TSTP Solution File: SEU168+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU168+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 : Tue Apr 30 15:22:46 EDT 2024
% Result : Theorem 0.14s 0.41s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 204 ( 21 unt; 0 def)
% Number of atoms : 716 ( 20 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 916 ( 404 ~; 372 |; 116 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 443 ( 394 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f501,plain,
$false,
inference(resolution,[],[f500,f52]) ).
fof(f52,plain,
! [X0] : in(X0,sK7(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ! [X2] :
( in(X2,sK7(X0))
| are_equipotent(X2,sK7(X0))
| ~ subset(X2,sK7(X0)) )
& ! [X3] :
( ( ! [X5] :
( in(X5,sK8(X0,X3))
| ~ subset(X5,X3) )
& in(sK8(X0,X3),sK7(X0)) )
| ~ in(X3,sK7(X0)) )
& ! [X6,X7] :
( in(X7,sK7(X0))
| ~ subset(X7,X6)
| ~ in(X6,sK7(X0)) )
& in(X0,sK7(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f15,f34,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( in(X2,sK7(X0))
| are_equipotent(X2,sK7(X0))
| ~ subset(X2,sK7(X0)) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,sK7(X0)) )
| ~ in(X3,sK7(X0)) )
& ! [X7,X6] :
( in(X7,sK7(X0))
| ~ subset(X7,X6)
| ~ in(X6,sK7(X0)) )
& in(X0,sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,sK7(X0)) )
=> ( ! [X5] :
( in(X5,sK8(X0,X3))
| ~ subset(X5,X3) )
& in(sK8(X0,X3),sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
~ ( ! [X3] :
~ ( ! [X4] :
( subset(X4,X2)
=> in(X4,X3) )
& in(X3,X1) )
& in(X2,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f500,plain,
! [X0] : ~ in(sK5,sK7(X0)),
inference(subsumption_resolution,[],[f499,f458]) ).
fof(f458,plain,
! [X0] :
( in(sK6(sK7(X0)),sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(resolution,[],[f454,f57]) ).
fof(f57,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f454,plain,
! [X0,X1] :
( ~ subset(X0,sK6(sK7(X1)))
| in(X0,sK7(X1))
| ~ in(sK5,sK7(X1)) ),
inference(subsumption_resolution,[],[f453,f224]) ).
fof(f224,plain,
! [X0] : ~ sP0(sK7(X0)),
inference(global_subsumption,[],[f57,f52,f44,f45,f46,f47,f49,f58,f68,f69,f48,f66,f72,f67,f73,f60,f61,f70,f71,f75,f78,f77,f83,f50,f84,f59,f87,f91,f92,f51,f93,f54,f79,f95,f81,f89,f99,f100,f94,f90,f102,f103,f104,f101,f53,f107,f108,f109,f110,f105,f112,f55,f120,f121,f122,f124,f125,f126,f115,f116,f130,f131,f113,f114,f117,f132,f127,f133,f134,f129,f56,f138,f111,f141,f142,f118,f145,f148,f150,f154,f155,f164,f165,f166,f147,f167,f170,f153,f156,f64,f174,f175,f176,f177,f178,f179,f180,f157,f123,f140,f182,f184,f171,f163,f159,f187,f65,f88,f190,f191,f192,f193,f194,f98,f197,f143,f198,f201,f196,f200,f149,f203,f204,f205,f206,f207,f158,f85,f211,f212,f106,f221,f215,f222,f216,f223,f217]) ).
fof(f217,plain,
! [X0] :
( in(sK6(powerset(sK3(sK7(X0)))),sK7(X0))
| ~ sP0(sK7(X0))
| sP0(powerset(sK3(sK7(X0))))
| ~ in(sK5,powerset(sK3(sK7(X0))))
| sP1(powerset(sK3(sK7(X0)))) ),
inference(resolution,[],[f106,f85]) ).
fof(f223,plain,
! [X0] : ~ sP0(sK7(X0)),
inference(global_subsumption,[],[f57,f52,f44,f45,f46,f47,f49,f58,f68,f69,f48,f66,f72,f67,f73,f60,f61,f70,f71,f75,f78,f77,f83,f50,f84,f59,f87,f91,f92,f51,f93,f54,f79,f95,f81,f89,f99,f100,f94,f90,f102,f103,f104,f101,f53,f107,f108,f109,f110,f105,f112,f55,f120,f121,f122,f124,f125,f126,f115,f116,f130,f131,f113,f114,f117,f132,f127,f133,f134,f129,f56,f138,f111,f141,f142,f118,f145,f148,f150,f154,f155,f164,f165,f166,f147,f167,f170,f153,f156,f64,f174,f175,f176,f177,f178,f179,f180,f157,f123,f140,f182,f184,f171,f163,f159,f187,f65,f88,f190,f191,f192,f193,f194,f98,f197,f143,f198,f201,f196,f200,f149,f203,f204,f205,f206,f207,f158,f85,f211,f212,f106,f221,f215,f222,f216]) ).
