%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET729+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 : n013.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 9.74s 2.25s
% Output : Refutation 10.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 29
% Syntax : Number of formulae : 316 ( 10 unt; 20 def)
% Number of atoms : 1328 ( 93 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1751 ( 739 ~; 830 |; 120 &)
% ( 42 <=>; 19 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 20 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-5 aty)
% Number of variables : 528 ( 0 sgn 490 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
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(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/sandbox2/benchmark/theBenchmark.p',compose_function) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox2/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/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(f20,axiom,
! [X0,X1,X2,X3] :
( inverse_predicate(X0,X1,X2,X3)
<=> ! [X4,X5] :
( ( member(X4,X2)
& member(X5,X3) )
=> ( apply(X1,X4,X5)
<=> apply(X0,X5,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_predicate) ).
fof(f29,conjecture,
! [X0,X1] :
( maps(X0,X1,X1)
=> ( ( one_to_one(X0,X1,X1)
& inverse_predicate(X0,X0,X1,X1) )
<=> identity(compose_function(X0,X0,X1,X1,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII20) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( maps(X0,X1,X1)
=> ( ( one_to_one(X0,X1,X1)
& inverse_predicate(X0,X0,X1,X1) )
<=> identity(compose_function(X0,X0,X1,X1,X1),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] :
( 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] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,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(f36,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,[],[f35]) ).
fof(f37,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(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f40,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,[],[f17]) ).
fof(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( inverse_predicate(X0,X1,X2,X3)
<=> ! [X4,X5] :
( ( apply(X1,X4,X5)
<=> apply(X0,X5,X4) )
| ~ member(X4,X2)
| ~ member(X5,X3) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( inverse_predicate(X0,X1,X2,X3)
<=> ! [X4,X5] :
( ( apply(X1,X4,X5)
<=> apply(X0,X5,X4) )
| ~ member(X4,X2)
| ~ member(X5,X3) ) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
? [X0,X1] :
( ( ( one_to_one(X0,X1,X1)
& inverse_predicate(X0,X0,X1,X1) )
<~> identity(compose_function(X0,X0,X1,X1,X1),X1) )
& maps(X0,X1,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f48,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f49]) ).
fof(f67,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))],[f36]) ).
fof(f68,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,[],[f38]) ).
fof(f69,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,[],[f68]) ).
fof(f70,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))],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( identity(X0,X1)
| ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f72,plain,
! [X0,X1] :
( ( identity(X0,X1)
| ? [X2] :
( ~ apply(X0,X2,X2)
& member(X2,X1) ) )
& ( ! [X3] :
( apply(X0,X3,X3)
| ~ member(X3,X1) )
| ~ identity(X0,X1) ) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( identity(X0,X1)
| ( ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
& member(sK5(X0,X1),X1) ) )
& ( ! [X3] :
( apply(X0,X3,X3)
| ~ member(X3,X1) )
| ~ identity(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f72]) ).
fof(f74,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) ) )
& ( ! [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(nnf_transformation,[],[f41]) ).
fof(f75,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) ) )
& ( ! [X6,X7,X8] :
( X6 = X7
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( injective(X0,X1,X2)
| ( sK6(X0,X1,X2) != sK7(X0,X1,X2)
& apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
& apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
& member(sK6(X0,X1,X2),X1)
& member(sK7(X0,X1,X2),X1)
& member(sK8(X0,X1,X2),X2) ) )
& ( ! [X6,X7,X8] :
( X6 = X7
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2) )
| ~ injective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X5,sK8(X0,X1,X2))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) )
& ( ! [X3] :
( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X3) )
| ~ member(X3,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,X3) )
& member(X3,X2) ) )
& ( ! [X5] :
( ? [X6] :
( member(X6,X1)
& apply(X0,X6,X5) )
| ~ member(X5,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ member(X4,X1)
| ~ apply(X0,X4,sK9(X0,X1,X2)) )
& member(sK9(X0,X1,X2),X2) ) )
& ( ! [X5] :
( ( member(sK10(X0,X1,X5),X1)
& apply(X0,sK10(X0,X1,X5),X5) )
| ~ member(X5,X2) )
| ~ surjective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X3,sK9(X0,X1,X2)),skolemize(X6,sK10(X0,X1,X5))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) )
& ( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ~ surjective(X0,X1,X2) )
& ( ( injective(X0,X1,X2)
& surjective(X0,X1,X2) )
| ~ one_to_one(X0,X1,X2) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ( inverse_predicate(X0,X1,X2,X3)
| ? [X4,X5] :
( ( ~ apply(X0,X5,X4)
| ~ apply(X1,X4,X5) )
& ( apply(X0,X5,X4)
| apply(X1,X4,X5) )
& member(X4,X2)
& member(X5,X3) ) )
& ( ! [X4,X5] :
( ( ( apply(X1,X4,X5)
| ~ apply(X0,X5,X4) )
& ( apply(X0,X5,X4)
| ~ apply(X1,X4,X5) ) )
| ~ member(X4,X2)
| ~ member(X5,X3) )
| ~ inverse_predicate(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ( inverse_predicate(X0,X1,X2,X3)
| ? [X4,X5] :
( ( ~ apply(X0,X5,X4)
| ~ apply(X1,X4,X5) )
& ( apply(X0,X5,X4)
| apply(X1,X4,X5) )
& member(X4,X2)
& member(X5,X3) ) )
& ( ! [X4,X5] :
( ( ( apply(X1,X4,X5)
| ~ apply(X0,X5,X4) )
& ( apply(X0,X5,X4)
| ~ apply(X1,X4,X5) ) )
| ~ member(X4,X2)
| ~ member(X5,X3) )
| ~ inverse_predicate(X0,X1,X2,X3) ) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ( inverse_predicate(X0,X1,X2,X3)
| ? [X4,X5] :
( ( ~ apply(X0,X5,X4)
| ~ apply(X1,X4,X5) )
& ( apply(X0,X5,X4)
| apply(X1,X4,X5) )
& member(X4,X2)
& member(X5,X3) ) )
& ( ! [X6,X7] :
( ( ( apply(X1,X6,X7)
| ~ apply(X0,X7,X6) )
& ( apply(X0,X7,X6)
| ~ apply(X1,X6,X7) ) )
| ~ member(X6,X2)
| ~ member(X7,X3) )
| ~ inverse_predicate(X0,X1,X2,X3) ) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ( inverse_predicate(X0,X1,X2,X3)
| ( ( ~ apply(X0,sK12(X0,X1,X2,X3),sK11(X0,X1,X2,X3))
| ~ apply(X1,sK11(X0,X1,X2,X3),sK12(X0,X1,X2,X3)) )
& ( apply(X0,sK12(X0,X1,X2,X3),sK11(X0,X1,X2,X3))
| apply(X1,sK11(X0,X1,X2,X3),sK12(X0,X1,X2,X3)) )
& member(sK11(X0,X1,X2,X3),X2)
& member(sK12(X0,X1,X2,X3),X3) ) )
& ( ! [X6,X7] :
( ( ( apply(X1,X6,X7)
| ~ apply(X0,X7,X6) )
& ( apply(X0,X7,X6)
| ~ apply(X1,X6,X7) ) )
| ~ member(X6,X2)
| ~ member(X7,X3) )
| ~ inverse_predicate(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X4,sK11(X0,X1,X2,X3)),skolemize(X5,sK12(X0,X1,X2,X3))],[f84]) ).
fof(f101,plain,
? [X0,X1] :
( ( ~ identity(compose_function(X0,X0,X1,X1,X1),X1)
| ~ one_to_one(X0,X1,X1)
| ~ inverse_predicate(X0,X0,X1,X1) )
& ( identity(compose_function(X0,X0,X1,X1,X1),X1)
| ( one_to_one(X0,X1,X1)
& inverse_predicate(X0,X0,X1,X1) ) )
& maps(X0,X1,X1) ),
inference(nnf_transformation,[],[f47]) ).
fof(f102,plain,
? [X0,X1] :
( ( ~ identity(compose_function(X0,X0,X1,X1,X1),X1)
| ~ one_to_one(X0,X1,X1)
| ~ inverse_predicate(X0,X0,X1,X1) )
& ( identity(compose_function(X0,X0,X1,X1,X1),X1)
| ( one_to_one(X0,X1,X1)
& inverse_predicate(X0,X0,X1,X1) ) )
& maps(X0,X1,X1) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
( ( ~ identity(compose_function(sK17,sK17,sK18,sK18,sK18),sK18)
| ~ one_to_one(sK17,sK18,sK18)
| ~ inverse_predicate(sK17,sK17,sK18,sK18) )
& ( identity(compose_function(sK17,sK17,sK18,sK18,sK18),sK18)
| ( one_to_one(sK17,sK18,sK18)
& inverse_predicate(sK17,sK17,sK18,sK18) ) )
& maps(sK17,sK18,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f102]) ).
