TSTP Solution File: SET726+4 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET726+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:22:00 EDT 2022
% Result : Theorem 1.52s 0.56s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 17 unt; 0 def)
% Number of atoms : 443 ( 39 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 514 ( 171 ~; 164 |; 133 &)
% ( 14 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 353 ( 307 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f277,plain,
$false,
inference(subsumption_resolution,[],[f276,f98]) ).
fof(f98,plain,
sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) != sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
inference(resolution,[],[f75,f82]) ).
fof(f82,plain,
! [X2,X3,X0,X1] :
( equal_maps(X2,X3,X1,X0)
| sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( equal_maps(X2,X3,X1,X0)
| ( apply(X2,sK8(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
& apply(X3,sK8(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& member(sK7(X0,X1,X2,X3),X0)
& member(sK6(X0,X1,X2,X3),X0)
& member(sK8(X0,X1,X2,X3),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f59,f60]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( apply(X2,X6,X5)
& X4 != X5
& apply(X3,X6,X4)
& member(X5,X0)
& member(X4,X0)
& member(X6,X1) )
=> ( apply(X2,sK8(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
& apply(X3,sK8(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& member(sK7(X0,X1,X2,X3),X0)
& member(sK6(X0,X1,X2,X3),X0)
& member(sK8(X0,X1,X2,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( equal_maps(X2,X3,X1,X0)
| ? [X4,X5,X6] :
( apply(X2,X6,X5)
& X4 != X5
& apply(X3,X6,X4)
& member(X5,X0)
& member(X4,X0)
& member(X6,X1) ) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X3,X2] :
( equal_maps(X3,X2,X1,X0)
| ? [X6,X5,X4] :
( apply(X3,X4,X5)
& X5 != X6
& apply(X2,X4,X6)
& member(X5,X0)
& member(X6,X0)
& member(X4,X1) ) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X1,X2,X3,X0] :
( equal_maps(X3,X2,X1,X0)
| ? [X5,X6,X4] :
( X5 != X6
& apply(X3,X4,X5)
& apply(X2,X4,X6)
& member(X4,X1)
& member(X5,X0)
& member(X6,X0) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,plain,
! [X1,X2,X3,X0] :
( ! [X5,X6,X4] :
( ( member(X4,X1)
& member(X5,X0)
& member(X6,X0) )
=> ( ( apply(X3,X4,X5)
& apply(X2,X4,X6) )
=> X5 = X6 ) )
=> equal_maps(X3,X2,X1,X0) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f32,plain,
! [X1,X2,X3,X0] :
( equal_maps(X3,X2,X1,X0)
<=> ! [X5,X6,X4] :
( ( member(X4,X1)
& member(X5,X0)
& member(X6,X0) )
=> ( ( apply(X3,X4,X5)
& apply(X2,X4,X6) )
=> X5 = X6 ) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X1,X0,X9,X5] :
( ! [X2,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X2,X0) )
=> ( ( apply(X5,X2,X6)
& apply(X9,X2,X7) )
=> X6 = X7 ) )
<=> equal_maps(X5,X9,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_maps) ).
fof(f75,plain,
~ equal_maps(inverse_function(sK2,sK4,sK5),sK3,sK5,sK4),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
( identity(compose_function(sK3,sK2,sK4,sK5,sK4),sK4)
& identity(compose_function(sK2,sK1,sK5,sK4,sK5),sK5)
& ~ equal_maps(inverse_function(sK2,sK4,sK5),sK3,sK5,sK4)
& maps(sK2,sK4,sK5)
& maps(sK1,sK5,sK4)
& maps(sK3,sK5,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f56,f57]) ).
fof(f57,plain,
( ? [X0,X1,X2,X3,X4] :
( identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X1,X0,X4,X3,X4),X4)
& ~ equal_maps(inverse_function(X1,X3,X4),X2,X4,X3)
& maps(X1,X3,X4)
& maps(X0,X4,X3)
& maps(X2,X4,X3) )
=> ( identity(compose_function(sK3,sK2,sK4,sK5,sK4),sK4)
& identity(compose_function(sK2,sK1,sK5,sK4,sK5),sK5)
& ~ equal_maps(inverse_function(sK2,sK4,sK5),sK3,sK5,sK4)
& maps(sK2,sK4,sK5)
& maps(sK1,sK5,sK4)
& maps(sK3,sK5,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
? [X0,X1,X2,X3,X4] :
( identity(compose_function(X2,X1,X3,X4,X3),X3)
& identity(compose_function(X1,X0,X4,X3,X4),X4)
& ~ equal_maps(inverse_function(X1,X3,X4),X2,X4,X3)
& maps(X1,X3,X4)
& maps(X0,X4,X3)
& maps(X2,X4,X3) ),
inference(rectify,[],[f46]) ).