fof(f216,plain,
! [X0] :
( in(sK3(powerset(sK3(sK7(X0)))),sK7(X0))
| ~ sP0(sK7(X0))
| ~ sP0(powerset(sK3(sK7(X0)))) ),
inference(resolution,[],[f106,f75]) ).
fof(f222,plain,
! [X0] : ~ sP0(sK7(X0)),
inference(global_subsumption,[],[f57,f52,f44,f45,f46,f47,f49,f58,f68,f69,f48,f66,f72,f67,f73,f60,f61,f70,f71,f75,f78,f77,f83,f50,f84,f59,f87,f91,f92,f51,f93,f54,f79,f95,f81,f89,f99,f100,f94,f90,f102,f103,f104,f101,f53,f107,f108,f109,f110,f105,f112,f55,f120,f121,f122,f124,f125,f126,f115,f116,f130,f131,f113,f114,f117,f132,f127,f133,f134,f129,f56,f138,f111,f141,f142,f118,f145,f148,f150,f154,f155,f164,f165,f166,f147,f167,f170,f153,f156,f64,f174,f175,f176,f177,f178,f179,f180,f157,f123,f140,f182,f184,f171,f163,f159,f187,f65,f88,f190,f191,f192,f193,f194,f98,f197,f143,f198,f201,f196,f200,f149,f203,f204,f205,f206,f207,f158,f85,f211,f212,f106,f221,f215]) ).
fof(f215,plain,
! [X0] :
( in(sK2(sK3(sK7(X0))),sK7(X0))
| ~ sP0(sK7(X0))
| ~ sP1(sK3(sK7(X0))) ),
inference(resolution,[],[f106,f44]) ).
fof(f221,plain,
! [X0] : ~ sP0(sK7(X0)),
inference(subsumption_resolution,[],[f220,f49]) ).
fof(f220,plain,
! [X0] :
( in(sK4(sK7(X0)),sK7(X0))
| ~ sP0(sK7(X0)) ),
inference(duplicate_literal_removal,[],[f213]) ).
fof(f213,plain,
! [X0] :
( in(sK4(sK7(X0)),sK7(X0))
| ~ sP0(sK7(X0))
| ~ sP0(sK7(X0)) ),
inference(resolution,[],[f106,f48]) ).
fof(f106,plain,
! [X0,X1] :
( ~ subset(X0,sK3(sK7(X1)))
| in(X0,sK7(X1))
| ~ sP0(sK7(X1)) ),
inference(resolution,[],[f53,f47]) ).
fof(f212,plain,
! [X0,X1] :
( ~ in(X1,sK6(powerset(X0)))
| ~ in(sK5,powerset(X0))
| sP1(powerset(X0))
| sP0(powerset(X0))
| in(X1,X0) ),
inference(resolution,[],[f85,f59]) ).
fof(f211,plain,
! [X0,X1] :
( sP0(powerset(X0))
| ~ in(sK5,powerset(X0))
| sP1(powerset(X0))
| ~ subset(X0,X1)
| in(sK6(powerset(X0)),sK7(X1)) ),
inference(resolution,[],[f85,f111]) ).
fof(f85,plain,
! [X0] :
( subset(sK6(powerset(X0)),X0)
| sP0(powerset(X0))
| ~ in(sK5,powerset(X0))
| sP1(powerset(X0)) ),
inference(resolution,[],[f50,f67]) ).
fof(f158,plain,
! [X0,X1] :
( ~ in(sK9(X0,sK7(X1)),powerset(X1))
| subset(X0,sK7(X1)) ),
inference(resolution,[],[f148,f61]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK10(X1,powerset(X2)))
| in(X0,sK7(X2))
| subset(sK10(X1,powerset(X2)),X1)
| powerset(X2) = powerset(X1) ),
inference(resolution,[],[f149,f64]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK9(powerset(X1),X2))
| in(X0,sK7(X1))
| subset(powerset(X1),X2) ),
inference(resolution,[],[f149,f60]) ).
fof(f205,plain,
! [X0,X1] :
( ~ subset(X0,sK6(powerset(X1)))
| in(X0,sK7(X1))
| sP1(powerset(X1))
| sP0(powerset(X1))
| ~ in(sK5,powerset(X1)) ),
inference(resolution,[],[f149,f50]) ).
fof(f204,plain,
! [X0,X1] :
( ~ subset(X0,sK3(sK2(powerset(X1))))
| in(X0,sK7(X1))
| ~ sP1(powerset(X1))
| ~ sP0(sK2(powerset(X1))) ),
inference(resolution,[],[f149,f90]) ).
fof(f203,plain,
! [X0,X1] :
( ~ subset(X0,sK3(powerset(X1)))
| in(X0,sK7(X1))
| ~ sP0(powerset(X1)) ),
inference(resolution,[],[f149,f47]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ in(X0,powerset(X1))
| ~ subset(X2,X0)
| in(X2,sK7(X1)) ),
inference(resolution,[],[f148,f53]) ).
fof(f200,plain,
! [X0,X1] :
( ~ in(sK7(X1),sK4(X0))
| ~ sP0(X0)
| ~ subset(sK3(X0),X1) ),
inference(resolution,[],[f143,f58]) ).
