TSTP Solution File: SEU298+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU298+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 : n027.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 : Sun May 5 09:32:39 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 74
% Syntax : Number of formulae : 400 ( 57 unt; 0 def)
% Number of atoms : 1337 ( 187 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1461 ( 524 ~; 526 |; 341 &)
% ( 23 <=>; 45 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 34 ( 32 usr; 16 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 12 con; 0-3 aty)
% Number of variables : 585 ( 459 !; 126 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f545,plain,
$false,
inference(avatar_sat_refutation,[],[f292,f318,f366,f392,f401,f404,f417,f424,f444,f456,f499,f510,f513,f519,f522,f524,f527,f529,f531,f544]) ).
fof(f544,plain,
( ~ spl34_5
| ~ spl34_7
| ~ spl34_9
| ~ spl34_14 ),
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f543,plain,
( $false
| ~ spl34_5
| ~ spl34_7
| ~ spl34_9
| ~ spl34_14 ),
inference(subsumption_resolution,[],[f542,f361]) ).
fof(f361,plain,
( sP5(sK7,sK6)
| ~ spl34_5 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f359,plain,
( spl34_5
<=> sP5(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_5])]) ).
fof(f542,plain,
( ~ sP5(sK7,sK6)
| ~ spl34_7
| ~ spl34_9
| ~ spl34_14 ),
inference(subsumption_resolution,[],[f541,f411]) ).
fof(f411,plain,
( sP3(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_9 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f410,plain,
( spl34_9
<=> sP3(sK8(sK14(sK7,sK6)),sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_9])]) ).
fof(f541,plain,
( ~ sP3(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ sP5(sK7,sK6)
| ~ spl34_7
| ~ spl34_9
| ~ spl34_14 ),
inference(resolution,[],[f534,f204]) ).
fof(f204,plain,
! [X3,X0,X1] :
( in(X3,sK14(X0,X1))
| ~ sP3(X3,X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK14(X0,X1))
| ~ sP3(X3,X1,X0) )
& ( sP3(X3,X1,X0)
| ~ in(X3,sK14(X0,X1)) ) )
| ~ sP5(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ sP3(X3,X1,X0) )
& ( sP3(X3,X1,X0)
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK14(X0,X1))
| ~ sP3(X3,X1,X0) )
& ( sP3(X3,X1,X0)
| ~ in(X3,sK14(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ sP3(X3,X1,X0) )
& ( sP3(X3,X1,X0)
| ~ in(X3,X2) ) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X1,X0] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ~ sP3(X8,X0,X1) )
& ( sP3(X8,X0,X1)
| ~ in(X8,X7) ) )
| ~ sP5(X1,X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X1,X0] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> sP3(X8,X0,X1) )
| ~ sP5(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f534,plain,
( ~ in(sK8(sK14(sK7,sK6)),sK14(sK7,sK6))
| ~ spl34_7
| ~ spl34_9
| ~ spl34_14 ),
inference(global_subsumption,[],[f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f348,f370,f334,f371,f335,f373,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f387,f408,f407,f368,f446,f447,f448,f449,f411,f460,f458,f372,f469,f470,f471,f472,f473,f474,f475,f466,f477,f374,f505,f462,f498,f459,f525,f532,f516]) ).
fof(f516,plain,
( ~ in(sK8(sK14(sK7,sK6)),sK14(sK7,sK6))
| ~ in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ spl34_14 ),
inference(equality_resolution,[],[f498]) ).
fof(f532,plain,
( ! [X0] :
( sP3(sK8(sK14(sK7,sK6)),sK6,X0)
| ~ in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),X0) )
| ~ spl34_7
| ~ spl34_9 ),
inference(global_subsumption,[],[f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f348,f370,f334,f371,f335,f373,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f387,f408,f407,f368,f446,f447,f448,f449,f411,f460,f458,f372,f469,f470,f471,f472,f473,f474,f475,f466,f477,f374,f505,f462,f459,f525]) ).