fof(f46,plain,
? [X2,X1,X3,X4,X0] :
( identity(compose_function(X3,X1,X4,X0,X4),X4)
& identity(compose_function(X1,X2,X0,X4,X0),X0)
& ~ equal_maps(inverse_function(X1,X4,X0),X3,X0,X4)
& maps(X1,X4,X0)
& maps(X2,X0,X4)
& maps(X3,X0,X4) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
? [X1,X0,X2,X3,X4] :
( ~ equal_maps(inverse_function(X1,X4,X0),X3,X0,X4)
& maps(X3,X0,X4)
& maps(X1,X4,X0)
& identity(compose_function(X3,X1,X4,X0,X4),X4)
& identity(compose_function(X1,X2,X0,X4,X0),X0)
& maps(X2,X0,X4) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X1,X0,X2,X3,X4] :
( ( maps(X3,X0,X4)
& maps(X1,X4,X0)
& identity(compose_function(X3,X1,X4,X0,X4),X4)
& identity(compose_function(X1,X2,X0,X4,X0),X0)
& maps(X2,X0,X4) )
=> equal_maps(inverse_function(X1,X4,X0),X3,X0,X4) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X1,X5,X8,X9,X0] :
( ( maps(X5,X0,X1)
& maps(X9,X1,X0)
& maps(X8,X1,X0)
& identity(compose_function(X9,X5,X0,X1,X0),X0)
& identity(compose_function(X5,X8,X1,X0,X1),X1) )
=> equal_maps(inverse_function(X5,X0,X1),X9,X1,X0) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X1,X5,X8,X9,X0] :
( ( maps(X5,X0,X1)
& maps(X9,X1,X0)
& maps(X8,X1,X0)
& identity(compose_function(X9,X5,X0,X1,X0),X0)
& identity(compose_function(X5,X8,X1,X0,X1),X1) )
=> equal_maps(inverse_function(X5,X0,X1),X9,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII17) ).
fof(f276,plain,
sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) = sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
inference(forward_demodulation,[],[f275,f151]) ).
fof(f151,plain,
sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
inference(subsumption_resolution,[],[f150,f101]) ).
fof(f101,plain,
member(sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4),
inference(resolution,[],[f75,f79]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( equal_maps(X2,X3,X1,X0)
| member(sK6(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f150,plain,
( sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)
| ~ member(sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4) ),
inference(subsumption_resolution,[],[f146,f102]) ).
fof(f102,plain,
member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5),
inference(resolution,[],[f75,f78]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( equal_maps(X2,X3,X1,X0)
| member(sK8(X0,X1,X2,X3),X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f146,plain,
( ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
| ~ member(sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4)
| sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) ),
inference(resolution,[],[f121,f99]) ).
fof(f99,plain,
apply(sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK6(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)),
inference(resolution,[],[f75,f81]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( equal_maps(X2,X3,X1,X0)
| apply(X3,sK8(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f121,plain,
! [X0,X1] :
( ~ apply(sK3,X0,X1)
| ~ member(X0,sK5)
| sK0(sK4,sK3,X0) = X1
| ~ member(X1,sK4) ),
inference(subsumption_resolution,[],[f120,f91]) ).
fof(f91,plain,
! [X4] :
( member(sK0(sK4,sK3,X4),sK4)
| ~ member(X4,sK5) ),
inference(resolution,[],[f72,f68]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ maps(X1,X2,X0)
| ~ member(X3,X2)
| member(sK0(X0,X1,X3),X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ~ member(X3,X2)
| ( apply(X1,X3,sK0(X0,X1,X3))
& member(sK0(X0,X1,X3),X0) ) )
& ! [X5,X6,X7] :
( X5 = X7
| ~ member(X7,X0)
| ~ apply(X1,X6,X5)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ member(X6,X2) ) )
| ~ maps(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f51,f52]) ).