fof(f196,plain,
! [X0] :
( ~ in(sK3(X0),sK3(sK4(X0)))
| ~ sP0(sK4(X0))
| ~ sP0(X0) ),
inference(resolution,[],[f98,f58]) ).
fof(f201,plain,
! [X0] :
( ~ subset(sK3(sK7(X0)),X0)
| ~ sP0(sK7(X0)) ),
inference(duplicate_literal_removal,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ~ subset(sK3(sK7(X0)),X0)
| ~ sP0(sK7(X0))
| ~ sP0(sK7(X0)) ),
inference(resolution,[],[f143,f49]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ subset(sK3(X0),X1)
| ~ sP0(X0)
| ~ subset(X2,sK4(X0))
| in(X2,sK7(X1)) ),
inference(resolution,[],[f143,f53]) ).
fof(f143,plain,
! [X0,X1] :
( in(sK4(X0),sK7(X1))
| ~ subset(sK3(X0),X1)
| ~ sP0(X0) ),
inference(resolution,[],[f111,f48]) ).
fof(f197,plain,
! [X0] :
( in(sK3(sK4(powerset(X0))),X0)
| ~ sP0(sK4(powerset(X0)))
| ~ sP0(powerset(X0)) ),
inference(duplicate_literal_removal,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ~ sP0(powerset(X0))
| ~ sP0(sK4(powerset(X0)))
| in(sK3(sK4(powerset(X0))),X0)
| ~ sP0(powerset(X0)) ),
inference(resolution,[],[f98,f88]) ).
fof(f98,plain,
! [X0] :
( in(sK3(sK4(X0)),sK3(X0))
| ~ sP0(X0)
| ~ sP0(sK4(X0)) ),
inference(resolution,[],[f89,f47]) ).
fof(f194,plain,
! [X0,X1] :
( in(sK10(X0,sK3(powerset(X1))),X1)
| ~ sP0(powerset(X1))
| subset(sK10(X0,sK3(powerset(X1))),X0)
| powerset(X0) = sK3(powerset(X1)) ),
inference(resolution,[],[f88,f64]) ).
fof(f193,plain,
! [X0,X1] :
( in(sK9(sK3(powerset(X0)),X1),X0)
| ~ sP0(powerset(X0))
| subset(sK3(powerset(X0)),X1) ),
inference(resolution,[],[f88,f60]) ).
fof(f192,plain,
! [X0] :
( in(sK6(sK3(powerset(X0))),X0)
| ~ sP0(powerset(X0))
| sP1(sK3(powerset(X0)))
| sP0(sK3(powerset(X0)))
| ~ in(sK5,sK3(powerset(X0))) ),
inference(resolution,[],[f88,f50]) ).
fof(f191,plain,
! [X0] :
( in(sK3(sK2(sK3(powerset(X0)))),X0)
| ~ sP0(powerset(X0))
| ~ sP1(sK3(powerset(X0)))
| ~ sP0(sK2(sK3(powerset(X0)))) ),
inference(resolution,[],[f88,f90]) ).
fof(f190,plain,
! [X0] :
( in(sK3(sK3(powerset(X0))),X0)
| ~ sP0(powerset(X0))
| ~ sP0(sK3(powerset(X0))) ),
inference(resolution,[],[f88,f47]) ).
fof(f88,plain,
! [X0,X1] :
( ~ in(X0,sK3(powerset(X1)))
| in(X0,X1)
| ~ sP0(powerset(X1)) ),
inference(resolution,[],[f59,f75]) ).
fof(f65,plain,
! [X0,X1] :
( ~ subset(sK10(X0,X1),X0)
| powerset(X0) = X1
| ~ in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK10(X0,X1),X0)
| ~ in(sK10(X0,X1),X1) )
& ( subset(sK10(X0,X1),X0)
| in(sK10(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f41,f42]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK10(X0,X1),X0)
| ~ in(sK10(X0,X1),X1) )
& ( subset(sK10(X0,X1),X0)
| in(sK10(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f187,plain,
! [X0] :
( ~ subset(powerset(sK6(sK7(X0))),X0)
| ~ in(sK5,sK7(X0))
| sP0(sK7(X0)) ),
inference(resolution,[],[f159,f66]) ).
fof(f159,plain,
! [X0] :
( ~ in(powerset(sK6(sK7(X0))),powerset(X0))
| sP0(sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(subsumption_resolution,[],[f151,f138]) ).
fof(f151,plain,
! [X0] :
( ~ in(powerset(sK6(sK7(X0))),powerset(X0))
| sP1(sK7(X0))
| sP0(sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(resolution,[],[f148,f51]) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(sK7(X1),powerset(X0))
| ~ in(sK7(X0),powerset(X1)) ),
inference(resolution,[],[f155,f148]) ).
fof(f171,plain,
! [X0] :
( ~ subset(sK7(sK6(sK7(X0))),X0)
| sP0(sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(subsumption_resolution,[],[f168,f138]) ).