fof(f104,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f105,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f130,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,[],[f67]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f133,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,[],[f70]) ).
fof(f134,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,[],[f70]) ).
fof(f135,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,[],[f70]) ).
fof(f136,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ apply(X1,X5,X7)
| ~ member(X7,X3)
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ apply(X0,X7,X6)
| ~ member(X5,X2)
| ~ member(X6,X4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f137,plain,
! [X3,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X3,X1)
| apply(X0,X3,X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f138,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| identity(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f139,plain,
! [X0,X1] :
( ~ apply(X0,sK5(X0,X1),sK5(X0,X1))
| identity(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f140,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ injective(X0,X1,X2)
| ~ apply(X0,X6,X8)
| ~ apply(X0,X7,X8)
| ~ member(X6,X1)
| ~ member(X7,X1)
| ~ member(X8,X2)
| X6 = X7 ),
inference(cnf_transformation,[],[f76]) ).
fof(f141,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f142,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f143,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f144,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f145,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f146,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) != sK7(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f149,plain,
! [X2,X0,X1] :
( member(sK9(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f150,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK9(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f155,plain,
! [X2,X3,X0,X1,X6,X7] :
( ~ inverse_predicate(X0,X1,X2,X3)
| ~ apply(X0,X7,X6)
| ~ member(X6,X2)
| ~ member(X7,X3)
| apply(X1,X6,X7) ),
inference(cnf_transformation,[],[f85]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( member(sK12(X0,X1,X2,X3),X3)
| inverse_predicate(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( member(sK11(X0,X1,X2,X3),X2)
| inverse_predicate(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK11(X0,X1,X2,X3),sK12(X0,X1,X2,X3))
| apply(X0,sK12(X0,X1,X2,X3),sK11(X0,X1,X2,X3))
| inverse_predicate(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( ~ apply(X1,sK11(X0,X1,X2,X3),sK12(X0,X1,X2,X3))
| ~ apply(X0,sK12(X0,X1,X2,X3),sK11(X0,X1,X2,X3))
| inverse_predicate(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f176,plain,
maps(sK17,sK18,sK18),
inference(cnf_transformation,[],[f103]) ).
fof(f177,plain,
( identity(compose_function(sK17,sK17,sK18,sK18,sK18),sK18)
| inverse_predicate(sK17,sK17,sK18,sK18) ),
inference(cnf_transformation,[],[f103]) ).
fof(f179,plain,
( ~ identity(compose_function(sK17,sK17,sK18,sK18,sK18),sK18)
| ~ one_to_one(sK17,sK18,sK18)
| ~ inverse_predicate(sK17,sK17,sK18,sK18) ),
inference(cnf_transformation,[],[f103]) ).
fof(f183,definition,
sF19 = compose_function(sK17,sK17,sK18,sK18,sK18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f184,plain,
compose_function(sK17,sK17,sK18,sK18,sK18) = sF19,
inference(reorient_equations,[],[f183]) ).
fof(f185,plain,
( ~ identity(sF19,sK18)
| ~ one_to_one(sK17,sK18,sK18)
| ~ inverse_predicate(sK17,sK17,sK18,sK18) ),
inference(definition_folding,[],[f179,f184]) ).
fof(f187,plain,
( identity(sF19,sK18)
| inverse_predicate(sK17,sK17,sK18,sK18) ),
inference(definition_folding,[],[f177,f184]) ).
fof(f189,definition,
( spl20_1
<=> inverse_predicate(sK17,sK17,sK18,sK18) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f190,plain,
( ~ inverse_predicate(sK17,sK17,sK18,sK18)
| spl20_1 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f191,plain,
( inverse_predicate(sK17,sK17,sK18,sK18)
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f193,definition,
( spl20_2
<=> identity(sF19,sK18) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f194,plain,
( ~ identity(sF19,sK18)
| spl20_2 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f195,plain,
( identity(sF19,sK18)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f187,f193,f189]) ).
fof(f198,definition,
( spl20_3
<=> one_to_one(sK17,sK18,sK18) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f199,plain,
( ~ one_to_one(sK17,sK18,sK18)
| spl20_3 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f202,plain,
( ~ spl20_1
| ~ spl20_3
| ~ spl20_2 ),
inference(avatar_split_clause,[],[f185,f193,f198,f189]) ).
fof(f203,plain,
( ! [X0] :
( apply(sF19,X0,X0)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f137,f195]) ).
fof(f204,plain,
! [X0,X1] :
( apply(sK17,sK4(sK17,sK17,sK18,X0,X1),X1)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(superposition,[],[f133,f184]) ).
fof(f205,plain,
! [X0,X1] :
( apply(sK17,X0,sK4(sK17,sK17,sK18,X0,X1))
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(superposition,[],[f134,f184]) ).
fof(f206,plain,
! [X0,X1] :
( member(sK4(sK17,sK17,sK18,X0,X1),sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(superposition,[],[f135,f184]) ).
fof(f216,plain,
! [X0] :
( apply(sK17,X0,sK3(sK17,sK18,X0))
| ~ member(X0,sK18) ),
inference(resolution,[],[f131,f176]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(sK17,sK18,X0),X3)
| ~ apply(sK17,X0,X1)
| sK3(sK17,sK18,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ member(X0,sK18)
| ~ maps(sK17,X2,X3) ),
inference(resolution,[],[f216,f130]) ).
fof(f218,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply(compose_function(X2,sK17,X3,X1,X4),X0,X5)
| ~ member(sK3(sK17,sK18,X0),X1)
| ~ member(X0,sK18)
| ~ apply(X2,sK3(sK17,sK18,X0),X5)
| ~ member(X0,X3)
| ~ member(X5,X4) ),
inference(resolution,[],[f216,f136]) ).
fof(f219,plain,
! [X0] :
( subset(X0,X0)
| subset(X0,X0) ),
inference(resolution,[],[f105,f106]) ).
fof(f220,plain,
! [X0] : subset(X0,X0),
inference(duplicate_literal_removal,[],[f219]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK17,sK17,sK18,X0,sK9(sK17,X1,X2)),X1)
| surjective(sK17,X1,X2)
| ~ apply(sF19,X0,sK9(sK17,X1,X2))
| ~ member(X0,sK18)
| ~ member(sK9(sK17,X1,X2),sK18) ),
inference(resolution,[],[f150,f204]) ).
fof(f223,plain,
! [X0,X1] :
( surjective(sK17,sK18,X0)
| ~ apply(sF19,X1,sK9(sK17,sK18,X0))
| ~ member(X1,sK18)
| ~ member(sK9(sK17,sK18,X0),sK18)
| ~ apply(sF19,X1,sK9(sK17,sK18,X0))
| ~ member(X1,sK18)
| ~ member(sK9(sK17,sK18,X0),sK18) ),
inference(resolution,[],[f222,f206]) ).
fof(f224,plain,
! [X0,X1] :
( ~ apply(sF19,X1,sK9(sK17,sK18,X0))
| surjective(sK17,sK18,X0)
| ~ member(X1,sK18)
| ~ member(sK9(sK17,sK18,X0),sK18) ),
inference(duplicate_literal_removal,[],[f223]) ).
fof(f225,plain,
( ! [X0] :
( surjective(sK17,sK18,X0)
| ~ member(sK9(sK17,sK18,X0),sK18)
| ~ member(sK9(sK17,sK18,X0),sK18)
| ~ member(sK9(sK17,sK18,X0),sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f224,f203]) ).
fof(f226,plain,
( ! [X0] :
( ~ member(sK9(sK17,sK18,X0),sK18)
| surjective(sK17,sK18,X0) )
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f227,plain,
( surjective(sK17,sK18,sK18)
| surjective(sK17,sK18,sK18)
| ~ spl20_2 ),
inference(resolution,[],[f226,f149]) ).
fof(f228,plain,
( surjective(sK17,sK18,sK18)
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f229,plain,
( ~ injective(sK17,sK18,sK18)
| one_to_one(sK17,sK18,sK18)
| ~ spl20_2 ),
inference(resolution,[],[f228,f153]) ).
fof(f230,plain,
( ~ injective(sK17,sK18,sK18)
| ~ spl20_2
| spl20_3 ),
inference(forward_subsumption_resolution,[],[f229,f199]) ).
fof(f238,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( apply(compose_function(X4,X0,X5,X3,X6),sK7(X0,X1,X2),X7)
| ~ member(sK8(X0,X1,X2),X3)
| injective(X0,X1,X2)
| ~ apply(X4,sK8(X0,X1,X2),X7)
| ~ member(sK7(X0,X1,X2),X5)
| ~ member(X7,X6) ),
inference(resolution,[],[f144,f136]) ).