fof(f52,plain,
! [X0,X1,X3] :
( ? [X4] :
( apply(X1,X3,X4)
& member(X4,X0) )
=> ( apply(X1,X3,sK0(X0,X1,X3))
& member(sK0(X0,X1,X3),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X1,X3,X4)
& member(X4,X0) ) )
& ! [X5,X6,X7] :
( X5 = X7
| ~ member(X7,X0)
| ~ apply(X1,X6,X5)
| ~ member(X5,X0)
| ~ apply(X1,X6,X7)
| ~ member(X6,X2) ) )
| ~ maps(X1,X2,X0) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X0,X2,X1] :
( ( ! [X6] :
( ~ member(X6,X1)
| ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) )
& ! [X5,X4,X3] :
( X3 = X5
| ~ member(X3,X0)
| ~ apply(X2,X4,X5)
| ~ member(X5,X0)
| ~ apply(X2,X4,X3)
| ~ member(X4,X1) ) )
| ~ maps(X2,X1,X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X2,X1,X0] :
( ( ! [X3,X5,X4] :
( X3 = X5
| ~ apply(X2,X4,X5)
| ~ apply(X2,X4,X3)
| ~ member(X4,X1)
| ~ member(X5,X0)
| ~ member(X3,X0) )
& ! [X6] :
( ~ member(X6,X1)
| ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) )
| ~ maps(X2,X1,X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,plain,
! [X2,X1,X0] :
( maps(X2,X1,X0)
=> ( ! [X3,X5,X4] :
( ( member(X4,X1)
& member(X5,X0)
& member(X3,X0) )
=> ( ( apply(X2,X4,X5)
& apply(X2,X4,X3) )
=> X3 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f34,plain,
! [X2,X1,X0] :
( ( ! [X3,X5,X4] :
( ( member(X4,X1)
& member(X5,X0)
& member(X3,X0) )
=> ( ( apply(X2,X4,X5)
& apply(X2,X4,X3) )
=> X3 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) )
<=> maps(X2,X1,X0) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X0,X5] :
( ( ! [X7,X2,X6] :
( ( member(X7,X1)
& member(X6,X1)
& member(X2,X0) )
=> ( ( apply(X5,X2,X6)
& apply(X5,X2,X7) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( member(X4,X1)
& apply(X5,X2,X4) ) ) )
<=> maps(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f72,plain,
maps(sK3,sK5,sK4),
inference(cnf_transformation,[],[f58]) ).
fof(f120,plain,
! [X0,X1] :
( ~ apply(sK3,X0,X1)
| ~ member(X1,sK4)
| ~ member(sK0(sK4,sK3,X0),sK4)
| sK0(sK4,sK3,X0) = X1
| ~ member(X0,sK5) ),
inference(duplicate_literal_removal,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ~ member(X1,sK4)
| ~ member(X0,sK5)
| ~ member(sK0(sK4,sK3,X0),sK4)
| ~ member(X0,sK5)
| sK0(sK4,sK3,X0) = X1
| ~ apply(sK3,X0,X1) ),
inference(resolution,[],[f89,f90]) ).
fof(f90,plain,
! [X3] :
( apply(sK3,X3,sK0(sK4,sK3,X3))
| ~ member(X3,sK5) ),
inference(resolution,[],[f72,f69]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( ~ maps(X1,X2,X0)
| ~ member(X3,X2)
| apply(X1,X3,sK0(X0,X1,X3)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ apply(sK3,X2,X1)
| ~ apply(sK3,X2,X0)
| ~ member(X0,sK4)
| X0 = X1
| ~ member(X2,sK5)
| ~ member(X1,sK4) ),
inference(resolution,[],[f72,f67]) ).
fof(f67,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ maps(X1,X2,X0)
| X5 = X7
| ~ member(X6,X2)
| ~ member(X5,X0)
| ~ apply(X1,X6,X5)
| ~ member(X7,X0)
| ~ apply(X1,X6,X7) ),
inference(cnf_transformation,[],[f53]) ).
fof(f275,plain,
sK0(sK4,sK3,sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) = sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
inference(forward_demodulation,[],[f156,f213]) ).
fof(f213,plain,
sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3) = sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
inference(subsumption_resolution,[],[f212,f100]) ).
fof(f100,plain,
member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4),
inference(resolution,[],[f75,f80]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( equal_maps(X2,X3,X1,X0)
| member(sK7(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f212,plain,
( ~ member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4)
| sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3) = sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3) ),
inference(subsumption_resolution,[],[f207,f102]) ).
fof(f207,plain,
( sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3) = sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)
| ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
| ~ member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4) ),
inference(resolution,[],[f144,f138]) ).
fof(f138,plain,
apply(sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)),
inference(subsumption_resolution,[],[f137,f102]) ).
