TSTP Solution File: SET724+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET724+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 : n025.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 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 92 ( 14 unt; 0 def)
% Number of atoms : 476 ( 43 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 607 ( 223 ~; 212 |; 132 &)
% ( 12 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-5 aty)
% Number of variables : 365 ( 312 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f215,plain,
$false,
inference(subsumption_resolution,[],[f214,f100]) ).
fof(f100,plain,
member(sK4(sK10,sK6,sK7,sK11),sK7),
inference(resolution,[],[f81,f74]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( equal_maps(X3,X0,X2,X1)
| member(sK4(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ( ! [X4,X5,X6] :
( X4 = X6
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ member(X6,X1)
| ~ member(X5,X2)
| ~ apply(X3,X5,X6) )
| ~ equal_maps(X3,X0,X2,X1) )
& ( equal_maps(X3,X0,X2,X1)
| ( sK3(X0,X1,X2,X3) != sK5(X0,X1,X2,X3)
& member(sK3(X0,X1,X2,X3),X1)
& apply(X0,sK4(X0,X1,X2,X3),sK3(X0,X1,X2,X3))
& member(sK5(X0,X1,X2,X3),X1)
& member(sK4(X0,X1,X2,X3),X2)
& apply(X3,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f58,f59]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ? [X7,X8,X9] :
( X7 != X9
& member(X7,X1)
& apply(X0,X8,X7)
& member(X9,X1)
& member(X8,X2)
& apply(X3,X8,X9) )
=> ( sK3(X0,X1,X2,X3) != sK5(X0,X1,X2,X3)
& member(sK3(X0,X1,X2,X3),X1)
& apply(X0,sK4(X0,X1,X2,X3),sK3(X0,X1,X2,X3))
& member(sK5(X0,X1,X2,X3),X1)
& member(sK4(X0,X1,X2,X3),X2)
& apply(X3,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ( ! [X4,X5,X6] :
( X4 = X6
| ~ member(X4,X1)
| ~ apply(X0,X5,X4)
| ~ member(X6,X1)
| ~ member(X5,X2)
| ~ apply(X3,X5,X6) )
| ~ equal_maps(X3,X0,X2,X1) )
& ( equal_maps(X3,X0,X2,X1)
| ? [X7,X8,X9] :
( X7 != X9
& member(X7,X1)
& apply(X0,X8,X7)
& member(X9,X1)
& member(X8,X2)
& apply(X3,X8,X9) ) ) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X1,X2,X0,X3] :
( ( ! [X5,X4,X6] :
( X5 = X6
| ~ member(X5,X2)
| ~ apply(X1,X4,X5)
| ~ member(X6,X2)
| ~ member(X4,X0)
| ~ apply(X3,X4,X6) )
| ~ equal_maps(X3,X1,X0,X2) )
& ( equal_maps(X3,X1,X0,X2)
| ? [X5,X4,X6] :
( X5 != X6
& member(X5,X2)
& apply(X1,X4,X5)
& member(X6,X2)
& member(X4,X0)
& apply(X3,X4,X6) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X1,X2,X0,X3] :
( ! [X5,X4,X6] :
( X5 = X6
| ~ member(X5,X2)
| ~ apply(X1,X4,X5)
| ~ member(X6,X2)
| ~ member(X4,X0)
| ~ apply(X3,X4,X6) )
<=> equal_maps(X3,X1,X0,X2) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X1,X2,X0,X3] :
( equal_maps(X3,X1,X0,X2)
<=> ! [X6,X4,X5] :
( X5 = X6
| ~ apply(X1,X4,X5)
| ~ apply(X3,X4,X6)
| ~ member(X4,X0)
| ~ member(X5,X2)
| ~ member(X6,X2) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X1,X2,X0,X3] :
( equal_maps(X3,X1,X0,X2)
<=> ! [X6,X4,X5] :
( ( member(X4,X0)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X1,X4,X5)
& apply(X3,X4,X6) )
=> X5 = X6 ) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X9,X1,X5] :
( ! [X2,X7,X6] :
( ( member(X6,X1)
& member(X2,X0)
& member(X7,X1) )
=> ( ( apply(X9,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) )
<=> equal_maps(X5,X9,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_maps) ).