fof(f246,plain,
! [X0,X1] :
( apply(sF19,X0,X1)
| ~ member(sK3(sK17,sK18,X0),sK18)
| ~ member(X0,sK18)
| ~ apply(sK17,sK3(sK17,sK18,X0),X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(superposition,[],[f218,f184]) ).
fof(f247,plain,
! [X0,X1] :
( ~ apply(sK17,sK3(sK17,sK18,X0),X1)
| ~ member(sK3(sK17,sK18,X0),sK18)
| ~ member(X0,sK18)
| apply(sF19,X0,X1)
| ~ member(X1,sK18) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f278,plain,
! [X0] :
( member(sK3(sK17,sK18,X0),sK18)
| ~ member(X0,sK18) ),
inference(resolution,[],[f132,f176]) ).
fof(f279,plain,
! [X2,X0,X1] :
( ~ member(X0,sK18)
| ~ apply(sK17,X0,X1)
| sK3(sK17,sK18,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK18)
| ~ member(X0,sK18)
| ~ maps(sK17,X2,sK18) ),
inference(resolution,[],[f278,f217]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ apply(sK17,X0,X1)
| ~ member(X0,sK18)
| sK3(sK17,sK18,X0) = X1
| ~ member(X0,X2)
| ~ member(X1,sK18)
| ~ maps(sK17,X2,sK18) ),
inference(duplicate_literal_removal,[],[f279]) ).
fof(f281,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK17,sK17,sK18,X0,X1),sK18)
| sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X1)) = X1
| ~ member(sK4(sK17,sK17,sK18,X0,X1),X2)
| ~ member(X1,sK18)
| ~ maps(sK17,X2,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(resolution,[],[f280,f204]) ).
fof(f282,plain,
! [X2,X0,X1] :
( ~ member(X0,sK18)
| sK4(sK17,sK17,sK18,X0,X1) = sK3(sK17,sK18,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK17,sK17,sK18,X0,X1),sK18)
| ~ maps(sK17,X2,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(resolution,[],[f280,f205]) ).
fof(f286,plain,
! [X2,X0,X1] :
( ~ member(sK8(sK17,X0,X1),sK18)
| sK8(sK17,X0,X1) = sK3(sK17,sK18,sK6(sK17,X0,X1))
| ~ member(sK6(sK17,X0,X1),X2)
| ~ member(sK6(sK17,X0,X1),sK18)
| ~ maps(sK17,X2,sK18)
| injective(sK17,X0,X1) ),
inference(resolution,[],[f280,f145]) ).
fof(f289,plain,
! [X2,X0,X1] :
( ~ member(X0,sK18)
| sK4(sK17,sK17,sK18,X0,X1) = sK3(sK17,sK18,X0)
| ~ member(X0,X2)
| ~ member(sK4(sK17,sK17,sK18,X0,X1),sK18)
| ~ maps(sK17,X2,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X1,sK18) ),
inference(duplicate_literal_removal,[],[f282]) ).
fof(f290,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK17,sK17,sK18,X0,X1),sK18)
| sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X1)) = X1
| ~ member(sK4(sK17,sK17,sK18,X0,X1),X2)
| ~ member(X1,sK18)
| ~ maps(sK17,X2,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18) ),
inference(duplicate_literal_removal,[],[f281]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ apply(sF19,X0,X1)
| sK4(sK17,sK17,sK18,X0,X1) = sK3(sK17,sK18,X0)
| ~ member(X0,X2)
| ~ maps(sK17,X2,sK18)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(forward_subsumption_resolution,[],[f289,f206]) ).
fof(f292,plain,
! [X2,X0,X1] :
( ~ member(sK4(sK17,sK17,sK18,X0,X1),X2)
| sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X1)) = X1
| ~ member(X1,sK18)
| ~ maps(sK17,X2,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18) ),
inference(forward_subsumption_resolution,[],[f290,f206]) ).
fof(f293,plain,
( ! [X0,X1] :
( sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0)
| ~ member(X0,X1)
| ~ maps(sK17,X1,sK18)
| ~ member(X0,sK18)
| ~ member(X0,sK18)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f291,f203]) ).
fof(f298,plain,
( ! [X0,X1] :
( ~ maps(sK17,X1,sK18)
| ~ member(X0,X1)
| sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f293]) ).
fof(f299,plain,
! [X0,X1] :
( sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X1)) = X1
| ~ member(X1,sK18)
| ~ maps(sK17,sK18,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18) ),
inference(resolution,[],[f292,f206]) ).
fof(f300,plain,
! [X0,X1] :
( sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X1)) = X1
| ~ member(X1,sK18)
| ~ maps(sK17,sK18,sK18)
| ~ apply(sF19,X0,X1)
| ~ member(X0,sK18) ),
inference(duplicate_literal_removal,[],[f299]) ).
fof(f301,plain,
! [X0,X1] :
( ~ apply(sF19,X0,X1)
| ~ member(X1,sK18)
| sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X1)) = X1
| ~ member(X0,sK18) ),
inference(forward_subsumption_resolution,[],[f300,f176]) ).
fof(f318,plain,
( ! [X0] :
( ~ member(X0,sK18)
| sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f298,f176]) ).
fof(f319,plain,
( ! [X0] :
( ~ member(X0,sK18)
| sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0) )
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f318]) ).
fof(f328,plain,
( ! [X2,X0,X1] :
( inverse_predicate(X0,X1,sK18,X2)
| sK4(sK17,sK17,sK18,sK11(X0,X1,sK18,X2),sK11(X0,X1,sK18,X2)) = sK3(sK17,sK18,sK11(X0,X1,sK18,X2)) )
| ~ spl20_2 ),
inference(resolution,[],[f319,f157]) ).
fof(f423,plain,
! [X2,X3,X0,X1,X4] :
( member(sK11(X0,X1,X2,X3),X4)
| ~ subset(X2,X4)
| inverse_predicate(X0,X1,X2,X3) ),
inference(resolution,[],[f104,f157]) ).
fof(f424,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2,X3),X4)
| ~ subset(X3,X4)
| inverse_predicate(X0,X1,X2,X3) ),
inference(resolution,[],[f104,f156]) ).
fof(f500,plain,
! [X2,X0,X1] :
( ~ apply(sK17,sK8(sK17,X0,X1),X2)
| ~ member(sK8(sK17,X0,X1),sK18)
| injective(sK17,X0,X1)
| apply(sF19,sK7(sK17,X0,X1),X2)
| ~ member(sK7(sK17,X0,X1),sK18)
| ~ member(X2,sK18) ),
inference(superposition,[],[f238,f184]) ).
fof(f547,plain,
! [X0,X1] :
( sK8(sK17,X0,sK18) = sK3(sK17,sK18,sK6(sK17,X0,sK18))
| ~ member(sK6(sK17,X0,sK18),X1)
| ~ member(sK6(sK17,X0,sK18),sK18)
| ~ maps(sK17,X1,sK18)
| injective(sK17,X0,sK18)
| injective(sK17,X0,sK18) ),
inference(resolution,[],[f286,f141]) ).
fof(f550,plain,
! [X0,X1] :
( ~ member(sK6(sK17,X0,sK18),sK18)
| ~ member(sK6(sK17,X0,sK18),X1)
| sK8(sK17,X0,sK18) = sK3(sK17,sK18,sK6(sK17,X0,sK18))
| ~ maps(sK17,X1,sK18)
| injective(sK17,X0,sK18) ),
inference(duplicate_literal_removal,[],[f547]) ).
fof(f551,plain,
! [X0] :
( ~ member(sK6(sK17,sK18,sK18),X0)
| sK8(sK17,sK18,sK18) = sK3(sK17,sK18,sK6(sK17,sK18,sK18))
| ~ maps(sK17,X0,sK18)
| injective(sK17,sK18,sK18)
| injective(sK17,sK18,sK18) ),
inference(resolution,[],[f550,f143]) ).
fof(f552,plain,
! [X0] :
( ~ member(sK6(sK17,sK18,sK18),X0)
| sK8(sK17,sK18,sK18) = sK3(sK17,sK18,sK6(sK17,sK18,sK18))
| ~ maps(sK17,X0,sK18)
| injective(sK17,sK18,sK18) ),
inference(duplicate_literal_removal,[],[f551]) ).