fof(f137,plain,
( ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
| apply(sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) ),
inference(subsumption_resolution,[],[f136,f100]) ).
fof(f136,plain,
( ~ member(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK4)
| ~ member(sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5)
| apply(sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)) ),
inference(resolution,[],[f103,f70]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(inverse_function(X3,X0,X2),X1,X4)
| ~ member(X4,X0)
| apply(X3,X4,X1)
| ~ member(X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X1,X2)
| ~ member(X4,X0)
| ( ( apply(inverse_function(X3,X0,X2),X1,X4)
| ~ apply(X3,X4,X1) )
& ( apply(X3,X4,X1)
| ~ apply(inverse_function(X3,X0,X2),X1,X4) ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,plain,
! [X0,X2,X4,X3,X1] :
( ~ member(X2,X4)
| ~ member(X1,X0)
| ( ( apply(inverse_function(X3,X0,X4),X2,X1)
| ~ apply(X3,X1,X2) )
& ( apply(X3,X1,X2)
| ~ apply(inverse_function(X3,X0,X4),X2,X1) ) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X2,X4,X3,X1] :
( ~ member(X2,X4)
| ~ member(X1,X0)
| ( apply(inverse_function(X3,X0,X4),X2,X1)
<=> apply(X3,X1,X2) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X4,X2,X3,X1,X0] :
( ( apply(inverse_function(X3,X0,X4),X2,X1)
<=> apply(X3,X1,X2) )
| ~ member(X2,X4)
| ~ member(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X4,X2,X3,X1,X0] :
( ( member(X2,X4)
& member(X1,X0) )
=> ( apply(inverse_function(X3,X0,X4),X2,X1)
<=> apply(X3,X1,X2) ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X2,X4,X5,X1] :
( ( member(X4,X1)
& member(X2,X0) )
=> ( apply(X5,X2,X4)
<=> apply(inverse_function(X5,X0,X1),X4,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
fof(f103,plain,
apply(inverse_function(sK2,sK4,sK5),sK8(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3)),
inference(resolution,[],[f75,f83]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( equal_maps(X2,X3,X1,X0)
| apply(X2,sK8(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f144,plain,
! [X0,X1] :
( ~ apply(sK2,X0,X1)
| ~ member(X0,sK4)
| ~ member(X1,sK5)
| sK9(X0,sK5,sK2,X0,sK3) = X1 ),
inference(subsumption_resolution,[],[f143,f117]) ).
fof(f117,plain,
! [X1] :
( member(sK9(X1,sK5,sK2,X1,sK3),sK5)
| ~ member(X1,sK4) ),
inference(duplicate_literal_removal,[],[f113]) ).
fof(f113,plain,
! [X1] :
( ~ member(X1,sK4)
| member(sK9(X1,sK5,sK2,X1,sK3),sK5)
| ~ member(X1,sK4)
| ~ member(X1,sK4) ),
inference(resolution,[],[f105,f87]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
| member(sK9(X0,X1,X2,X3,X6),X1)
| ~ member(X3,X4)
| ~ member(X0,X5) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X3,X4)
| ( ( ( member(sK9(X0,X1,X2,X3,X6),X1)
& apply(X6,sK9(X0,X1,X2,X3,X6),X0)
& apply(X2,X3,sK9(X0,X1,X2,X3,X6)) )
| ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0) )
& ( apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
| ! [X8] :
( ~ member(X8,X1)
| ~ apply(X6,X8,X0)
| ~ apply(X2,X3,X8) ) ) )
| ~ member(X0,X5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f63,f64]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X6] :
( ? [X7] :
( member(X7,X1)
& apply(X6,X7,X0)
& apply(X2,X3,X7) )
=> ( member(sK9(X0,X1,X2,X3,X6),X1)
& apply(X6,sK9(X0,X1,X2,X3,X6),X0)
& apply(X2,X3,sK9(X0,X1,X2,X3,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X3,X4)
| ( ( ? [X7] :
( member(X7,X1)
& apply(X6,X7,X0)
& apply(X2,X3,X7) )
| ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0) )
& ( apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
| ! [X8] :
( ~ member(X8,X1)
| ~ apply(X6,X8,X0)
| ~ apply(X2,X3,X8) ) ) )