fof(f525,plain,
( ! [X0] :
( sP3(sK8(sK14(sK7,sK6)),sK6,X0)
| ~ in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),X0) )
| ~ spl34_9 ),
inference(forward_demodulation,[],[f463,f458]) ).
fof(f463,plain,
( ! [X0] :
( ~ in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),X0)
| sP3(set_difference(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),singleton(sK6)),sK6,X0) )
| ~ spl34_9 ),
inference(superposition,[],[f254,f458]) ).
fof(f459,plain,
( sK8(sK14(sK7,sK6)) = sK18(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_9 ),
inference(resolution,[],[f411,f211]) ).
fof(f498,plain,
( ! [X0] :
( sK8(X0) != sK8(sK14(sK7,sK6))
| ~ in(sK8(X0),X0)
| ~ in(sK8(X0),powerset(sK6)) )
| ~ spl34_14 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f497,plain,
( spl34_14
<=> ! [X0] :
( sK8(X0) != sK8(sK14(sK7,sK6))
| ~ in(sK8(X0),X0)
| ~ in(sK8(X0),powerset(sK6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_14])]) ).
fof(f462,plain,
( ! [X0] :
( sK8(X0) != sK8(sK14(sK7,sK6))
| ~ in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),sK7)
| ~ in(sK8(X0),powerset(sK6))
| ~ in(sK8(X0),X0) )
| ~ spl34_9 ),
inference(superposition,[],[f149,f458]) ).
fof(f505,plain,
! [X2,X0,X1] :
( ~ sP5(X0,X1)
| sK20(sK17(sK14(X0,X1),X2),X2,sK14(X0,X1)) = sK18(sK20(sK17(sK14(X0,X1),X2),X2,sK14(X0,X1)),X1,X0)
| ~ sP4(sK14(X0,X1),X2) ),
inference(resolution,[],[f374,f208]) ).
fof(f374,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X2,X3,sK14(X0,X1))
| ~ sP5(X0,X1)
| sK20(X2,X3,sK14(X0,X1)) = sK18(sK20(X2,X3,sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f335,f211]) ).
fof(f477,plain,
( ! [X0,X1] :
( ~ sP3(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),X1,X0)
| sP3(sK8(sK14(sK7,sK6)),sK6,sK14(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl34_7
| ~ spl34_9 ),
inference(resolution,[],[f466,f204]) ).
fof(f466,plain,
( ! [X0] :
( ~ in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),X0)
| sP3(sK8(sK14(sK7,sK6)),sK6,X0) )
| ~ spl34_7
| ~ spl34_9 ),
inference(forward_demodulation,[],[f465,f458]) ).
fof(f465,plain,
( ! [X0] :
( ~ in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),X0)
| sP3(set_difference(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),singleton(sK6)),sK6,X0) )
| ~ spl34_7
| ~ spl34_9 ),
inference(subsumption_resolution,[],[f463,f460]) ).
fof(f475,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP5(X0,X1)
| sK19(sK21(X2,X3,sK14(sK14(X0,X1),X4)),X4,sK14(X0,X1)) = sK18(sK19(sK21(X2,X3,sK14(sK14(X0,X1),X4)),X4,sK14(X0,X1)),X1,X0)
| ~ sP5(sK14(X0,X1),X4)
| ~ sP1(X2,X3,sK14(sK14(X0,X1),X4)) ),
inference(resolution,[],[f372,f336]) ).
fof(f474,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP5(X0,X1)
| sK19(sK20(X2,X3,sK14(sK14(X0,X1),X4)),X4,sK14(X0,X1)) = sK18(sK19(sK20(X2,X3,sK14(sK14(X0,X1),X4)),X4,sK14(X0,X1)),X1,X0)
| ~ sP5(sK14(X0,X1),X4)
| ~ sP2(X2,X3,sK14(sK14(X0,X1),X4)) ),
inference(resolution,[],[f372,f335]) ).