fof(f168,plain,
! [X0] :
( ~ subset(sK7(sK6(sK7(X0))),X0)
| sP1(sK7(X0))
| sP0(sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(resolution,[],[f147,f51]) ).
fof(f184,plain,
! [X0,X1] :
( ~ in(sK7(X1),sK2(X0))
| ~ sP1(X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f140,f58]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ subset(X2,sK2(X0))
| ~ sP1(X0)
| ~ subset(X0,X1)
| in(X2,sK7(X1)) ),
inference(resolution,[],[f140,f53]) ).
fof(f140,plain,
! [X0,X1] :
( in(sK2(X0),sK7(X1))
| ~ subset(X0,X1)
| ~ sP1(X0) ),
inference(resolution,[],[f111,f44]) ).
fof(f123,plain,
! [X0,X1] :
( ~ subset(sK7(sK8(X0,X1)),X1)
| ~ in(X1,sK7(X0)) ),
inference(resolution,[],[f55,f68]) ).
fof(f157,plain,
! [X0,X1] :
( ~ in(sK7(X0),powerset(X1))
| ~ subset(sK7(X1),X0) ),
inference(resolution,[],[f148,f116]) ).
fof(f180,plain,
! [X2,X0,X1] :
( subset(sK10(X0,sK7(X1)),X0)
| powerset(X0) = sK7(X1)
| ~ subset(X2,sK10(X0,sK7(X1)))
| in(X2,sK7(X1)) ),
inference(resolution,[],[f64,f53]) ).
fof(f179,plain,
! [X0,X1] :
( subset(sK10(X0,sK4(X1)),X0)
| powerset(X0) = sK4(X1)
| in(sK10(X0,sK4(X1)),sK3(X1))
| ~ sP0(X1) ),
inference(resolution,[],[f64,f89]) ).
fof(f178,plain,
! [X0,X1] :
( subset(sK10(X0,sK2(X1)),X0)
| powerset(X0) = sK2(X1)
| in(sK10(X0,sK2(X1)),X1)
| ~ sP1(X1) ),
inference(resolution,[],[f64,f87]) ).
fof(f177,plain,
! [X0,X1] :
( subset(sK10(X0,powerset(X1)),X0)
| powerset(X0) = powerset(X1)
| subset(sK10(X0,powerset(X1)),X1) ),
inference(resolution,[],[f64,f67]) ).
fof(f176,plain,
! [X0,X1] :
( ~ in(X1,sK10(X0,X1))
| powerset(X0) = X1
| subset(sK10(X0,X1),X0) ),
inference(resolution,[],[f64,f58]) ).
fof(f175,plain,
! [X2,X0,X1] :
( in(sK10(X0,X1),X1)
| powerset(X0) = X1
| ~ in(X2,sK10(X0,X1))
| in(X2,X0) ),
inference(resolution,[],[f64,f59]) ).
fof(f174,plain,
! [X2,X0,X1] :
( in(sK10(X0,X1),X1)
| powerset(X0) = X1
| ~ subset(X0,X2)
| in(sK10(X0,X1),sK7(X2)) ),
inference(resolution,[],[f64,f111]) ).
fof(f64,plain,
! [X0,X1] :
( subset(sK10(X0,X1),X0)
| in(sK10(X0,X1),X1)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f156,plain,
! [X0,X1] :
( ~ in(powerset(X0),powerset(X1))
| ~ subset(sK7(X1),X0) ),
inference(resolution,[],[f148,f73]) ).
fof(f153,plain,
! [X0] :
( ~ in(sK4(sK7(X0)),powerset(X0))
| ~ sP0(sK7(X0)) ),
inference(resolution,[],[f148,f49]) ).
fof(f170,plain,
! [X0,X1] :
( ~ subset(sK7(X0),X1)
| ~ in(sK7(X1),powerset(X0)) ),
inference(resolution,[],[f147,f58]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ subset(sK7(X0),X1)
| ~ subset(X2,powerset(X0))
| in(X2,sK7(X1)) ),
inference(resolution,[],[f147,f53]) ).
fof(f147,plain,
! [X0,X1] :
( in(powerset(X0),sK7(X1))
| ~ subset(sK7(X0),X1) ),
inference(resolution,[],[f145,f111]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ in(sK8(X0,X1),powerset(X2))
| ~ subset(sK7(X2),X1)
| ~ in(X1,sK7(X0)) ),
inference(resolution,[],[f155,f55]) ).
fof(f165,plain,
! [X0,X1] :
( ~ in(powerset(X0),powerset(X1))
| ~ subset(sK7(X1),X0) ),
inference(resolution,[],[f155,f66]) ).
fof(f164,plain,
! [X0,X1] :
( ~ in(sK7(X0),powerset(X1))
| ~ subset(sK7(X1),X0) ),
inference(resolution,[],[f155,f105]) ).
fof(f155,plain,
! [X0,X1] :
( ~ in(sK7(X1),X0)
| ~ in(X0,powerset(X1)) ),
inference(resolution,[],[f148,f58]) ).