fof(f81,plain,
~ equal_maps(sK11,sK10,sK7,sK6),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( maps(sK9,sK8,sK7)
& surjective(sK9,sK8,sK7)
& equal_maps(compose_function(sK11,sK9,sK8,sK7,sK6),compose_function(sK10,sK9,sK8,sK7,sK6),sK8,sK6)
& maps(sK10,sK7,sK6)
& ~ equal_maps(sK11,sK10,sK7,sK6)
& maps(sK11,sK7,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11])],[f61,f62]) ).
fof(f62,plain,
( ? [X0,X1,X2,X3,X4,X5] :
( maps(X3,X2,X1)
& surjective(X3,X2,X1)
& equal_maps(compose_function(X5,X3,X2,X1,X0),compose_function(X4,X3,X2,X1,X0),X2,X0)
& maps(X4,X1,X0)
& ~ equal_maps(X5,X4,X1,X0)
& maps(X5,X1,X0) )
=> ( maps(sK9,sK8,sK7)
& surjective(sK9,sK8,sK7)
& equal_maps(compose_function(sK11,sK9,sK8,sK7,sK6),compose_function(sK10,sK9,sK8,sK7,sK6),sK8,sK6)
& maps(sK10,sK7,sK6)
& ~ equal_maps(sK11,sK10,sK7,sK6)
& maps(sK11,sK7,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
? [X0,X1,X2,X3,X4,X5] :
( maps(X3,X2,X1)
& surjective(X3,X2,X1)
& equal_maps(compose_function(X5,X3,X2,X1,X0),compose_function(X4,X3,X2,X1,X0),X2,X0)
& maps(X4,X1,X0)
& ~ equal_maps(X5,X4,X1,X0)
& maps(X5,X1,X0) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
? [X4,X2,X0,X1,X3,X5] :
( maps(X1,X0,X2)
& surjective(X1,X0,X2)
& equal_maps(compose_function(X5,X1,X0,X2,X4),compose_function(X3,X1,X0,X2,X4),X0,X4)
& maps(X3,X2,X4)
& ~ equal_maps(X5,X3,X2,X4)
& maps(X5,X2,X4) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
? [X2,X0,X5,X1,X3,X4] :
( ~ equal_maps(X5,X3,X2,X4)
& maps(X1,X0,X2)
& maps(X3,X2,X4)
& maps(X5,X2,X4)
& surjective(X1,X0,X2)
& equal_maps(compose_function(X5,X1,X0,X2,X4),compose_function(X3,X1,X0,X2,X4),X0,X4) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X2,X0,X5,X1,X3,X4] :
( ( maps(X1,X0,X2)
& maps(X3,X2,X4)
& maps(X5,X2,X4)
& surjective(X1,X0,X2)
& equal_maps(compose_function(X5,X1,X0,X2,X4),compose_function(X3,X1,X0,X2,X4),X0,X4) )
=> equal_maps(X5,X3,X2,X4) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X5,X1,X8,X10,X9] :
( ( maps(X8,X1,X10)
& maps(X9,X1,X10)
& surjective(X5,X0,X1)
& equal_maps(compose_function(X9,X5,X0,X1,X10),compose_function(X8,X5,X0,X1,X10),X0,X10)
& maps(X5,X0,X1) )
=> equal_maps(X9,X8,X1,X10) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X5,X1,X8,X10,X9] :
( ( maps(X8,X1,X10)
& maps(X9,X1,X10)
& surjective(X5,X0,X1)
& equal_maps(compose_function(X9,X5,X0,X1,X10),compose_function(X8,X5,X0,X1,X10),X0,X10)
& maps(X5,X0,X1) )
=> equal_maps(X9,X8,X1,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII15) ).
fof(f214,plain,
~ member(sK4(sK10,sK6,sK7,sK11),sK7),
inference(resolution,[],[f212,f93]) ).
fof(f93,plain,
! [X1] :
( member(sK2(sK8,sK9,X1),sK8)
| ~ member(X1,sK7) ),
inference(resolution,[],[f84,f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X1,X0,X2)
| member(sK2(X0,X1,X3),X0)
| ~ member(X3,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ! [X3] :
( ~ member(X3,X2)
| ( apply(X1,sK2(X0,X1,X3),X3)
& member(sK2(X0,X1,X3),X0) ) )
| ~ surjective(X1,X0,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f54,f55]) ).