fof(f473,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP5(X0,X1)
| sK19(sK19(X2,X3,sK14(sK14(X0,X1),X4)),X4,sK14(X0,X1)) = sK18(sK19(sK19(X2,X3,sK14(sK14(X0,X1),X4)),X4,sK14(X0,X1)),X1,X0)
| ~ sP5(sK14(X0,X1),X4)
| ~ sP3(X2,X3,sK14(sK14(X0,X1),X4)) ),
inference(resolution,[],[f372,f334]) ).
fof(f472,plain,
! [X2,X0,X1] :
( ~ sP5(X0,X1)
| sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)) = sK18(sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)),X1,X0)
| ~ sP5(sK14(X0,X1),X2)
| in(sK9(sK14(sK14(X0,X1),X2)),sK7) ),
inference(resolution,[],[f372,f333]) ).
fof(f471,plain,
! [X2,X0,X1] :
( ~ sP5(X0,X1)
| sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)) = sK18(sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)),X1,X0)
| ~ sP5(sK14(X0,X1),X2)
| ~ in(sK7,sK9(sK14(sK14(X0,X1),X2))) ),
inference(resolution,[],[f372,f332]) ).
fof(f470,plain,
! [X2,X0,X1] :
( ~ sP5(X0,X1)
| sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)) = sK18(sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)),X1,X0)
| in(sK8(sK14(sK14(X0,X1),X2)),powerset(sK6))
| ~ sP5(sK14(X0,X1),X2) ),
inference(resolution,[],[f372,f331]) ).
fof(f469,plain,
! [X2,X0,X1] :
( ~ sP5(X0,X1)
| sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)) = sK18(sK19(sK8(sK14(sK14(X0,X1),X2)),X2,sK14(X0,X1)),X1,X0)
| ~ sP5(sK14(X0,X1),X2)
| sK8(sK14(sK14(X0,X1),X2)) = set_difference(sK9(sK14(sK14(X0,X1),X2)),singleton(sK6)) ),
inference(resolution,[],[f372,f330]) ).
fof(f372,plain,
! [X2,X3,X0,X1] :
( ~ sP3(X2,X3,sK14(X0,X1))
| ~ sP5(X0,X1)
| sK19(X2,X3,sK14(X0,X1)) = sK18(sK19(X2,X3,sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f334,f211]) ).
fof(f458,plain,
( sK8(sK14(sK7,sK6)) = set_difference(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),singleton(sK6))
| ~ spl34_9 ),
inference(resolution,[],[f411,f213]) ).
fof(f460,plain,
( in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ spl34_7
| ~ spl34_9 ),
inference(subsumption_resolution,[],[f408,f411]) ).
fof(f449,plain,
! [X0] :
( set_difference(sK9(sK14(sK13(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK13(powerset(succ(X0))),X0))
| sK8(sK14(sK13(powerset(succ(X0))),X0)) = set_difference(sK19(sK8(sK14(sK13(powerset(succ(X0))),X0)),X0,sK13(powerset(succ(X0)))),singleton(X0))
| sP4(sK13(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f368,f354]) ).
fof(f448,plain,
! [X0] :
( set_difference(sK9(sK14(sK12(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK12(powerset(succ(X0))),X0))
| sK8(sK14(sK12(powerset(succ(X0))),X0)) = set_difference(sK19(sK8(sK14(sK12(powerset(succ(X0))),X0)),X0,sK12(powerset(succ(X0)))),singleton(X0))
| sP4(sK12(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f368,f353]) ).
fof(f447,plain,
! [X0] :
( set_difference(sK9(sK14(sK11(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK11(powerset(succ(X0))),X0))
| sK8(sK14(sK11(powerset(succ(X0))),X0)) = set_difference(sK19(sK8(sK14(sK11(powerset(succ(X0))),X0)),X0,sK11(powerset(succ(X0)))),singleton(X0))
| sP4(sK11(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f368,f357]) ).
fof(f446,plain,
! [X0] :
( set_difference(sK9(sK14(sK10(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK10(powerset(succ(X0))),X0))
| sK8(sK14(sK10(powerset(succ(X0))),X0)) = set_difference(sK19(sK8(sK14(sK10(powerset(succ(X0))),X0)),X0,sK10(powerset(succ(X0)))),singleton(X0))
| sP4(sK10(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f368,f356]) ).