fof(f555,definition,
( spl20_6
<=> sK8(sK17,sK18,sK18) = sK3(sK17,sK18,sK6(sK17,sK18,sK18)) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
fof(f557,plain,
( sK8(sK17,sK18,sK18) = sK3(sK17,sK18,sK6(sK17,sK18,sK18))
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f559,definition,
( spl20_7
<=> ! [X0] :
( ~ member(sK6(sK17,sK18,sK18),X0)
| ~ maps(sK17,X0,sK18) ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
fof(f560,plain,
( ! [X0] :
( ~ member(sK6(sK17,sK18,sK18),X0)
| ~ maps(sK17,X0,sK18) )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f563,definition,
( spl20_8
<=> injective(sK17,sK18,sK18) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
fof(f564,plain,
( ~ injective(sK17,sK18,sK18)
| spl20_8 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f565,plain,
( injective(sK17,sK18,sK18)
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f566,plain,
( spl20_8
| spl20_6
| spl20_7 ),
inference(avatar_split_clause,[],[f552,f559,f555,f563]) ).
fof(f574,definition,
( spl20_9
<=> member(sK6(sK17,sK18,sK18),sK18) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
fof(f575,plain,
( member(sK6(sK17,sK18,sK18),sK18)
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f576,plain,
( ~ member(sK6(sK17,sK18,sK18),sK18)
| spl20_9 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f608,plain,
( sK4(sK17,sK17,sK18,sK11(sK17,sK17,sK18,sK18),sK11(sK17,sK17,sK18,sK18)) = sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18))
| spl20_1
| ~ spl20_2 ),
inference(resolution,[],[f190,f328]) ).
fof(f616,plain,
( apply(sK17,sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)),sK11(sK17,sK17,sK18,sK18))
| ~ apply(sF19,sK11(sK17,sK17,sK18,sK18),sK11(sK17,sK17,sK18,sK18))
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| spl20_1
| ~ spl20_2 ),
inference(superposition,[],[f204,f608]) ).
fof(f617,plain,
( apply(sK17,sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)),sK11(sK17,sK17,sK18,sK18))
| ~ apply(sF19,sK11(sK17,sK17,sK18,sK18),sK11(sK17,sK17,sK18,sK18))
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| spl20_1
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f622,plain,
( apply(sK17,sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)),sK11(sK17,sK17,sK18,sK18))
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| spl20_1
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f617,f203]) ).
fof(f626,definition,
( spl20_16
<=> member(sK11(sK17,sK17,sK18,sK18),sK18) ),
introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition]) ).
fof(f627,plain,
( member(sK11(sK17,sK17,sK18,sK18),sK18)
| ~ spl20_16 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f628,plain,
( ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| spl20_16 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f630,definition,
( spl20_17
<=> apply(sK17,sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)),sK11(sK17,sK17,sK18,sK18)) ),
introduced(definition,[new_symbols(definition,[spl20_17])],[avatar_definition]) ).
fof(f632,plain,
( apply(sK17,sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)),sK11(sK17,sK17,sK18,sK18))
| ~ spl20_17 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f633,plain,
( ~ spl20_16
| spl20_17
| spl20_1
| ~ spl20_2 ),
inference(avatar_split_clause,[],[f622,f193,f189,f630,f626]) ).
fof(f643,plain,
( ~ subset(sK18,sK18)
| inverse_predicate(sK17,sK17,sK18,sK18)
| spl20_16 ),
inference(resolution,[],[f628,f423]) ).
fof(f644,plain,
( inverse_predicate(sK17,sK17,sK18,sK18)
| spl20_16 ),
inference(forward_subsumption_resolution,[],[f643,f220]) ).
fof(f647,plain,
( $false
| spl20_1
| spl20_16 ),
inference(forward_subsumption_resolution,[],[f644,f190]) ).
fof(f648,plain,
( spl20_1
| spl20_16 ),
inference(avatar_contradiction_clause,[],[f647]) ).
fof(f653,plain,
( ! [X0,X1] :
( ~ apply(sK17,X0,X1)
| ~ member(X1,sK18)
| ~ member(X0,sK18)
| apply(sK17,X1,X0) )
| ~ spl20_1 ),
inference(resolution,[],[f191,f155]) ).
fof(f656,plain,
( ! [X0] :
( ~ member(sK3(sK17,sK18,X0),sK18)
| ~ member(X0,sK18)
| apply(sK17,sK3(sK17,sK18,X0),X0)
| ~ member(X0,sK18) )
| ~ spl20_1 ),
inference(resolution,[],[f653,f216]) ).
fof(f661,plain,
( ! [X0] :
( ~ member(sK3(sK17,sK18,X0),sK18)
| ~ member(X0,sK18)
| apply(sK17,sK3(sK17,sK18,X0),X0) )
| ~ spl20_1 ),
inference(duplicate_literal_removal,[],[f656]) ).
fof(f664,plain,
( ! [X0] :
( apply(sK17,sK3(sK17,sK18,X0),X0)
| ~ member(X0,sK18) )
| ~ spl20_1 ),
inference(forward_subsumption_resolution,[],[f661,f278]) ).
fof(f676,plain,
( ! [X0] :
( ~ member(X0,sK18)
| ~ member(sK3(sK17,sK18,X0),sK18)
| ~ member(X0,sK18)
| apply(sF19,X0,X0)
| ~ member(X0,sK18) )
| ~ spl20_1 ),
inference(resolution,[],[f664,f247]) ).
fof(f685,plain,
( ! [X0] :
( ~ member(X0,sK18)
| ~ member(sK3(sK17,sK18,X0),sK18)
| apply(sF19,X0,X0) )
| ~ spl20_1 ),
inference(duplicate_literal_removal,[],[f676]) ).
fof(f687,plain,
( ! [X0] :
( apply(sF19,X0,X0)
| ~ member(X0,sK18) )
| ~ spl20_1 ),
inference(forward_subsumption_resolution,[],[f685,f278]) ).
fof(f695,plain,
( ! [X0] :
( ~ member(sK5(sF19,X0),sK18)
| identity(sF19,X0) )
| ~ spl20_1 ),
inference(resolution,[],[f687,f139]) ).
fof(f700,plain,
( identity(sF19,sK18)
| identity(sF19,sK18)
| ~ spl20_1 ),
inference(resolution,[],[f695,f138]) ).
fof(f703,plain,
( identity(sF19,sK18)
| ~ spl20_1 ),
inference(duplicate_literal_removal,[],[f700]) ).
fof(f704,plain,
( $false
| ~ spl20_1
| spl20_2 ),
inference(forward_subsumption_resolution,[],[f703,f194]) ).
fof(f705,plain,
( ~ spl20_1
| spl20_2 ),
inference(avatar_contradiction_clause,[],[f704]) ).
fof(f708,plain,
( ! [X0] :
( apply(sF19,X0,X0)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f195,f137]) ).
fof(f748,plain,
( injective(sK17,sK18,sK18)
| spl20_9 ),
inference(resolution,[],[f576,f143]) ).
fof(f749,plain,
( $false
| spl20_8
| spl20_9 ),
inference(forward_subsumption_resolution,[],[f748,f564]) ).
fof(f750,plain,
( spl20_8
| spl20_9 ),
inference(avatar_contradiction_clause,[],[f749]) ).
fof(f752,plain,
( ! [X0] :
( ~ member(X0,sK18)
| ~ member(X0,sK18)
| sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X0)) = X0
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f708,f301]) ).
fof(f753,plain,
( ! [X0,X1] :
( ~ member(X0,sK18)
| sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0)
| ~ member(X0,X1)
| ~ maps(sK17,X1,sK18)
| ~ member(X0,sK18)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f708,f291]) ).
fof(f759,plain,
( ! [X0,X1] :
( ~ maps(sK17,X1,sK18)
| sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0)
| ~ member(X0,X1)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f753]) ).
fof(f760,plain,
( ! [X0] :
( ~ member(X0,sK18)
| sK3(sK17,sK18,sK4(sK17,sK17,sK18,X0,X0)) = X0 )
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f752]) ).
fof(f770,plain,
( ! [X2,X0,X1] :
( ~ apply(sK17,X2,X1)
| ~ apply(sK17,X0,X1)
| ~ member(X0,sK18)
| ~ member(X2,sK18)
| ~ member(X1,sK18)
| X0 = X2 )
| ~ spl20_8 ),
inference(resolution,[],[f565,f140]) ).
fof(f966,plain,
( ! [X0] :
( sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0)
| ~ member(X0,sK18)
| ~ member(X0,sK18) )
| ~ spl20_2 ),
inference(resolution,[],[f759,f176]) ).
fof(f967,plain,
( ! [X0] :
( ~ member(X0,sK18)
| sK3(sK17,sK18,X0) = sK4(sK17,sK17,sK18,X0,X0) )
| ~ spl20_2 ),
inference(duplicate_literal_removal,[],[f966]) ).