fof(f55,plain,
! [X0,X1,X3] :
( ? [X4] :
( apply(X1,X4,X3)
& member(X4,X0) )
=> ( apply(X1,sK2(X0,X1,X3),X3)
& member(sK2(X0,X1,X3),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X1,X4,X3)
& member(X4,X0) ) )
| ~ surjective(X1,X0,X2) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X0,X2,X1] :
( ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X2,X4,X3)
& member(X4,X0) ) )
| ~ surjective(X2,X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X1,X2,X0] :
( surjective(X2,X0,X1)
=> ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X2,X4,X3)
& member(X4,X0) ) ) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f32,plain,
! [X1,X2,X0] :
( surjective(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X2,X4,X3)
& member(X4,X0) ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X5] :
( surjective(X5,X0,X1)
<=> ! [X4] :
( member(X4,X1)
=> ? [X3] :
( apply(X5,X3,X4)
& member(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f84,plain,
surjective(sK9,sK8,sK7),
inference(cnf_transformation,[],[f63]) ).
fof(f212,plain,
~ member(sK2(sK8,sK9,sK4(sK10,sK6,sK7,sK11)),sK8),
inference(duplicate_literal_removal,[],[f210]) ).
fof(f210,plain,
( ~ member(sK2(sK8,sK9,sK4(sK10,sK6,sK7,sK11)),sK8)
| ~ member(sK2(sK8,sK9,sK4(sK10,sK6,sK7,sK11)),sK8) ),
inference(resolution,[],[f208,f159]) ).
fof(f159,plain,
( apply(sK9,sK2(sK8,sK9,sK4(sK10,sK6,sK7,sK11)),sK4(sK10,sK6,sK7,sK11))
| ~ member(sK2(sK8,sK9,sK4(sK10,sK6,sK7,sK11)),sK8) ),
inference(superposition,[],[f95,f147]) ).
fof(f147,plain,
sK4(sK10,sK6,sK7,sK11) = sK1(sK7,sK9,sK2(sK8,sK9,sK4(sK10,sK6,sK7,sK11))),
inference(resolution,[],[f146,f100]) ).
fof(f146,plain,
! [X0] :
( ~ member(X0,sK7)
| sK1(sK7,sK9,sK2(sK8,sK9,X0)) = X0 ),
inference(subsumption_resolution,[],[f144,f93]) ).
fof(f144,plain,
! [X0] :
( ~ member(X0,sK7)
| ~ member(sK2(sK8,sK9,X0),sK8)
| sK1(sK7,sK9,sK2(sK8,sK9,X0)) = X0 ),
inference(duplicate_literal_removal,[],[f142]) ).
fof(f142,plain,
! [X0] :
( ~ member(sK2(sK8,sK9,X0),sK8)
| ~ member(X0,sK7)
| ~ member(X0,sK7)
| sK1(sK7,sK9,sK2(sK8,sK9,X0)) = X0 ),
inference(resolution,[],[f128,f92]) ).
fof(f92,plain,
! [X0] :
( apply(sK9,sK2(sK8,sK9,X0),X0)
| ~ member(X0,sK7) ),
inference(resolution,[],[f84,f72]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ surjective(X1,X0,X2)
| ~ member(X3,X2)
| apply(X1,sK2(X0,X1,X3),X3) ),
inference(cnf_transformation,[],[f56]) ).
fof(f128,plain,
! [X2,X3] :
( ~ apply(sK9,X2,X3)
| ~ member(X3,sK7)
| sK1(sK7,sK9,X2) = X3
| ~ member(X2,sK8) ),
inference(subsumption_resolution,[],[f125,f96]) ).
fof(f96,plain,
! [X4] :
( member(sK1(sK7,sK9,X4),sK7)
| ~ member(X4,sK8) ),
inference(resolution,[],[f85,f68]) ).
fof(f68,plain,
! [X2,X0,X1,X6] :
( ~ maps(X1,X2,X0)
| ~ member(X6,X2)
| member(sK1(X0,X1,X6),X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ maps(X1,X2,X0)
| ( ! [X3,X4,X5] :
( ~ member(X5,X0)
| X4 = X5
| ~ apply(X1,X3,X4)
| ~ apply(X1,X3,X5)
| ~ member(X3,X2)
| ~ member(X4,X0) )
& ! [X6] :
( ~ member(X6,X2)
| ( apply(X1,X6,sK1(X0,X1,X6))
& member(sK1(X0,X1,X6),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f51,f52]) ).