| ~ member(X0,X5) ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
! [X2,X6,X1,X5,X4,X0,X3] :
( ~ member(X5,X4)
| ( ( ? [X7] :
( member(X7,X6)
& apply(X3,X7,X2)
& apply(X1,X5,X7) )
| ~ apply(compose_function(X3,X1,X4,X6,X0),X5,X2) )
& ( apply(compose_function(X3,X1,X4,X6,X0),X5,X2)
| ! [X7] :
( ~ member(X7,X6)
| ~ apply(X3,X7,X2)
| ~ apply(X1,X5,X7) ) ) )
| ~ member(X2,X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X2,X6,X1,X5,X4,X0,X3] :
( ~ member(X5,X4)
| ( ? [X7] :
( member(X7,X6)
& apply(X3,X7,X2)
& apply(X1,X5,X7) )
<=> apply(compose_function(X3,X1,X4,X6,X0),X5,X2) )
| ~ member(X2,X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X3,X4,X5,X2,X1,X6,X0] :
( ( ? [X7] :
( member(X7,X6)
& apply(X3,X7,X2)
& apply(X1,X5,X7) )
<=> apply(compose_function(X3,X1,X4,X6,X0),X5,X2) )
| ~ member(X2,X0)
| ~ member(X5,X4) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X3,X4,X5,X2,X1,X6,X0] :
( ( member(X2,X0)
& member(X5,X4) )
=> ( ? [X7] :
( member(X7,X6)
& apply(X3,X7,X2)
& apply(X1,X5,X7) )
<=> apply(compose_function(X3,X1,X4,X6,X0),X5,X2) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X10,X5,X11,X9,X0,X2,X1] :
( ( member(X11,X10)
& member(X2,X0) )
=> ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
<=> ? [X4] :
( member(X4,X1)
& apply(X9,X4,X11)
& apply(X5,X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
fof(f105,plain,
! [X0] :
( apply(compose_function(sK3,sK2,sK4,sK5,sK4),X0,X0)
| ~ member(X0,sK4) ),
inference(resolution,[],[f77,f88]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| apply(X0,X2,X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ~ identity(X0,X1)
| ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) ) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
! [X1,X0] :
( ~ identity(X1,X0)
| ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X1,X0] :
( identity(X1,X0)
=> ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f35,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
<=> identity(X1,X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X0,X5] :
( identity(X5,X0)
<=> ! [X2] :
( member(X2,X0)
=> apply(X5,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f77,plain,
identity(compose_function(sK3,sK2,sK4,sK5,sK4),sK4),
inference(cnf_transformation,[],[f58]) ).
fof(f143,plain,
! [X0,X1] :
( sK9(X0,sK5,sK2,X0,sK3) = X1
| ~ member(X0,sK4)
| ~ apply(sK2,X0,X1)
| ~ member(sK9(X0,sK5,sK2,X0,sK3),sK5)
| ~ member(X1,sK5) ),
inference(duplicate_literal_removal,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ~ member(sK9(X0,sK5,sK2,X0,sK3),sK5)
| ~ member(X1,sK5)
| ~ member(X0,sK4)
| sK9(X0,sK5,sK2,X0,sK3) = X1
| ~ apply(sK2,X0,X1)
| ~ member(X0,sK4) ),
inference(resolution,[],[f116,f95]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ apply(sK2,X2,X0)
| ~ apply(sK2,X2,X1)
| ~ member(X2,sK4)
| X0 = X1
| ~ member(X1,sK5)
| ~ member(X0,sK5) ),
inference(resolution,[],[f74,f67]) ).
fof(f74,plain,
maps(sK2,sK4,sK5),
inference(cnf_transformation,[],[f58]) ).
fof(f116,plain,
! [X2] :
( apply(sK2,X2,sK9(X2,sK5,sK2,X2,sK3))
| ~ member(X2,sK4) ),
inference(duplicate_literal_removal,[],[f114]) ).
fof(f114,plain,
! [X2] :
( ~ member(X2,sK4)
| ~ member(X2,sK4)
| apply(sK2,X2,sK9(X2,sK5,sK2,X2,sK3))
| ~ member(X2,sK4) ),
inference(resolution,[],[f105,f85]) ).
fof(f85,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
| apply(X2,X3,sK9(X0,X1,X2,X3,X6))
| ~ member(X0,X5)
| ~ member(X3,X4) ),
inference(cnf_transformation,[],[f65]) ).
fof(f156,plain,
sK0(sK4,sK3,sK9(sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK5,sK2,sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),sK3)) = sK7(sK4,sK5,inverse_function(sK2,sK4,sK5),sK3),
inference(resolution,[],[f152,f100]) ).