fof(f1159,plain,
( ! [X0] :
( ~ apply(sK17,X0,sK11(sK17,sK17,sK18,sK18))
| ~ member(X0,sK18)
| ~ member(sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)),sK18)
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = X0 )
| ~ spl20_8
| ~ spl20_17 ),
inference(resolution,[],[f770,f632]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( ~ apply(sK17,X0,X1)
| ~ member(X0,sK18)
| ~ member(sK4(sK17,sK17,sK18,X2,X1),sK18)
| ~ member(X1,sK18)
| sK4(sK17,sK17,sK18,X2,X1) = X0
| ~ apply(sF19,X2,X1)
| ~ member(X2,sK18)
| ~ member(X1,sK18) )
| ~ spl20_8 ),
inference(resolution,[],[f770,f204]) ).
fof(f1171,plain,
( ! [X2,X0,X1] :
( ~ apply(sK17,X0,X1)
| ~ member(X0,sK18)
| ~ member(sK4(sK17,sK17,sK18,X2,X1),sK18)
| ~ member(X1,sK18)
| sK4(sK17,sK17,sK18,X2,X1) = X0
| ~ apply(sF19,X2,X1)
| ~ member(X2,sK18) )
| ~ spl20_8 ),
inference(duplicate_literal_removal,[],[f1160]) ).
fof(f1179,plain,
( ! [X2,X0,X1] :
( ~ apply(sF19,X2,X1)
| ~ member(X0,sK18)
| ~ member(X1,sK18)
| sK4(sK17,sK17,sK18,X2,X1) = X0
| ~ apply(sK17,X0,X1)
| ~ member(X2,sK18) )
| ~ spl20_8 ),
inference(forward_subsumption_resolution,[],[f1171,f206]) ).
fof(f1180,plain,
( ! [X0] :
( ~ apply(sK17,X0,sK11(sK17,sK17,sK18,sK18))
| ~ member(X0,sK18)
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = X0 )
| ~ spl20_8
| ~ spl20_17 ),
inference(forward_subsumption_resolution,[],[f1159,f278]) ).
fof(f1187,plain,
( ! [X0] :
( ~ apply(sK17,X0,sK11(sK17,sK17,sK18,sK18))
| ~ member(X0,sK18)
| sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = X0 )
| ~ spl20_8
| ~ spl20_16
| ~ spl20_17 ),
inference(forward_subsumption_resolution,[],[f1180,f627]) ).
fof(f1198,plain,
( ! [X0,X1] :
( ~ member(X0,sK18)
| ~ member(X1,sK18)
| sK4(sK17,sK17,sK18,X1,X1) = X0
| ~ apply(sK17,X0,X1)
| ~ member(X1,sK18)
| ~ member(X1,sK18) )
| ~ spl20_2
| ~ spl20_8 ),
inference(resolution,[],[f1179,f708]) ).
fof(f1205,plain,
( ! [X0,X1] :
( ~ apply(sK17,X0,X1)
| ~ member(X1,sK18)
| sK4(sK17,sK17,sK18,X1,X1) = X0
| ~ member(X0,sK18) )
| ~ spl20_2
| ~ spl20_8 ),
inference(duplicate_literal_removal,[],[f1198]) ).
fof(f1552,plain,
( ~ member(sK12(sK17,sK17,sK18,sK18),sK18)
| sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = sK12(sK17,sK17,sK18,sK18)
| apply(sK17,sK11(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| inverse_predicate(sK17,sK17,sK18,sK18)
| ~ spl20_8
| ~ spl20_16
| ~ spl20_17 ),
inference(resolution,[],[f1187,f158]) ).
fof(f1553,plain,
( sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = sK12(sK17,sK17,sK18,sK18)
| apply(sK17,sK11(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| inverse_predicate(sK17,sK17,sK18,sK18)
| ~ spl20_8
| ~ spl20_16
| ~ spl20_17 ),
inference(forward_subsumption_resolution,[],[f1552,f156]) ).
fof(f1556,plain,
( sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = sK12(sK17,sK17,sK18,sK18)
| apply(sK17,sK11(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| spl20_1
| ~ spl20_8
| ~ spl20_16
| ~ spl20_17 ),
inference(forward_subsumption_resolution,[],[f1553,f190]) ).
fof(f1559,definition,
( spl20_35
<=> apply(sK17,sK11(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18)) ),
introduced(definition,[new_symbols(definition,[spl20_35])],[avatar_definition]) ).
fof(f1560,plain,
( ~ apply(sK17,sK11(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| spl20_35 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1561,plain,
( apply(sK17,sK11(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| ~ spl20_35 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1563,definition,
( spl20_36
<=> sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = sK12(sK17,sK17,sK18,sK18) ),
introduced(definition,[new_symbols(definition,[spl20_36])],[avatar_definition]) ).
fof(f1564,plain,
( sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) != sK12(sK17,sK17,sK18,sK18)
| spl20_36 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f1565,plain,
( sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = sK12(sK17,sK17,sK18,sK18)
| ~ spl20_36 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f1566,plain,
( spl20_35
| spl20_36
| spl20_1
| ~ spl20_8
| ~ spl20_16
| ~ spl20_17 ),
inference(avatar_split_clause,[],[f1556,f630,f626,f563,f189,f1563,f1559]) ).
fof(f1568,plain,
( ~ member(sK12(sK17,sK17,sK18,sK18),sK18)
| sK11(sK17,sK17,sK18,sK18) = sK4(sK17,sK17,sK18,sK12(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_8
| ~ spl20_35 ),
inference(resolution,[],[f1561,f1205]) ).
fof(f1571,plain,
( ~ apply(sK17,sK12(sK17,sK17,sK18,sK18),sK11(sK17,sK17,sK18,sK18))
| inverse_predicate(sK17,sK17,sK18,sK18)
| ~ spl20_35 ),
inference(resolution,[],[f1561,f159]) ).
fof(f1574,plain,
( ~ apply(sK17,sK12(sK17,sK17,sK18,sK18),sK11(sK17,sK17,sK18,sK18))
| spl20_1
| ~ spl20_35 ),
inference(forward_subsumption_resolution,[],[f1571,f190]) ).
fof(f1577,plain,
( ~ member(sK12(sK17,sK17,sK18,sK18),sK18)
| sK11(sK17,sK17,sK18,sK18) = sK4(sK17,sK17,sK18,sK12(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| ~ spl20_2
| ~ spl20_8
| ~ spl20_16
| ~ spl20_35 ),
inference(forward_subsumption_resolution,[],[f1568,f627]) ).
fof(f1580,definition,
( spl20_37
<=> member(sK12(sK17,sK17,sK18,sK18),sK18) ),
introduced(definition,[new_symbols(definition,[spl20_37])],[avatar_definition]) ).
fof(f1581,plain,
( member(sK12(sK17,sK17,sK18,sK18),sK18)
| ~ spl20_37 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1582,plain,
( ~ member(sK12(sK17,sK17,sK18,sK18),sK18)
| spl20_37 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1589,definition,
( spl20_39
<=> sK11(sK17,sK17,sK18,sK18) = sK4(sK17,sK17,sK18,sK12(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18)) ),
introduced(definition,[new_symbols(definition,[spl20_39])],[avatar_definition]) ).
fof(f1591,plain,
( sK11(sK17,sK17,sK18,sK18) = sK4(sK17,sK17,sK18,sK12(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| ~ spl20_39 ),
inference(avatar_component_clause,[],[f1589]) ).
fof(f1592,plain,
( spl20_39
| ~ spl20_37
| ~ spl20_2
| ~ spl20_8
| ~ spl20_16
| ~ spl20_35 ),
inference(avatar_split_clause,[],[f1577,f1559,f626,f563,f193,f1580,f1589]) ).
fof(f1600,plain,
( ~ subset(sK18,sK18)
| inverse_predicate(sK17,sK17,sK18,sK18)
| spl20_37 ),
inference(resolution,[],[f1582,f424]) ).
fof(f1601,plain,
( inverse_predicate(sK17,sK17,sK18,sK18)
| spl20_37 ),
inference(forward_subsumption_resolution,[],[f1600,f220]) ).
fof(f1604,plain,
( $false
| spl20_1
| spl20_37 ),
inference(forward_subsumption_resolution,[],[f1601,f190]) ).
fof(f1605,plain,
( spl20_1
| spl20_37 ),
inference(avatar_contradiction_clause,[],[f1604]) ).
fof(f1606,plain,
( apply(sK17,sK12(sK17,sK17,sK18,sK18),sK11(sK17,sK17,sK18,sK18))
| ~ spl20_17
| ~ spl20_36 ),
inference(superposition,[],[f632,f1565]) ).
fof(f1613,plain,
( apply(sK17,sK11(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18))
| ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| ~ spl20_36 ),
inference(superposition,[],[f216,f1565]) ).