fof(f52,plain,
! [X0,X1,X6] :
( ? [X7] :
( apply(X1,X6,X7)
& member(X7,X0) )
=> ( apply(X1,X6,sK1(X0,X1,X6))
& member(sK1(X0,X1,X6),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ maps(X1,X2,X0)
| ( ! [X3,X4,X5] :
( ~ member(X5,X0)
| X4 = X5
| ~ apply(X1,X3,X4)
| ~ apply(X1,X3,X5)
| ~ member(X3,X2)
| ~ member(X4,X0) )
& ! [X6] :
( ~ member(X6,X2)
| ? [X7] :
( apply(X1,X6,X7)
& member(X7,X0) ) ) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X2,X1,X0] :
( ~ maps(X1,X0,X2)
| ( ! [X5,X4,X3] :
( ~ member(X3,X2)
| X3 = X4
| ~ apply(X1,X5,X4)
| ~ apply(X1,X5,X3)
| ~ member(X5,X0)
| ~ member(X4,X2) )
& ! [X6] :
( ~ member(X6,X0)
| ? [X7] :
( apply(X1,X6,X7)
& member(X7,X2) ) ) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ( ! [X6] :
( ~ member(X6,X0)
| ? [X7] :
( apply(X1,X6,X7)
& member(X7,X2) ) )
& ! [X3,X4,X5] :
( X3 = X4
| ~ apply(X1,X5,X3)
| ~ apply(X1,X5,X4)
| ~ member(X4,X2)
| ~ member(X3,X2)
| ~ member(X5,X0) ) )
| ~ maps(X1,X0,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X2,X0,X1] :
( maps(X1,X0,X2)
=> ( ! [X6] :
( member(X6,X0)
=> ? [X7] :
( apply(X1,X6,X7)
& member(X7,X2) ) )
& ! [X3,X4,X5] :
( ( member(X4,X2)
& member(X3,X2)
& member(X5,X0) )
=> ( ( apply(X1,X5,X3)
& apply(X1,X5,X4) )
=> X3 = X4 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ( ! [X6] :
( member(X6,X0)
=> ? [X7] :
( apply(X1,X6,X7)
& member(X7,X2) ) )
& ! [X3,X4,X5] :
( ( member(X4,X2)
& member(X3,X2)
& member(X5,X0) )
=> ( ( apply(X1,X5,X3)
& apply(X1,X5,X4) )
=> X3 = X4 ) ) )
<=> maps(X1,X0,X2) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X5,X1] :
( maps(X5,X0,X1)
<=> ( ! [X7,X6,X2] :
( ( member(X7,X1)
& member(X2,X0)
& member(X6,X1) )
=> ( ( apply(X5,X2,X6)
& apply(X5,X2,X7) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f85,plain,
maps(sK9,sK8,sK7),
inference(cnf_transformation,[],[f63]) ).
fof(f125,plain,
! [X2,X3] :
( ~ member(X3,sK7)
| ~ apply(sK9,X2,X3)
| ~ member(sK1(sK7,sK9,X2),sK7)
| ~ member(X2,sK8)
| sK1(sK7,sK9,X2) = X3 ),
inference(duplicate_literal_removal,[],[f124]) ).
fof(f124,plain,
! [X2,X3] :
( ~ member(X2,sK8)
| ~ member(X3,sK7)
| sK1(sK7,sK9,X2) = X3
| ~ apply(sK9,X2,X3)
| ~ member(sK1(sK7,sK9,X2),sK7)
| ~ member(X2,sK8) ),
inference(resolution,[],[f94,f95]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ apply(sK9,X0,X1)
| X1 = X2
| ~ member(X0,sK8)
| ~ apply(sK9,X0,X2)
| ~ member(X2,sK7)
| ~ member(X1,sK7) ),
inference(resolution,[],[f85,f70]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ maps(X1,X2,X0)
| ~ member(X3,X2)
| ~ apply(X1,X3,X5)
| ~ member(X5,X0)
| ~ apply(X1,X3,X4)
| X4 = X5
| ~ member(X4,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f95,plain,
! [X3] :
( apply(sK9,X3,sK1(sK7,sK9,X3))
| ~ member(X3,sK8) ),
inference(resolution,[],[f85,f69]) ).
fof(f69,plain,
! [X2,X0,X1,X6] :
( ~ maps(X1,X2,X0)
| apply(X1,X6,sK1(X0,X1,X6))
| ~ member(X6,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f208,plain,
! [X2] :
( ~ apply(sK9,X2,sK4(sK10,sK6,sK7,sK11))
| ~ member(X2,sK8) ),
inference(subsumption_resolution,[],[f207,f101]) ).