fof(f152,plain,
! [X1] :
( ~ member(X1,sK4)
| sK0(sK4,sK3,sK9(X1,sK5,sK2,X1,sK3)) = X1 ),
inference(subsumption_resolution,[],[f149,f117]) ).
fof(f149,plain,
! [X1] :
( ~ member(sK9(X1,sK5,sK2,X1,sK3),sK5)
| sK0(sK4,sK3,sK9(X1,sK5,sK2,X1,sK3)) = X1
| ~ member(X1,sK4) ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f147,plain,
! [X1] :
( ~ member(X1,sK4)
| ~ member(sK9(X1,sK5,sK2,X1,sK3),sK5)
| sK0(sK4,sK3,sK9(X1,sK5,sK2,X1,sK3)) = X1
| ~ member(X1,sK4) ),
inference(resolution,[],[f121,f115]) ).
fof(f115,plain,
! [X0] :
( apply(sK3,sK9(X0,sK5,sK2,X0,sK3),X0)
| ~ member(X0,sK4) ),
inference(duplicate_literal_removal,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ~ member(X0,sK4)
| ~ member(X0,sK4)
| ~ member(X0,sK4)
| apply(sK3,sK9(X0,sK5,sK2,X0,sK3),X0) ),
inference(resolution,[],[f105,f86]) ).
fof(f86,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ apply(compose_function(X6,X2,X4,X1,X5),X3,X0)
| ~ member(X0,X5)
| ~ member(X3,X4)
| apply(X6,sK9(X0,X1,X2,X3,X6),X0) ),
inference(cnf_transformation,[],[f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET726+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.06/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 14:12:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.48 % (14931)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.49 % (14939)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50 % (14939)Instruction limit reached!
% 0.19/0.50 % (14939)------------------------------
% 0.19/0.50 % (14939)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (14939)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (14939)Termination reason: Unknown
% 0.19/0.50 % (14939)Termination phase: Property scanning
% 0.19/0.50
% 0.19/0.50 % (14939)Memory used [KB]: 1535
% 0.19/0.50 % (14939)Time elapsed: 0.004 s
% 0.19/0.50 % (14939)Instructions burned: 3 (million)
% 0.19/0.50 % (14939)------------------------------
% 0.19/0.50 % (14939)------------------------------
% 0.19/0.51 % (14930)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.52 % (14931)Instruction limit reached!
% 0.19/0.52 % (14931)------------------------------
% 0.19/0.52 % (14931)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (14931)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (14931)Termination reason: Unknown
% 0.19/0.52 % (14931)Termination phase: Saturation
% 0.19/0.52
% 0.19/0.52 % (14931)Memory used [KB]: 6524
% 0.19/0.52 % (14931)Time elapsed: 0.112 s
% 0.19/0.52 % (14931)Instructions burned: 39 (million)
% 0.19/0.52 % (14931)------------------------------
% 0.19/0.52 % (14931)------------------------------
% 0.19/0.53 % (14947)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.53 % (14940)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53 % (14930)First to succeed.
% 0.19/0.54 % (14954)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.54 % (14932)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.54 % (14946)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.55 % (14948)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.55 % (14938)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55 % (14940)Instruction limit reached!
% 0.19/0.55 % (14940)------------------------------
% 0.19/0.55 % (14940)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (14940)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55 % (14940)Termination reason: Unknown
% 0.19/0.55 % (14940)Termination phase: Saturation
% 0.19/0.55
% 0.19/0.55 % (14940)Memory used [KB]: 6140
% 0.19/0.55 % (14940)Time elapsed: 0.101 s
% 0.19/0.55 % (14940)Instructions burned: 7 (million)
% 0.19/0.55 % (14940)------------------------------
% 0.19/0.55 % (14940)------------------------------
% 1.52/0.56 % (14930)Refutation found. Thanks to Tanya!
% 1.52/0.56 % SZS status Theorem for theBenchmark
% 1.52/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.52/0.56 % (14930)------------------------------
% 1.52/0.56 % (14930)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.56 % (14930)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.56 % (14930)Termination reason: Refutation
% 1.52/0.56
% 1.52/0.56 % (14930)Memory used [KB]: 1663
% 1.52/0.56 % (14930)Time elapsed: 0.138 s
% 1.52/0.56 % (14930)Instructions burned: 13 (million)
% 1.52/0.56 % (14930)------------------------------
% 1.52/0.56 % (14930)------------------------------
% 1.52/0.56 % (14923)Success in time 0.215 s
%------------------------------------------------------------------------------