fof(f368,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| set_difference(sK9(sK14(X0,X1)),singleton(sK6)) = sK8(sK14(X0,X1))
| sK8(sK14(X0,X1)) = set_difference(sK19(sK8(sK14(X0,X1)),X1,X0),singleton(X1)) ),
inference(resolution,[],[f330,f213]) ).
fof(f407,plain,
( ~ in(powerset(sK6),sK8(sK14(sK7,sK6)))
| ~ sP3(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_7 ),
inference(superposition,[],[f329,f387]) ).
fof(f408,plain,
( in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ sP3(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_7 ),
inference(superposition,[],[f210,f387]) ).
fof(f387,plain,
( sK8(sK14(sK7,sK6)) = sK18(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_7 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f385,plain,
( spl34_7
<=> sK8(sK14(sK7,sK6)) = sK18(sK8(sK14(sK7,sK6)),sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_7])]) ).
fof(f383,plain,
! [X0] :
( set_difference(sK9(sK14(sK13(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK13(powerset(succ(X0))),X0))
| sK8(sK14(sK13(powerset(succ(X0))),X0)) = sK18(sK8(sK14(sK13(powerset(succ(X0))),X0)),X0,sK13(powerset(succ(X0))))
| sP4(sK13(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f369,f354]) ).
fof(f382,plain,
! [X0] :
( set_difference(sK9(sK14(sK12(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK12(powerset(succ(X0))),X0))
| sK8(sK14(sK12(powerset(succ(X0))),X0)) = sK18(sK8(sK14(sK12(powerset(succ(X0))),X0)),X0,sK12(powerset(succ(X0))))
| sP4(sK12(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f369,f353]) ).
fof(f381,plain,
! [X0] :
( set_difference(sK9(sK14(sK11(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK11(powerset(succ(X0))),X0))
| sK8(sK14(sK11(powerset(succ(X0))),X0)) = sK18(sK8(sK14(sK11(powerset(succ(X0))),X0)),X0,sK11(powerset(succ(X0))))
| sP4(sK11(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f369,f357]) ).
fof(f380,plain,
! [X0] :
( set_difference(sK9(sK14(sK10(powerset(succ(X0))),X0)),singleton(sK6)) = sK8(sK14(sK10(powerset(succ(X0))),X0))
| sK8(sK14(sK10(powerset(succ(X0))),X0)) = sK18(sK8(sK14(sK10(powerset(succ(X0))),X0)),X0,sK10(powerset(succ(X0))))
| sP4(sK10(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f369,f356]) ).
fof(f369,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| set_difference(sK9(sK14(X0,X1)),singleton(sK6)) = sK8(sK14(X0,X1))
| sK8(sK14(X0,X1)) = sK18(sK8(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f330,f211]) ).
fof(f378,plain,
! [X0,X1] :
( ~ in(powerset(sK6),sK8(sK14(X0,X1)))
| sK8(sK14(X0,X1)) = set_difference(sK19(sK8(sK14(X0,X1)),X1,X0),singleton(X1))
| ~ sP5(X0,X1) ),
inference(resolution,[],[f347,f201]) ).
fof(f347,plain,
! [X0,X1] :
( in(sK8(sK14(X0,X1)),powerset(sK6))
| ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = set_difference(sK19(sK8(sK14(X0,X1)),X1,X0),singleton(X1)) ),
inference(resolution,[],[f331,f213]) ).
fof(f343,plain,
! [X0,X1] :
( ~ in(sK7,sK9(sK14(X0,X1)))
| ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = set_difference(sK19(sK8(sK14(X0,X1)),X1,X0),singleton(X1)) ),
inference(resolution,[],[f213,f332]) ).
fof(f377,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = set_difference(sK19(sK8(sK14(X0,X1)),X1,X0),singleton(X1))
| ~ in(sK7,sK9(sK14(X0,X1))) ),
inference(resolution,[],[f344,f201]) ).