fof(f101,plain,
sK3(sK10,sK6,sK7,sK11) != sK5(sK10,sK6,sK7,sK11),
inference(resolution,[],[f81,f78]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( equal_maps(X3,X0,X2,X1)
| sK3(X0,X1,X2,X3) != sK5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f60]) ).
fof(f207,plain,
! [X2] :
( ~ apply(sK9,X2,sK4(sK10,sK6,sK7,sK11))
| sK3(sK10,sK6,sK7,sK11) = sK5(sK10,sK6,sK7,sK11)
| ~ member(X2,sK8) ),
inference(subsumption_resolution,[],[f206,f98]) ).
fof(f98,plain,
member(sK3(sK10,sK6,sK7,sK11),sK6),
inference(resolution,[],[f81,f77]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( equal_maps(X3,X0,X2,X1)
| member(sK3(X0,X1,X2,X3),X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f206,plain,
! [X2] :
( ~ member(X2,sK8)
| ~ member(sK3(sK10,sK6,sK7,sK11),sK6)
| ~ apply(sK9,X2,sK4(sK10,sK6,sK7,sK11))
| sK3(sK10,sK6,sK7,sK11) = sK5(sK10,sK6,sK7,sK11) ),
inference(subsumption_resolution,[],[f205,f100]) ).
fof(f205,plain,
! [X2] :
( ~ member(sK4(sK10,sK6,sK7,sK11),sK7)
| ~ apply(sK9,X2,sK4(sK10,sK6,sK7,sK11))
| sK3(sK10,sK6,sK7,sK11) = sK5(sK10,sK6,sK7,sK11)
| ~ member(X2,sK8)
| ~ member(sK3(sK10,sK6,sK7,sK11),sK6) ),
inference(duplicate_literal_removal,[],[f203]) ).
fof(f203,plain,
! [X2] :
( ~ member(X2,sK8)
| ~ member(sK3(sK10,sK6,sK7,sK11),sK6)
| ~ apply(sK9,X2,sK4(sK10,sK6,sK7,sK11))
| sK3(sK10,sK6,sK7,sK11) = sK5(sK10,sK6,sK7,sK11)
| ~ apply(sK9,X2,sK4(sK10,sK6,sK7,sK11))
| ~ member(sK4(sK10,sK6,sK7,sK11),sK7) ),
inference(resolution,[],[f174,f102]) ).
fof(f102,plain,
apply(sK10,sK4(sK10,sK6,sK7,sK11),sK3(sK10,sK6,sK7,sK11)),
inference(resolution,[],[f81,f76]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( equal_maps(X3,X0,X2,X1)
| apply(X0,sK4(X0,X1,X2,X3),sK3(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ apply(sK10,X2,X1)
| ~ member(X2,sK7)
| sK5(sK10,sK6,sK7,sK11) = X1
| ~ apply(sK9,X0,X2)
| ~ apply(sK9,X0,sK4(sK10,sK6,sK7,sK11))
| ~ member(X0,sK8)
| ~ member(X1,sK6) ),
inference(duplicate_literal_removal,[],[f173]) ).
fof(f173,plain,
! [X2,X0,X1] :
( sK5(sK10,sK6,sK7,sK11) = X1
| ~ member(X1,sK6)
| ~ apply(sK9,X0,sK4(sK10,sK6,sK7,sK11))
| ~ member(X1,sK6)
| ~ member(X0,sK8)
| ~ member(X2,sK7)
| ~ apply(sK10,X2,X1)
| ~ member(X0,sK8)
| ~ apply(sK9,X0,X2) ),
inference(resolution,[],[f158,f64]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X8,X6,X4,X5] :
( apply(compose_function(X5,X1,X0,X3,X6),X4,X2)
| ~ apply(X1,X4,X8)
| ~ member(X4,X0)
| ~ apply(X5,X8,X2)
| ~ member(X8,X3)
| ~ member(X2,X6) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( ( apply(X5,sK0(X1,X2,X3,X4,X5),X2)
& member(sK0(X1,X2,X3,X4,X5),X3)
& apply(X1,X4,sK0(X1,X2,X3,X4,X5)) )
| ~ apply(compose_function(X5,X1,X0,X3,X6),X4,X2) )
& ( apply(compose_function(X5,X1,X0,X3,X6),X4,X2)
| ! [X8] :
( ~ apply(X5,X8,X2)
| ~ member(X8,X3)
| ~ apply(X1,X4,X8) ) ) )
| ~ member(X2,X6)
| ~ member(X4,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f48,f49]) ).