fof(f1623,plain,
( ~ member(sK11(sK17,sK17,sK18,sK18),sK18)
| spl20_35
| ~ spl20_36 ),
inference(forward_subsumption_resolution,[],[f1613,f1560]) ).
fof(f1631,plain,
( $false
| ~ spl20_16
| spl20_35
| ~ spl20_36 ),
inference(forward_subsumption_resolution,[],[f1623,f627]) ).
fof(f1632,plain,
( ~ spl20_16
| spl20_35
| ~ spl20_36 ),
inference(avatar_contradiction_clause,[],[f1631]) ).
fof(f1634,plain,
( $false
| spl20_1
| ~ spl20_17
| ~ spl20_35
| ~ spl20_36 ),
inference(forward_subsumption_resolution,[],[f1574,f1606]) ).
fof(f1635,plain,
( spl20_1
| ~ spl20_17
| ~ spl20_35
| ~ spl20_36 ),
inference(avatar_contradiction_clause,[],[f1634]) ).
fof(f1644,plain,
( sK12(sK17,sK17,sK18,sK18) = sK3(sK17,sK18,sK4(sK17,sK17,sK18,sK12(sK17,sK17,sK18,sK18),sK12(sK17,sK17,sK18,sK18)))
| ~ spl20_2
| ~ spl20_37 ),
inference(resolution,[],[f1581,f760]) ).
fof(f1660,plain,
( sK3(sK17,sK18,sK11(sK17,sK17,sK18,sK18)) = sK12(sK17,sK17,sK18,sK18)
| ~ spl20_2
| ~ spl20_37
| ~ spl20_39 ),
inference(forward_demodulation,[],[f1644,f1591]) ).
fof(f1665,plain,
( $false
| ~ spl20_2
| spl20_36
| ~ spl20_37
| ~ spl20_39 ),
inference(forward_subsumption_resolution,[],[f1660,f1564]) ).
fof(f1666,plain,
( ~ spl20_2
| spl20_36
| ~ spl20_37
| ~ spl20_39 ),
inference(avatar_contradiction_clause,[],[f1665]) ).
fof(f1671,plain,
( ~ spl20_8
| ~ spl20_2
| spl20_3 ),
inference(avatar_split_clause,[],[f230,f198,f193,f563]) ).
fof(f1678,plain,
( ~ maps(sK17,sK18,sK18)
| injective(sK17,sK18,sK18)
| ~ spl20_7 ),
inference(resolution,[],[f560,f143]) ).
fof(f1679,plain,
( injective(sK17,sK18,sK18)
| ~ spl20_7 ),
inference(forward_subsumption_resolution,[],[f1678,f176]) ).
fof(f1680,plain,
( $false
| ~ spl20_7
| spl20_8 ),
inference(forward_subsumption_resolution,[],[f1679,f564]) ).
fof(f1681,plain,
( ~ spl20_7
| spl20_8 ),
inference(avatar_contradiction_clause,[],[f1680]) ).
fof(f1695,plain,
( sK3(sK17,sK18,sK6(sK17,sK18,sK18)) = sK4(sK17,sK17,sK18,sK6(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ spl20_2
| ~ spl20_9 ),
inference(resolution,[],[f575,f967]) ).
fof(f1697,plain,
( sK8(sK17,sK18,sK18) = sK4(sK17,sK17,sK18,sK6(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_demodulation,[],[f1695,f557]) ).
fof(f1698,plain,
( apply(sK17,sK8(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ apply(sF19,sK6(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ member(sK6(sK17,sK18,sK18),sK18)
| ~ member(sK6(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(superposition,[],[f204,f1697]) ).
fof(f1707,plain,
( apply(sK17,sK8(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ apply(sF19,sK6(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ member(sK6(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(duplicate_literal_removal,[],[f1698]) ).
fof(f1710,plain,
( apply(sK17,sK8(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ member(sK6(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1707,f708]) ).
fof(f1713,plain,
( apply(sK17,sK8(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1710,f575]) ).
fof(f1723,plain,
( ~ member(sK8(sK17,sK18,sK18),sK18)
| injective(sK17,sK18,sK18)
| apply(sF19,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ member(sK7(sK17,sK18,sK18),sK18)
| ~ member(sK6(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(resolution,[],[f1713,f500]) ).
fof(f1728,plain,
( injective(sK17,sK18,sK18)
| apply(sF19,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ member(sK7(sK17,sK18,sK18),sK18)
| ~ member(sK6(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1723,f141]) ).
fof(f1729,plain,
( injective(sK17,sK18,sK18)
| apply(sF19,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ member(sK6(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1728,f142]) ).
fof(f1730,plain,
( injective(sK17,sK18,sK18)
| apply(sF19,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ spl20_2
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1729,f143]) ).
fof(f1731,plain,
( apply(sF19,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18))
| ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1730,f564]) ).
fof(f1732,plain,
( ! [X0] :
( sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18)) = sK3(sK17,sK18,sK7(sK17,sK18,sK18))
| ~ member(sK7(sK17,sK18,sK18),X0)
| ~ maps(sK17,X0,sK18)
| ~ member(sK7(sK17,sK18,sK18),sK18)
| ~ member(sK6(sK17,sK18,sK18),sK18) )
| ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9 ),
inference(resolution,[],[f1731,f291]) ).
fof(f1733,plain,
( ~ member(sK6(sK17,sK18,sK18),sK18)
| sK6(sK17,sK18,sK18) = sK3(sK17,sK18,sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18)))
| ~ member(sK7(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9 ),
inference(resolution,[],[f1731,f301]) ).
fof(f1741,definition,
( spl20_44
<=> sK6(sK17,sK18,sK18) = sK7(sK17,sK18,sK18) ),
introduced(definition,[new_symbols(definition,[spl20_44])],[avatar_definition]) ).
fof(f1742,plain,
( sK6(sK17,sK18,sK18) != sK7(sK17,sK18,sK18)
| spl20_44 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f1743,plain,
( sK6(sK17,sK18,sK18) = sK7(sK17,sK18,sK18)
| ~ spl20_44 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f1745,definition,
( spl20_45
<=> member(sK7(sK17,sK18,sK18),sK18) ),
introduced(definition,[new_symbols(definition,[spl20_45])],[avatar_definition]) ).
fof(f1746,plain,
( member(sK7(sK17,sK18,sK18),sK18)
| ~ spl20_45 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f1747,plain,
( ~ member(sK7(sK17,sK18,sK18),sK18)
| spl20_45 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f1749,plain,
( sK6(sK17,sK18,sK18) = sK3(sK17,sK18,sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18)))
| ~ member(sK7(sK17,sK18,sK18),sK18)
| ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1733,f575]) ).
fof(f1750,plain,
( ! [X0] :
( sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18)) = sK3(sK17,sK18,sK7(sK17,sK18,sK18))
| ~ member(sK7(sK17,sK18,sK18),X0)
| ~ maps(sK17,X0,sK18)
| ~ member(sK7(sK17,sK18,sK18),sK18) )
| ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f1732,f575]) ).
fof(f1752,definition,
( spl20_46
<=> sK6(sK17,sK18,sK18) = sK3(sK17,sK18,sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18))) ),
introduced(definition,[new_symbols(definition,[spl20_46])],[avatar_definition]) ).
fof(f1754,plain,
( sK6(sK17,sK18,sK18) = sK3(sK17,sK18,sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18)))
| ~ spl20_46 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f1755,plain,
( ~ spl20_45
| spl20_46
| ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9 ),
inference(avatar_split_clause,[],[f1749,f574,f563,f555,f193,f1752,f1745]) ).
fof(f1757,definition,
( spl20_47
<=> ! [X0] :
( ~ member(sK7(sK17,sK18,sK18),X0)
| ~ maps(sK17,X0,sK18) ) ),
introduced(definition,[new_symbols(definition,[spl20_47])],[avatar_definition]) ).
fof(f1758,plain,
( ! [X0] :
( ~ member(sK7(sK17,sK18,sK18),X0)
| ~ maps(sK17,X0,sK18) )
| ~ spl20_47 ),
inference(avatar_component_clause,[],[f1757]) ).
fof(f1760,definition,
( spl20_48
<=> sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18)) = sK3(sK17,sK18,sK7(sK17,sK18,sK18)) ),
introduced(definition,[new_symbols(definition,[spl20_48])],[avatar_definition]) ).
fof(f1762,plain,
( sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK6(sK17,sK18,sK18)) = sK3(sK17,sK18,sK7(sK17,sK18,sK18))
| ~ spl20_48 ),
inference(avatar_component_clause,[],[f1760]) ).