fof(f344,plain,
! [X0,X1] :
( in(sK9(sK14(X0,X1)),sK7)
| ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = set_difference(sK19(sK8(sK14(X0,X1)),X1,X0),singleton(X1)) ),
inference(resolution,[],[f213,f333]) ).
fof(f340,plain,
! [X2,X3,X0,X1] :
( ~ sP3(sK14(X2,X3),X1,X0)
| ~ sP5(X0,X1)
| ~ sP3(sK14(X0,X1),X3,X2)
| ~ sP5(X2,X3) ),
inference(resolution,[],[f338,f204]) ).
fof(f376,plain,
! [X2,X3,X0,X1] :
( ~ sP5(X0,X1)
| ~ sP1(X2,X3,sK14(X0,X1))
| sK21(X2,X3,sK14(X0,X1)) = sK18(sK21(X2,X3,sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f336,f211]) ).
fof(f375,plain,
! [X2,X3,X0,X1] :
( ~ sP5(X0,X1)
| ~ sP1(X2,X3,sK14(X0,X1))
| sK21(X2,X3,sK14(X0,X1)) = set_difference(sK19(sK21(X2,X3,sK14(X0,X1)),X1,X0),singleton(X1)) ),
inference(resolution,[],[f336,f213]) ).
fof(f336,plain,
! [X2,X3,X0,X1] :
( sP3(sK21(X0,X1,sK14(X2,X3)),X3,X2)
| ~ sP5(X2,X3)
| ~ sP1(X0,X1,sK14(X2,X3)) ),
inference(resolution,[],[f203,f217]) ).
fof(f373,plain,
! [X2,X3,X0,X1] :
( ~ sP5(X0,X1)
| ~ sP2(X2,X3,sK14(X0,X1))
| sK20(X2,X3,sK14(X0,X1)) = set_difference(sK19(sK20(X2,X3,sK14(X0,X1)),X1,X0),singleton(X1)) ),
inference(resolution,[],[f335,f213]) ).
fof(f335,plain,
! [X2,X3,X0,X1] :
( sP3(sK20(X0,X1,sK14(X2,X3)),X3,X2)
| ~ sP5(X2,X3)
| ~ sP2(X0,X1,sK14(X2,X3)) ),
inference(resolution,[],[f203,f215]) ).
fof(f371,plain,
! [X2,X3,X0,X1] :
( ~ sP5(X0,X1)
| ~ sP3(X2,X3,sK14(X0,X1))
| sK19(X2,X3,sK14(X0,X1)) = set_difference(sK19(sK19(X2,X3,sK14(X0,X1)),X1,X0),singleton(X1)) ),
inference(resolution,[],[f334,f213]) ).
fof(f334,plain,
! [X2,X3,X0,X1] :
( sP3(sK19(X0,X1,sK14(X2,X3)),X3,X2)
| ~ sP5(X2,X3)
| ~ sP3(X0,X1,sK14(X2,X3)) ),
inference(resolution,[],[f203,f212]) ).
fof(f370,plain,
! [X0,X1] :
( ~ in(powerset(sK6),sK8(sK14(X0,X1)))
| sK8(sK14(X0,X1)) = sK18(sK8(sK14(X0,X1)),X1,X0)
| ~ sP5(X0,X1) ),
inference(resolution,[],[f348,f201]) ).
fof(f348,plain,
! [X0,X1] :
( in(sK8(sK14(X0,X1)),powerset(sK6))
| ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = sK18(sK8(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f331,f211]) ).
fof(f330,plain,
! [X0,X1] :
( sP3(sK8(sK14(X0,X1)),X1,X0)
| ~ sP5(X0,X1)
| set_difference(sK9(sK14(X0,X1)),singleton(sK6)) = sK8(sK14(X0,X1)) ),
inference(resolution,[],[f203,f148]) ).
fof(f342,plain,
! [X0,X1] :
( ~ in(sK7,sK9(sK14(X0,X1)))
| ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = sK18(sK8(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f332,f211]) ).