fof(f49,plain,
! [X1,X2,X3,X4,X5] :
( ? [X7] :
( apply(X5,X7,X2)
& member(X7,X3)
& apply(X1,X4,X7) )
=> ( apply(X5,sK0(X1,X2,X3,X4,X5),X2)
& member(sK0(X1,X2,X3,X4,X5),X3)
& apply(X1,X4,sK0(X1,X2,X3,X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( ? [X7] :
( apply(X5,X7,X2)
& member(X7,X3)
& apply(X1,X4,X7) )
| ~ apply(compose_function(X5,X1,X0,X3,X6),X4,X2) )
& ( apply(compose_function(X5,X1,X0,X3,X6),X4,X2)
| ! [X8] :
( ~ apply(X5,X8,X2)
| ~ member(X8,X3)
| ~ apply(X1,X4,X8) ) ) )
| ~ member(X2,X6)
| ~ member(X4,X0) ),
inference(rectify,[],[f47]) ).
fof(f47,plain,
! [X0,X6,X5,X3,X2,X4,X1] :
( ( ( ? [X7] :
( apply(X4,X7,X5)
& member(X7,X3)
& apply(X6,X2,X7) )
| ~ apply(compose_function(X4,X6,X0,X3,X1),X2,X5) )
& ( apply(compose_function(X4,X6,X0,X3,X1),X2,X5)
| ! [X7] :
( ~ apply(X4,X7,X5)
| ~ member(X7,X3)
| ~ apply(X6,X2,X7) ) ) )
| ~ member(X5,X1)
| ~ member(X2,X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X6,X5,X3,X2,X4,X1] :
( ( ? [X7] :
( apply(X4,X7,X5)
& member(X7,X3)
& apply(X6,X2,X7) )
<=> apply(compose_function(X4,X6,X0,X3,X1),X2,X5) )
| ~ member(X5,X1)
| ~ member(X2,X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X6,X0,X4,X5,X3,X1,X2] :
( ( ? [X7] :
( apply(X4,X7,X5)
& member(X7,X3)
& apply(X6,X2,X7) )
<=> apply(compose_function(X4,X6,X0,X3,X1),X2,X5) )
| ~ member(X5,X1)
| ~ member(X2,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X6,X0,X4,X5,X3,X1,X2] :
( ( member(X5,X1)
& member(X2,X0) )
=> ( ? [X7] :
( apply(X4,X7,X5)
& member(X7,X3)
& apply(X6,X2,X7) )
<=> apply(compose_function(X4,X6,X0,X3,X1),X2,X5) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X10,X2,X1,X9,X11,X5] :
( ( member(X11,X10)
& member(X2,X0) )
=> ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
<=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1)
& apply(X9,X4,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
fof(f158,plain,
! [X3,X4] :
( ~ apply(compose_function(sK10,sK9,sK8,sK7,sK6),X3,X4)
| ~ member(X3,sK8)
| ~ apply(sK9,X3,sK4(sK10,sK6,sK7,sK11))
| sK5(sK10,sK6,sK7,sK11) = X4
| ~ member(X4,sK6) ),
inference(subsumption_resolution,[],[f157,f99]) ).
fof(f99,plain,
member(sK5(sK10,sK6,sK7,sK11),sK6),
inference(resolution,[],[f81,f75]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( equal_maps(X3,X0,X2,X1)
| member(sK5(X0,X1,X2,X3),X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f157,plain,
! [X3,X4] :
( ~ member(X4,sK6)
| ~ apply(sK9,X3,sK4(sK10,sK6,sK7,sK11))
| ~ apply(compose_function(sK10,sK9,sK8,sK7,sK6),X3,X4)
| ~ member(sK5(sK10,sK6,sK7,sK11),sK6)
| sK5(sK10,sK6,sK7,sK11) = X4
| ~ member(X3,sK8) ),
inference(subsumption_resolution,[],[f154,f100]) ).