fof(f1763,plain,
( ~ spl20_45
| spl20_47
| spl20_48
| ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9 ),
inference(avatar_split_clause,[],[f1750,f574,f563,f555,f193,f1760,f1757,f1745]) ).
fof(f1814,plain,
( injective(sK17,sK18,sK18)
| spl20_45 ),
inference(resolution,[],[f1747,f142]) ).
fof(f1815,plain,
( $false
| spl20_8
| spl20_45 ),
inference(forward_subsumption_resolution,[],[f1814,f564]) ).
fof(f1816,plain,
( spl20_8
| spl20_45 ),
inference(avatar_contradiction_clause,[],[f1815]) ).
fof(f1826,plain,
( sK6(sK17,sK18,sK18) != sK6(sK17,sK18,sK18)
| injective(sK17,sK18,sK18)
| ~ spl20_44 ),
inference(superposition,[],[f146,f1743]) ).
fof(f1828,plain,
( injective(sK17,sK18,sK18)
| ~ spl20_44 ),
inference(trivial_inequality_removal,[],[f1826]) ).
fof(f1829,plain,
( $false
| spl20_8
| ~ spl20_44 ),
inference(forward_subsumption_resolution,[],[f1828,f564]) ).
fof(f1830,plain,
( spl20_8
| ~ spl20_44 ),
inference(avatar_contradiction_clause,[],[f1829]) ).
fof(f1845,definition,
( spl20_49
<=> sK6(sK17,sK18,sK18) = sK3(sK17,sK18,sK3(sK17,sK18,sK7(sK17,sK18,sK18))) ),
introduced(definition,[new_symbols(definition,[spl20_49])],[avatar_definition]) ).
fof(f1847,plain,
( sK6(sK17,sK18,sK18) = sK3(sK17,sK18,sK3(sK17,sK18,sK7(sK17,sK18,sK18)))
| ~ spl20_49 ),
inference(avatar_component_clause,[],[f1845]) ).
fof(f1852,plain,
( sK6(sK17,sK18,sK18) = sK3(sK17,sK18,sK3(sK17,sK18,sK7(sK17,sK18,sK18)))
| ~ spl20_46
| ~ spl20_48 ),
inference(superposition,[],[f1754,f1762]) ).
fof(f1864,plain,
( spl20_49
| ~ spl20_46
| ~ spl20_48 ),
inference(avatar_split_clause,[],[f1852,f1760,f1752,f1845]) ).
fof(f1919,plain,
( ~ maps(sK17,sK18,sK18)
| injective(sK17,sK18,sK18)
| ~ spl20_47 ),
inference(resolution,[],[f1758,f142]) ).
fof(f1920,plain,
( injective(sK17,sK18,sK18)
| ~ spl20_47 ),
inference(forward_subsumption_resolution,[],[f1919,f176]) ).
fof(f1921,plain,
( $false
| spl20_8
| ~ spl20_47 ),
inference(forward_subsumption_resolution,[],[f1920,f564]) ).
fof(f1922,plain,
( spl20_8
| ~ spl20_47 ),
inference(avatar_contradiction_clause,[],[f1921]) ).
fof(f1935,plain,
( sK7(sK17,sK18,sK18) = sK3(sK17,sK18,sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK7(sK17,sK18,sK18)))
| ~ spl20_2
| ~ spl20_45 ),
inference(resolution,[],[f1746,f760]) ).
fof(f1937,plain,
( sK3(sK17,sK18,sK7(sK17,sK18,sK18)) = sK4(sK17,sK17,sK18,sK7(sK17,sK18,sK18),sK7(sK17,sK18,sK18))
| ~ spl20_2
| ~ spl20_45 ),
inference(resolution,[],[f1746,f967]) ).
fof(f1939,plain,
( sK7(sK17,sK18,sK18) = sK3(sK17,sK18,sK3(sK17,sK18,sK7(sK17,sK18,sK18)))
| ~ spl20_2
| ~ spl20_45 ),
inference(forward_demodulation,[],[f1935,f1937]) ).
fof(f1940,plain,
( sK6(sK17,sK18,sK18) = sK7(sK17,sK18,sK18)
| ~ spl20_2
| ~ spl20_45
| ~ spl20_49 ),
inference(forward_demodulation,[],[f1939,f1847]) ).
fof(f1941,plain,
( $false
| ~ spl20_2
| spl20_44
| ~ spl20_45
| ~ spl20_49 ),
inference(forward_subsumption_resolution,[],[f1940,f1742]) ).
fof(f1942,plain,
( ~ spl20_2
| spl20_44
| ~ spl20_45
| ~ spl20_49 ),
inference(avatar_contradiction_clause,[],[f1941]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f196]) ).
cnf(s3,plain,
( ~ spl20_1
| ~ spl20_2
| ~ spl20_3 ),
inference(sat_conversion,[],[f202]) ).
cnf(s6,plain,
( spl20_6
| spl20_7
| spl20_8 ),
inference(sat_conversion,[],[f566]) ).
cnf(s14,plain,
( spl20_1
| ~ spl20_2
| ~ spl20_16
| spl20_17 ),
inference(sat_conversion,[],[f633]) ).
cnf(s17,plain,
( spl20_1
| spl20_16 ),
inference(sat_conversion,[],[f648]) ).
cnf(s18,plain,
( ~ spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f705]) ).
cnf(s20,plain,
( spl20_8
| spl20_9 ),
inference(sat_conversion,[],[f750]) ).
cnf(s37,plain,
( spl20_1
| ~ spl20_8
| ~ spl20_16
| ~ spl20_17
| spl20_35
| spl20_36 ),
inference(sat_conversion,[],[f1566]) ).
cnf(s40,plain,
( ~ spl20_2
| ~ spl20_8
| ~ spl20_16
| ~ spl20_35
| ~ spl20_37
| spl20_39 ),
inference(sat_conversion,[],[f1592]) ).
cnf(s43,plain,
( spl20_1
| spl20_37 ),
inference(sat_conversion,[],[f1605]) ).
cnf(s47,plain,
( ~ spl20_16
| spl20_35
| ~ spl20_36 ),
inference(sat_conversion,[],[f1632]) ).
cnf(s48,plain,
( spl20_1
| ~ spl20_17
| ~ spl20_35
| ~ spl20_36 ),
inference(sat_conversion,[],[f1635]) ).
cnf(s50,plain,
( ~ spl20_2
| spl20_36
| ~ spl20_37
| ~ spl20_39 ),
inference(sat_conversion,[],[f1666]) ).
cnf(s53,plain,
( ~ spl20_2
| spl20_3
| ~ spl20_8 ),
inference(sat_conversion,[],[f1671]) ).
cnf(s54,plain,
( ~ spl20_7
| spl20_8 ),
inference(sat_conversion,[],[f1681]) ).
cnf(s57,plain,
( ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9
| ~ spl20_45
| spl20_46 ),
inference(sat_conversion,[],[f1755]) ).
cnf(s58,plain,
( ~ spl20_2
| ~ spl20_6
| spl20_8
| ~ spl20_9
| ~ spl20_45
| spl20_47
| spl20_48 ),
inference(sat_conversion,[],[f1763]) ).
cnf(s61,plain,
( spl20_8
| spl20_45 ),
inference(sat_conversion,[],[f1816]) ).
cnf(s62,plain,
( spl20_8
| ~ spl20_44 ),
inference(sat_conversion,[],[f1830]) ).
cnf(s64,plain,
( ~ spl20_46
| ~ spl20_48
| spl20_49 ),
inference(sat_conversion,[],[f1864]) ).
cnf(s74,plain,
( spl20_8
| ~ spl20_47 ),
inference(sat_conversion,[],[f1922]) ).
cnf(s77,plain,
( ~ spl20_2
| spl20_44
| ~ spl20_45
| ~ spl20_49 ),
inference(sat_conversion,[],[f1942]) ).
cnf(s78,plain,
( spl20_8
| ~ spl20_2 ),
inference(rat,[],[s64,s57,s58,s6,s77,s20,s54,s61,s62,s74]) ).
cnf(s79,plain,
( spl20_35
| spl20_1 ),
inference(rat,[],[s37,s47,s14,s17,s78,s1]) ).
cnf(s80,plain,
spl20_1,
inference(rat,[],[s50,s48,s40,s79,s78,s14,s1,s17,s43]) ).
cnf(s81,plain,
spl20_2,
inference(rat,[],[s18,s80]) ).
cnf(s82,plain,
~ spl20_3,
inference(rat,[],[s3,s80,s81]) ).
cnf(s83,plain,
spl20_8,
inference(rat,[],[s78,s81]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s53,s81,s83,s82]) ).
fof(f1943,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET729+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n013.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 02:38:51 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.44 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
% 9.74/2.25 % (753098)Detected formulas, will run a generic FOF schedule.