fof(f367,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = sK18(sK8(sK14(X0,X1)),X1,X0)
| ~ in(sK7,sK9(sK14(X0,X1))) ),
inference(resolution,[],[f341,f201]) ).
fof(f341,plain,
! [X0,X1] :
( in(sK9(sK14(X0,X1)),sK7)
| ~ sP5(X0,X1)
| sK8(sK14(X0,X1)) = sK18(sK8(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f333,f211]) ).
fof(f346,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| sK16(X0,X1) = set_difference(sK21(sK16(X0,X1),X1,X0),singleton(X1)) ),
inference(resolution,[],[f218,f206]) ).
fof(f345,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| sK17(X0,X1) = set_difference(sK20(sK17(X0,X1),X1,X0),singleton(X1)) ),
inference(resolution,[],[f216,f208]) ).
fof(f254,plain,
! [X2,X1,X4] :
( ~ in(set_difference(X4,singleton(X1)),powerset(X1))
| ~ in(X4,X2)
| sP3(set_difference(X4,singleton(X1)),X1,X2) ),
inference(equality_resolution,[],[f253]) ).
fof(f253,plain,
! [X2,X3,X1,X4] :
( sP3(set_difference(X4,singleton(X1)),X1,X2)
| ~ in(X4,X2)
| set_difference(X4,singleton(X1)) != X3
| ~ in(X3,powerset(X1)) ),
inference(equality_resolution,[],[f214]) ).
fof(f214,plain,
! [X2,X3,X0,X1,X4] :
( sP3(X0,X1,X2)
| set_difference(X4,singleton(X1)) != X0
| ~ in(X4,X2)
| X0 != X3
| ~ in(X3,powerset(X1)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ! [X3] :
( ! [X4] :
( set_difference(X4,singleton(X1)) != X0
| ~ in(X4,X2) )
| X0 != X3
| ~ in(X3,powerset(X1)) ) )
& ( ( set_difference(sK19(X0,X1,X2),singleton(X1)) = X0
& in(sK19(X0,X1,X2),X2)
& sK18(X0,X1,X2) = X0
& in(sK18(X0,X1,X2),powerset(X1)) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f108,f110,f109]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ? [X5] :
( ? [X6] :
( set_difference(X6,singleton(X1)) = X0
& in(X6,X2) )
& X0 = X5
& in(X5,powerset(X1)) )
=> ( ? [X6] :
( set_difference(X6,singleton(X1)) = X0
& in(X6,X2) )
& sK18(X0,X1,X2) = X0
& in(sK18(X0,X1,X2),powerset(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ? [X6] :
( set_difference(X6,singleton(X1)) = X0
& in(X6,X2) )
=> ( set_difference(sK19(X0,X1,X2),singleton(X1)) = X0
& in(sK19(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ! [X3] :
( ! [X4] :
( set_difference(X4,singleton(X1)) != X0
| ~ in(X4,X2) )
| X0 != X3
| ~ in(X3,powerset(X1)) ) )
& ( ? [X5] :
( ? [X6] :
( set_difference(X6,singleton(X1)) = X0
& in(X6,X2) )
& X0 = X5
& in(X5,powerset(X1)) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f107]) ).
fof(f107,plain,
! [X8,X0,X1] :
( ( sP3(X8,X0,X1)
| ! [X9] :
( ! [X10] :
( set_difference(X10,singleton(X0)) != X8
| ~ in(X10,X1) )
| X8 != X9
| ~ in(X9,powerset(X0)) ) )
& ( ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) )
| ~ sP3(X8,X0,X1) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X8,X0,X1] :
( sP3(X8,X0,X1)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f149,plain,
! [X2,X4] :
( set_difference(X4,singleton(sK6)) != sK8(X2)
| ~ in(X4,sK7)
| ~ in(sK8(X2),powerset(sK6))
| ~ in(sK8(X2),X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( ! [X2] :
( ( ! [X4] :
( set_difference(X4,singleton(sK6)) != sK8(X2)
| ~ in(X4,sK7) )
| ~ in(sK8(X2),powerset(sK6))
| ~ in(sK8(X2),X2) )
& ( ( sK8(X2) = set_difference(sK9(X2),singleton(sK6))
& in(sK9(X2),sK7)
& in(sK8(X2),powerset(sK6)) )
| in(sK8(X2),X2) ) )
& element(sK7,powerset(powerset(succ(sK6))))
& ordinal(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f85,f88,f87,f86]) ).