fof(f154,plain,
! [X0] : ~ in(sK7(sK7(X0)),powerset(X0)),
inference(resolution,[],[f148,f68]) ).
fof(f150,plain,
! [X0] : ~ in(sK7(X0),powerset(X0)),
inference(resolution,[],[f148,f133]) ).
fof(f148,plain,
! [X0,X1] :
( in(X0,sK7(X1))
| ~ in(X0,powerset(X1)) ),
inference(resolution,[],[f145,f59]) ).
fof(f145,plain,
! [X0] : subset(powerset(X0),sK7(X0)),
inference(duplicate_literal_removal,[],[f144]) ).
fof(f144,plain,
! [X0] :
( subset(powerset(X0),sK7(X0))
| subset(powerset(X0),sK7(X0)) ),
inference(resolution,[],[f118,f79]) ).
fof(f118,plain,
! [X0,X1] :
( ~ subset(sK9(X0,sK7(X1)),X1)
| subset(X0,sK7(X1)) ),
inference(resolution,[],[f105,f61]) ).
fof(f142,plain,
! [X2,X0,X1] :
( in(sK9(powerset(X0),X2),sK7(X1))
| ~ subset(X0,X1)
| subset(powerset(X0),X2) ),
inference(resolution,[],[f111,f79]) ).
fof(f141,plain,
! [X0,X1] :
( in(sK3(powerset(X0)),sK7(X1))
| ~ subset(X0,X1)
| ~ sP0(powerset(X0)) ),
inference(resolution,[],[f111,f75]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ subset(X0,X1)
| in(X2,sK7(X1)) ),
inference(resolution,[],[f105,f53]) ).
fof(f138,plain,
! [X0] : ~ sP1(sK7(X0)),
inference(subsumption_resolution,[],[f137,f44]) ).
fof(f137,plain,
! [X0] :
( ~ subset(sK2(sK7(X0)),sK7(X0))
| ~ sP1(sK7(X0)) ),
inference(subsumption_resolution,[],[f136,f46]) ).
fof(f136,plain,
! [X0] :
( in(sK2(sK7(X0)),sK7(X0))
| ~ subset(sK2(sK7(X0)),sK7(X0))
| ~ sP1(sK7(X0)) ),
inference(resolution,[],[f56,f45]) ).
fof(f56,plain,
! [X2,X0] :
( are_equipotent(X2,sK7(X0))
| in(X2,sK7(X0))
| ~ subset(X2,sK7(X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f129,plain,
! [X0,X1] :
( ~ subset(sK7(X1),X0)
| ~ subset(sK7(X0),X1) ),
inference(resolution,[],[f116,f105]) ).
fof(f134,plain,
! [X0] : ~ subset(sK7(X0),X0),
inference(resolution,[],[f133,f105]) ).
fof(f133,plain,
! [X0] : ~ in(sK7(X0),sK7(X0)),
inference(resolution,[],[f127,f57]) ).
fof(f127,plain,
! [X0,X1] :
( ~ subset(sK7(X0),X1)
| ~ in(X1,sK7(X0)) ),
inference(duplicate_literal_removal,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ~ subset(sK7(X0),X1)
| ~ in(X1,sK7(X0))
| ~ in(X1,sK7(X0)) ),
inference(resolution,[],[f55,f94]) ).
fof(f132,plain,
! [X0] : ~ subset(powerset(sK7(X0)),X0),
inference(resolution,[],[f117,f57]) ).
fof(f117,plain,
! [X0,X1] :
( ~ subset(sK7(X1),X0)
| ~ subset(powerset(X0),X1) ),
inference(resolution,[],[f105,f73]) ).
fof(f114,plain,
! [X0] :
( ~ subset(sK4(sK7(X0)),X0)
| ~ sP0(sK7(X0)) ),
inference(resolution,[],[f105,f49]) ).
fof(f113,plain,
! [X0] :
( ~ subset(sK2(sK7(X0)),X0)
| ~ sP1(sK7(X0)) ),
inference(resolution,[],[f105,f46]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ subset(sK8(X0,X1),X2)
| ~ subset(sK7(X2),X1)
| ~ in(X1,sK7(X0)) ),
inference(resolution,[],[f116,f55]) ).
fof(f130,plain,
! [X0,X1] :
( ~ subset(powerset(X0),X1)
| ~ subset(sK7(X1),X0) ),
inference(resolution,[],[f116,f66]) ).
fof(f116,plain,
! [X0,X1] :
( ~ in(sK7(X1),X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f105,f58]) ).
fof(f115,plain,
! [X0] : ~ subset(sK7(sK7(X0)),X0),
inference(resolution,[],[f105,f68]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ subset(sK9(X0,sK8(X1,X2)),X2)
| ~ in(X2,sK7(X1))
| subset(X0,sK8(X1,X2)) ),
inference(resolution,[],[f55,f61]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ subset(sK8(X2,X1),X0)
| ~ in(X1,sK7(X2))
| ~ subset(powerset(X0),X1) ),
inference(resolution,[],[f55,f73]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ in(sK8(X2,X1),X0)
| ~ in(X1,sK7(X2))
| ~ subset(X0,X1) ),
inference(resolution,[],[f55,f58]) ).
