrs+1011_1_sil=32000:sp=occurrence:random_seed=218082177:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.02/1.31 % (2942024)Refutation found. Thanks to Tanya!
% 3.02/1.31 % SZS status Theorem for theBenchmark
% 3.02/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.51 % (2942024)------------------------------
% 0.17/1.51 % (2942024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.51 % (2942024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.51 % (2942024)CaDiCaL version: 2.1.3
% 0.17/1.51 % (2942024)Termination reason: Refutation
% 0.17/1.51 % (2942024)Time elapsed: 0.029 s
% 0.17/1.51 % (2942024)Peak memory usage: 91 MB
% 0.17/1.51 % (2942024)Instructions burned: 86 (million)
% 0.17/1.51 % (2942024)------------------------------
% 0.17/1.51 % (2942024)------------------------------
% 0.17/1.51 % (2942005)Success in time 0.48 s
% 0.17/1.51 % Vampire exiting
%------------------------------------------------------------------------------