% 9.74/2.25 % (753105)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=1322560519:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.74/2.25 % (753106)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=125251782:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.74/2.25 % (753103)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=1570193499:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.74/2.25 % (753104)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=2773586026:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.74/2.25 % (753107)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1311156606:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.74/2.25 % (753109)dis-21_1_sil=8000:lcm=predicate:random_seed=3728031592: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)
% 9.74/2.25 % (753108)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=866359888:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.74/2.25 % (753106)Instruction limit reached!
% 9.74/2.25 % (753106)------------------------------
% 9.74/2.25 % (753106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753106)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753106)Termination reason: Instruction limit
% 9.74/2.25 % (753106)Termination phase: Saturation
% 9.74/2.25 % (753106)Time elapsed: 0.061 s
% 9.74/2.25 % (753106)Peak memory usage: 89 MB
% 9.74/2.25 % (753106)Instructions burned: 109 (million)
% 9.74/2.25 % (753107)Instruction limit reached!
% 9.74/2.25 % (753107)------------------------------
% 9.74/2.25 % (753107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753107)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753107)Termination reason: Instruction limit
% 9.74/2.25 % (753107)Termination phase: Saturation
% 9.74/2.25 % (753107)Time elapsed: 0.070 s
% 9.74/2.25 % (753107)Peak memory usage: 88 MB
% 9.74/2.25 % (753107)Instructions burned: 120 (million)
% 9.74/2.25 % (753109)Instruction limit reached!
% 9.74/2.25 % (753109)------------------------------
% 9.74/2.25 % (753109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753109)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753109)Termination reason: Instruction limit
% 9.74/2.25 % (753109)Termination phase: Saturation
% 9.74/2.25 % (753109)Time elapsed: 0.081 s
% 9.74/2.25 % (753109)Peak memory usage: 89 MB
% 9.74/2.25 % (753109)Instructions burned: 130 (million)
% 9.74/2.25 % (753108)Instruction limit reached!
% 9.74/2.25 % (753108)------------------------------
% 9.74/2.25 % (753108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753108)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753108)Termination reason: Instruction limit
% 9.74/2.25 % (753108)Termination phase: Saturation
% 9.74/2.25 % (753108)Time elapsed: 0.090 s
% 9.74/2.25 % (753108)Peak memory usage: 89 MB
% 9.74/2.25 % (753108)Instructions burned: 140 (million)
% 9.74/2.25 % (753117)lrs+10_1_sil=8000:sp=occurrence:random_seed=250450388:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.74/2.25 % (753118)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1100244512:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.74/2.25 % (753118)Refutation not found, incomplete strategy
% 9.74/2.25 % (753118)------------------------------
% 9.74/2.25 % (753118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753118)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753118)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.25 % (753118)Time elapsed: 0.003 s
% 9.74/2.25 % (753118)Peak memory usage: 88 MB
% 9.74/2.25 % (753118)Instructions burned: 2 (million)
% 9.74/2.25 % (753120)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=1039526614:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.74/2.25 % (753119)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3763299784:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.74/2.25 % (753120)Instruction limit reached!
% 9.74/2.25 % (753120)------------------------------
% 9.74/2.25 % (753120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753120)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753120)Termination reason: Instruction limit
% 9.74/2.25 % (753120)Termination phase: Saturation
% 9.74/2.25 % (753120)Time elapsed: 0.130 s
% 9.74/2.25 % (753120)Peak memory usage: 92 MB
% 9.74/2.25 % (753120)Instructions burned: 248 (million)
% 9.74/2.25 % (753117)Instruction limit reached!
% 9.74/2.25 % (753117)------------------------------
% 9.74/2.25 % (753117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753117)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753117)Termination reason: Instruction limit
% 9.74/2.25 % (753117)Termination phase: Saturation
% 9.74/2.25 % (753117)Time elapsed: 0.175 s
% 9.74/2.25 % (753117)Peak memory usage: 91 MB
% 9.74/2.25 % (753117)Instructions burned: 286 (million)
% 9.74/2.25 % (753119)Instruction limit reached!
% 9.74/2.25 % (753119)------------------------------
% 9.74/2.25 % (753119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753119)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753119)Termination reason: Instruction limit
% 9.74/2.25 % (753119)Termination phase: Saturation
% 9.74/2.25 % (753119)Time elapsed: 0.199 s
% 9.74/2.25 % (753119)Peak memory usage: 92 MB
% 9.74/2.25 % (753119)Instructions burned: 326 (million)
% 9.74/2.25 % (753118)------------------------------
% 9.74/2.25 % (753118)------------------------------
% 9.74/2.25 % (753125)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1787027653:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 9.74/2.25 % (753125)Refutation not found, incomplete strategy
% 9.74/2.25 % (753125)------------------------------
% 9.74/2.25 % (753125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753125)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753125)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.25 % (753125)Time elapsed: 0.002 s
% 9.74/2.25 % (753125)Peak memory usage: 88 MB
% 9.74/2.25 % (753125)Instructions burned: 2 (million)
% 9.74/2.25 % (753126)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4025888498:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.74/2.25 % (753127)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=839495665:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 9.74/2.25 % (753128)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=714389178:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 9.74/2.25 % (753127)Instruction limit reached!
% 9.74/2.25 % (753127)------------------------------
% 9.74/2.25 % (753127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753127)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753127)Termination reason: Instruction limit
% 9.74/2.25 % (753127)Termination phase: Saturation
% 9.74/2.25 % (753127)Time elapsed: 0.075 s
% 9.74/2.25 % (753127)Peak memory usage: 89 MB
% 9.74/2.25 % (753127)Instructions burned: 114 (million)
% 9.74/2.25 % (753128)Instruction limit reached!
% 9.74/2.25 % (753128)------------------------------
% 9.74/2.25 % (753128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753128)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753128)Termination reason: Instruction limit
% 9.74/2.25 % (753128)Termination phase: Saturation
% 9.74/2.25 % (753128)Time elapsed: 0.067 s
% 9.74/2.25 % (753128)Peak memory usage: 89 MB
% 9.74/2.25 % (753128)Instructions burned: 127 (million)
% 9.74/2.25 % (753125)------------------------------
% 9.74/2.25 % (753125)------------------------------
% 9.74/2.25 % (753133)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=772389496:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 9.74/2.25 % (753134)lrs+10_1_sil=8000:sp=occurrence:random_seed=2314468372:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.74/2.25 % (753133)Instruction limit reached!
% 9.74/2.25 % (753133)------------------------------
% 9.74/2.25 % (753133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753133)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753133)Termination reason: Instruction limit
% 9.74/2.25 % (753133)Termination phase: Saturation
% 9.74/2.25 % (753133)Time elapsed: 0.070 s
% 9.74/2.25 % (753133)Peak memory usage: 89 MB
% 9.74/2.25 % (753133)Instructions burned: 115 (million)
% 9.74/2.25 % (753103)First to succeed.
% 9.74/2.25 % (753135)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=554823426:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.74/2.25 % (753135)Refutation not found, incomplete strategy
% 9.74/2.25 % (753135)------------------------------
% 9.74/2.25 % (753135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.74/2.25 % (753135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.74/2.25 % (753135)CaDiCaL version: 2.1.3
% 9.74/2.25 % (753135)Termination reason: Refutation not found, incomplete strategy
% 9.74/2.25 % (753135)Time elapsed: 0.002 s
% 9.74/2.25 % (753135)Peak memory usage: 88 MB
% 9.74/2.25 % (753135)Instructions burned: 1 (million)
% 9.74/2.25 % (753103)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-753098"
% 9.74/2.25 % (753138)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2226977110:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 9.74/2.25 % (753135)------------------------------
% 9.74/2.25 % (753135)------------------------------
% 9.74/2.25 % (753103)Refutation found. Thanks to Tanya!
% 9.74/2.25 % SZS status Theorem for theBenchmark
% 9.74/2.25 % SZS output start Proof for theBenchmark
% See solution above
% 10.25/2.44 % (753103)------------------------------
% 10.25/2.44 % (753103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.25/2.44 % (753103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.25/2.44 % (753103)CaDiCaL version: 2.1.3
% 10.25/2.44 % (753103)Termination reason: Refutation
% 10.25/2.44 % (753103)Time elapsed: 0.933 s
% 10.25/2.44 % (753103)Peak memory usage: 132 MB
% 10.25/2.44 % (753103)Instructions burned: 1396 (million)
% 10.25/2.44 % (753103)------------------------------
% 10.25/2.44 % (753103)------------------------------
% 10.25/2.44 % (753098)Success in time 1.367 s
% 10.25/2.44 % Vampire exiting
%------------------------------------------------------------------------------