fof(f122,plain,
! [X0,X1] :
( ~ subset(sK4(sK8(X0,X1)),X1)
| ~ in(X1,sK7(X0))
| ~ sP0(sK8(X0,X1)) ),
inference(resolution,[],[f55,f49]) ).
fof(f121,plain,
! [X0,X1] :
( ~ subset(sK2(sK8(X0,X1)),X1)
| ~ in(X1,sK7(X0))
| ~ sP1(sK8(X0,X1)) ),
inference(resolution,[],[f55,f46]) ).
fof(f120,plain,
! [X0,X1] :
( ~ subset(powerset(sK6(sK8(X0,X1))),X1)
| ~ in(X1,sK7(X0))
| sP1(sK8(X0,X1))
| sP0(sK8(X0,X1))
| ~ in(sK5,sK8(X0,X1)) ),
inference(resolution,[],[f55,f51]) ).
fof(f55,plain,
! [X3,X0,X5] :
( in(X5,sK8(X0,X3))
| ~ subset(X5,X3)
| ~ in(X3,sK7(X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f112,plain,
! [X0] :
( ~ subset(powerset(sK6(sK7(X0))),X0)
| sP1(sK7(X0))
| sP0(sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(resolution,[],[f105,f51]) ).
fof(f105,plain,
! [X0,X1] :
( in(X0,sK7(X1))
| ~ subset(X0,X1) ),
inference(resolution,[],[f53,f52]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK9(sK7(X1),X2))
| in(X0,sK7(X1))
| subset(sK7(X1),X2) ),
inference(resolution,[],[f53,f60]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK8(X1,X2))
| in(X0,sK7(X1))
| ~ in(X2,sK7(X1)) ),
inference(resolution,[],[f53,f54]) ).
fof(f108,plain,
! [X0,X1] :
( ~ subset(X0,sK6(sK7(X1)))
| in(X0,sK7(X1))
| sP1(sK7(X1))
| sP0(sK7(X1))
| ~ in(sK5,sK7(X1)) ),
inference(resolution,[],[f53,f50]) ).
fof(f107,plain,
! [X0,X1] :
( ~ subset(X0,sK3(sK2(sK7(X1))))
| in(X0,sK7(X1))
| ~ sP1(sK7(X1))
| ~ sP0(sK2(sK7(X1))) ),
inference(resolution,[],[f53,f90]) ).
fof(f53,plain,
! [X0,X6,X7] :
( ~ in(X6,sK7(X0))
| ~ subset(X7,X6)
| in(X7,sK7(X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f101,plain,
! [X0] :
( ~ in(X0,sK3(sK2(X0)))
| ~ sP0(sK2(X0))
| ~ sP1(X0) ),
inference(resolution,[],[f90,f58]) ).
fof(f104,plain,
! [X0] :
( ~ sP1(sK4(X0))
| ~ sP0(sK2(sK4(X0)))
| in(sK3(sK2(sK4(X0))),sK3(X0))
| ~ sP0(X0) ),
inference(resolution,[],[f90,f89]) ).
fof(f103,plain,
! [X0] :
( ~ sP1(sK2(X0))
| ~ sP0(sK2(sK2(X0)))
| in(sK3(sK2(sK2(X0))),X0)
| ~ sP1(X0) ),
inference(resolution,[],[f90,f87]) ).
fof(f102,plain,
! [X0] :
( subset(sK3(sK2(powerset(X0))),X0)
| ~ sP0(sK2(powerset(X0)))
| ~ sP1(powerset(X0)) ),
inference(resolution,[],[f90,f67]) ).
fof(f90,plain,
! [X0] :
( in(sK3(sK2(X0)),X0)
| ~ sP1(X0)
| ~ sP0(sK2(X0)) ),
inference(resolution,[],[f87,f47]) ).
fof(f94,plain,
! [X0,X1] :
( ~ in(sK7(X1),sK8(X1,X0))
| ~ in(X0,sK7(X1)) ),
inference(resolution,[],[f54,f58]) ).
fof(f100,plain,
! [X0,X1] :
( in(sK9(sK4(X0),X1),sK3(X0))
| ~ sP0(X0)
| subset(sK4(X0),X1) ),
inference(resolution,[],[f89,f60]) ).
fof(f99,plain,
! [X0] :
( in(sK6(sK4(X0)),sK3(X0))
| ~ sP0(X0)
| sP1(sK4(X0))
| sP0(sK4(X0))
| ~ in(sK5,sK4(X0)) ),
inference(resolution,[],[f89,f50]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(X0,sK4(X1))
| in(X0,sK3(X1))
| ~ sP0(X1) ),
inference(resolution,[],[f59,f48]) ).
fof(f81,plain,
! [X0,X1] :
( ~ subset(sK9(X0,powerset(X1)),X1)
| subset(X0,powerset(X1)) ),
inference(resolution,[],[f61,f66]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ in(X2,sK9(powerset(X0),X1))
| subset(powerset(X0),X1)
| in(X2,X0) ),
inference(resolution,[],[f79,f59]) ).