fof(f154,plain,
! [X3,X4] :
( ~ member(sK4(sK10,sK6,sK7,sK11),sK7)
| ~ member(sK5(sK10,sK6,sK7,sK11),sK6)
| ~ apply(compose_function(sK10,sK9,sK8,sK7,sK6),X3,X4)
| ~ member(X4,sK6)
| ~ apply(sK9,X3,sK4(sK10,sK6,sK7,sK11))
| ~ member(X3,sK8)
| sK5(sK10,sK6,sK7,sK11) = X4 ),
inference(resolution,[],[f137,f97]) ).
fof(f97,plain,
apply(sK11,sK4(sK10,sK6,sK7,sK11),sK5(sK10,sK6,sK7,sK11)),
inference(resolution,[],[f81,f73]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( equal_maps(X3,X0,X2,X1)
| apply(X3,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK11,X3,X2)
| ~ member(X1,sK8)
| ~ member(X2,sK6)
| X0 = X2
| ~ apply(sK9,X1,X3)
| ~ apply(compose_function(sK10,sK9,sK8,sK7,sK6),X1,X0)
| ~ member(X0,sK6)
| ~ member(X3,sK7) ),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ member(X2,sK6)
| ~ apply(sK11,X3,X2)
| ~ member(X1,sK8)
| ~ member(X1,sK8)
| ~ apply(sK9,X1,X3)
| ~ member(X2,sK6)
| ~ member(X0,sK6)
| ~ member(X3,sK7)
| ~ apply(compose_function(sK10,sK9,sK8,sK7,sK6),X1,X0) ),
inference(resolution,[],[f103,f64]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ apply(compose_function(sK11,sK9,sK8,sK7,sK6),X0,X1)
| ~ member(X2,sK6)
| ~ member(X0,sK8)
| ~ member(X1,sK6)
| X1 = X2
| ~ apply(compose_function(sK10,sK9,sK8,sK7,sK6),X0,X2) ),
inference(resolution,[],[f83,f79]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ equal_maps(X3,X0,X2,X1)
| ~ member(X5,X2)
| ~ apply(X3,X5,X6)
| ~ apply(X0,X5,X4)
| X4 = X6
| ~ member(X6,X1)
| ~ member(X4,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f83,plain,
equal_maps(compose_function(sK11,sK9,sK8,sK7,sK6),compose_function(sK10,sK9,sK8,sK7,sK6),sK8,sK6),
inference(cnf_transformation,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET724+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.10/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 30 14:24:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49 % (306)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)
% 0.19/0.49 % (323)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)
% 0.19/0.49 % (301)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.49 % (315)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)
% 0.19/0.49 % (305)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.49 % (303)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.49 % (302)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.49 % (303)Instruction limit reached!
% 0.19/0.49 % (303)------------------------------
% 0.19/0.49 % (303)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (303)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (303)Termination reason: Unknown
% 0.19/0.49 % (303)Termination phase: Preprocessing 3
% 0.19/0.49
% 0.19/0.49 % (303)Memory used [KB]: 1535
% 0.19/0.49 % (303)Time elapsed: 0.002 s
% 0.19/0.49 % (303)Instructions burned: 3 (million)
% 0.19/0.49 % (303)------------------------------
% 0.19/0.49 % (303)------------------------------
% 0.19/0.50 % (315)Instruction limit reached!
% 0.19/0.50 % (315)------------------------------
% 0.19/0.50 % (315)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (315)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (315)Termination reason: Unknown
% 0.19/0.50 % (315)Termination phase: Saturation
% 0.19/0.50
% 0.19/0.50 % (315)Memory used [KB]: 6012
% 0.19/0.50 % (315)Time elapsed: 0.005 s
% 0.19/0.50 % (315)Instructions burned: 4 (million)
% 0.19/0.50 % (315)------------------------------
% 0.19/0.50 % (315)------------------------------
% 0.19/0.50 % (307)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)
% 0.19/0.50 % (322)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)
% 0.19/0.50 % (314)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)
% 0.19/0.50 % (306)First to succeed.
% 0.19/0.51 % (326)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.51 % (304)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (327)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51 % (325)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51 % (329)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.52 % (330)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)
% 0.19/0.52 % (312)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52 % (306)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (306)------------------------------
% 0.19/0.52 % (306)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (306)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (306)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (306)Memory used [KB]: 1663
% 0.19/0.52 % (306)Time elapsed: 0.115 s
% 0.19/0.52 % (306)Instructions burned: 9 (million)
% 0.19/0.52 % (306)------------------------------
% 0.19/0.52 % (306)------------------------------
% 0.19/0.52 % (300)Success in time 0.182 s
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