fof(f79,plain,
! [X0,X1] :
( subset(sK9(powerset(X0),X1),X0)
| subset(powerset(X0),X1) ),
inference(resolution,[],[f60,f67]) ).
fof(f54,plain,
! [X3,X0] :
( in(sK8(X0,X3),sK7(X0))
| ~ in(X3,sK7(X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f93,plain,
! [X0] :
( ~ subset(powerset(sK6(powerset(X0))),X0)
| sP0(powerset(X0))
| ~ in(sK5,powerset(X0))
| sP1(powerset(X0)) ),
inference(resolution,[],[f51,f66]) ).
fof(f51,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| sP1(X1)
| sP0(X1)
| ~ in(sK5,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1] :
( sP1(X1)
| ( ~ in(powerset(sK6(X1)),X1)
& in(sK6(X1),X1) )
| sP0(X1)
| ~ in(sK5,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f29,f31,f30]) ).
fof(f30,plain,
( ? [X0] :
! [X1] :
( sP1(X1)
| ? [X2] :
( ~ in(powerset(X2),X1)
& in(X2,X1) )
| sP0(X1)
| ~ in(X0,X1) )
=> ! [X1] :
( sP1(X1)
| ? [X2] :
( ~ in(powerset(X2),X1)
& in(X2,X1) )
| sP0(X1)
| ~ in(sK5,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X1] :
( ? [X2] :
( ~ in(powerset(X2),X1)
& in(X2,X1) )
=> ( ~ in(powerset(sK6(X1)),X1)
& in(sK6(X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0] :
! [X1] :
( sP1(X1)
| ? [X2] :
( ~ in(powerset(X2),X1)
& in(X2,X1) )
| sP0(X1)
| ~ in(X0,X1) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
? [X0] :
! [X1] :
( sP1(X1)
| ? [X3] :
( ~ in(powerset(X3),X1)
& in(X3,X1) )
| sP0(X1)
| ~ in(X0,X1) ),
inference(definition_folding,[],[f13,f19,f18]) ).
fof(f18,plain,
! [X1] :
( ? [X4,X5] :
( ~ in(X5,X1)
& subset(X5,X4)
& in(X4,X1) )
| ~ sP0(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f19,plain,
! [X1] :
( ? [X2] :
( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
| ~ sP1(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f13,plain,
? [X0] :
! [X1] :
( ? [X2] :
( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
| ? [X3] :
( ~ in(powerset(X3),X1)
& in(X3,X1) )
| ? [X4,X5] :
( ~ in(X5,X1)
& subset(X5,X4)
& in(X4,X1) )
| ~ in(X0,X1) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
? [X0] :
! [X1] :
( ? [X2] :
( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
| ? [X3] :
( ~ in(powerset(X3),X1)
& in(X3,X1) )
| ? [X4,X5] :
( ~ in(X5,X1)
& subset(X5,X4)
& in(X4,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
~ ! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f92,plain,
! [X0,X1] :
( in(sK9(sK2(X0),X1),X0)
| ~ sP1(X0)
| subset(sK2(X0),X1) ),
inference(resolution,[],[f87,f60]) ).
fof(f91,plain,
! [X0] :
( in(sK6(sK2(X0)),X0)
| ~ sP1(X0)
| sP1(sK2(X0))
| sP0(sK2(X0))
| ~ in(sK5,sK2(X0)) ),
inference(resolution,[],[f87,f50]) ).
fof(f87,plain,
! [X0,X1] :
( ~ in(X0,sK2(X1))
| in(X0,X1)
| ~ sP1(X1) ),
inference(resolution,[],[f59,f44]) ).
fof(f59,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f37,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f84,plain,
! [X0] :
( ~ in(X0,sK6(X0))
| sP0(X0)
| ~ in(sK5,X0)
| sP1(X0) ),
inference(resolution,[],[f50,f58]) ).
fof(f50,plain,
! [X1] :
( in(sK6(X1),X1)
| sP1(X1)
| sP0(X1)
| ~ in(sK5,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f83,plain,
! [X0] : ~ subset(powerset(powerset(X0)),X0),
inference(resolution,[],[f77,f57]) ).
fof(f77,plain,
! [X0,X1] :
( ~ subset(powerset(X1),X0)
| ~ subset(powerset(X0),X1) ),
inference(resolution,[],[f73,f66]) ).
fof(f78,plain,
! [X0,X1] :
( ~ in(X0,sK9(X0,X1))
| subset(X0,X1) ),
inference(resolution,[],[f60,f58]) ).
fof(f75,plain,
! [X0] :
( subset(sK3(powerset(X0)),X0)
| ~ sP0(powerset(X0)) ),
inference(resolution,[],[f67,f47]) ).
fof(f71,plain,
! [X0] :
( ~ subset(sK4(powerset(X0)),X0)
| ~ sP0(powerset(X0)) ),
inference(resolution,[],[f66,f49]) ).
fof(f70,plain,
! [X0] :
( ~ subset(sK2(powerset(X0)),X0)
| ~ sP1(powerset(X0)) ),
inference(resolution,[],[f66,f46]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
! [X0,X1] :
( in(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f73,plain,
! [X0,X1] :
( ~ in(powerset(X1),X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f66,f58]) ).
fof(f67,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f62]) ).
fof(f62,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f72,plain,
! [X0] : ~ subset(sK7(powerset(X0)),X0),
inference(resolution,[],[f66,f68]) ).
fof(f66,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f63]) ).
fof(f63,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f48,plain,
! [X0] :
( subset(sK4(X0),sK3(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ( ~ in(sK4(X0),X0)
& subset(sK4(X0),sK3(X0))
& in(sK3(X0),X0) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f26,f27]) ).
fof(f27,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X0)
& subset(X2,X1)
& in(X1,X0) )
=> ( ~ in(sK4(X0),X0)
& subset(sK4(X0),sK3(X0))
& in(sK3(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X0)
& subset(X2,X1)
& in(X1,X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X1] :
( ? [X4,X5] :
( ~ in(X5,X1)
& subset(X5,X4)
& in(X4,X1) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f18]) ).
fof(f69,plain,
! [X0] :
( ~ in(X0,sK3(X0))
| ~ sP0(X0) ),
inference(resolution,[],[f58,f47]) ).
fof(f68,plain,
! [X0] : ~ in(sK7(X0),X0),
inference(resolution,[],[f58,f52]) ).
fof(f58,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f49,plain,
! [X0] :
( ~ in(sK4(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X0] :
( in(sK3(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X0] :
( ~ in(sK2(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ( ~ in(sK2(X0),X0)
& ~ are_equipotent(sK2(X0),X0)
& subset(sK2(X0),X0) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f23]) ).
fof(f23,plain,
! [X0] :
( ? [X1] :
( ~ in(X1,X0)
& ~ are_equipotent(X1,X0)
& subset(X1,X0) )
=> ( ~ in(sK2(X0),X0)
& ~ are_equipotent(sK2(X0),X0)
& subset(sK2(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0] :
( ? [X1] :
( ~ in(X1,X0)
& ~ are_equipotent(X1,X0)
& subset(X1,X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1] :
( ? [X2] :
( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
| ~ sP1(X1) ),
inference(nnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X0] :
( ~ are_equipotent(sK2(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0] :
( subset(sK2(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f453,plain,
! [X0,X1] :
( ~ subset(X0,sK6(sK7(X1)))
| in(X0,sK7(X1))
| sP0(sK7(X1))
| ~ in(sK5,sK7(X1)) ),
inference(subsumption_resolution,[],[f108,f138]) ).
fof(f499,plain,
! [X0] :
( ~ in(sK6(sK7(X0)),sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(subsumption_resolution,[],[f498,f224]) ).
fof(f498,plain,
! [X0] :
( ~ in(sK6(sK7(X0)),sK7(X0))
| sP0(sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(subsumption_resolution,[],[f495,f138]) ).
fof(f495,plain,
! [X0] :
( ~ in(sK6(sK7(X0)),sK7(X0))
| sP1(sK7(X0))
| sP0(sK7(X0))
| ~ in(sK5,sK7(X0)) ),
inference(resolution,[],[f493,f51]) ).
fof(f493,plain,
! [X0,X1] :
( in(powerset(X0),sK7(X1))
| ~ in(X0,sK7(X1)) ),
inference(duplicate_literal_removal,[],[f488]) ).
fof(f488,plain,
! [X0,X1] :
( ~ in(X0,sK7(X1))
| in(powerset(X0),sK7(X1))
| ~ in(X0,sK7(X1)) ),
inference(resolution,[],[f485,f109]) ).
fof(f485,plain,
! [X0,X1] :
( subset(powerset(X0),sK8(X1,X0))
| ~ in(X0,sK7(X1)) ),
inference(duplicate_literal_removal,[],[f484]) ).
fof(f484,plain,
! [X0,X1] :
( ~ in(X0,sK7(X1))
| subset(powerset(X0),sK8(X1,X0))
| subset(powerset(X0),sK8(X1,X0)) ),
inference(resolution,[],[f126,f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU168+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 21:08:27 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (25551)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (25554)WARNING: value z3 for option sas not known
% 0.14/0.38 % (25556)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (25553)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (25555)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (25558)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (25557)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (25554)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (25552)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [4]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [5]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 % (25554)First to succeed.
% 0.14/0.41 % (25554)Refutation found. Thanks to Tanya!
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41 % (25554)------------------------------
% 0.14/0.41 % (25554)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.41 % (25554)Termination reason: Refutation
% 0.14/0.41
% 0.14/0.41 % (25554)Memory used [KB]: 1072
% 0.14/0.41 % (25554)Time elapsed: 0.026 s
% 0.14/0.41 % (25554)Instructions burned: 44 (million)
% 0.14/0.41 % (25554)------------------------------
% 0.14/0.41 % (25554)------------------------------
% 0.14/0.41 % (25551)Success in time 0.042 s
%------------------------------------------------------------------------------