fof(f86,plain,
( ? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(sK6)) != X3
| ~ in(X4,sK7) )
| ~ in(X3,powerset(sK6))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(sK6)) = X3
& in(X5,sK7) )
& in(X3,powerset(sK6)) )
| in(X3,X2) ) )
& element(sK7,powerset(powerset(succ(sK6))))
& ordinal(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X2] :
( ? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(sK6)) != X3
| ~ in(X4,sK7) )
| ~ in(X3,powerset(sK6))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(sK6)) = X3
& in(X5,sK7) )
& in(X3,powerset(sK6)) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( set_difference(X4,singleton(sK6)) != sK8(X2)
| ~ in(X4,sK7) )
| ~ in(sK8(X2),powerset(sK6))
| ~ in(sK8(X2),X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(sK6)) = sK8(X2)
& in(X5,sK7) )
& in(sK8(X2),powerset(sK6)) )
| in(sK8(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X2] :
( ? [X5] :
( set_difference(X5,singleton(sK6)) = sK8(X2)
& in(X5,sK7) )
=> ( sK8(X2) = set_difference(sK9(X2),singleton(sK6))
& in(sK9(X2),sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(rectify,[],[f84]) ).
fof(f84,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| ~ in(X3,X2) )
& ( ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) )
| in(X3,X2) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) )
& element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( set_difference(X4,singleton(X0)) = X3
& in(X4,X1) )
& in(X3,powerset(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(f357,plain,
! [X0] :
( sP5(sK11(powerset(succ(X0))),X0)
| sP4(sK11(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(subsumption_resolution,[],[f352,f151]) ).
fof(f352,plain,
! [X0] :
( sP4(sK11(powerset(succ(X0))),X0)
| sP5(sK11(powerset(succ(X0))),X0)
| ~ ordinal(X0)
| empty(powerset(succ(X0))) ),
inference(resolution,[],[f219,f157]) ).
fof(f356,plain,
! [X0] :
( sP5(sK10(powerset(succ(X0))),X0)
| sP4(sK10(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(subsumption_resolution,[],[f351,f151]) ).
fof(f351,plain,
! [X0] :
( sP4(sK10(powerset(succ(X0))),X0)
| sP5(sK10(powerset(succ(X0))),X0)
| ~ ordinal(X0)
| empty(powerset(succ(X0))) ),
inference(resolution,[],[f219,f155]) ).
fof(f354,plain,
! [X0] :
( sP5(sK13(powerset(succ(X0))),X0)
| sP4(sK13(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f219,f191]) ).
fof(f353,plain,
! [X0] :
( sP5(sK12(powerset(succ(X0))),X0)
| sP4(sK12(powerset(succ(X0))),X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f219,f189]) ).
fof(f355,plain,
( sP4(sK7,sK6)
| sP5(sK7,sK6) ),
inference(subsumption_resolution,[],[f350,f144]) ).
fof(f350,plain,
( sP4(sK7,sK6)
| sP5(sK7,sK6)
| ~ ordinal(sK6) ),
inference(resolution,[],[f219,f145]) ).
fof(f219,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| sP4(X1,X0)
| sP5(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( sP5(X1,X0)
| sP4(X1,X0)
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(definition_folding,[],[f74,f81,f80,f79,f78,f77]) ).
fof(f77,plain,
! [X3,X0,X1] :
( ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
| ~ sP1(X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f78,plain,
! [X4,X0,X1] :
( ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
| ~ sP2(X4,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f80,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& sP2(X4,X0,X1)
& X2 = X4
& sP1(X3,X0,X1)
& X2 = X3 )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
| ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
& X2 = X4
& ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) ) ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( set_difference(X6,singleton(X0)) = X4
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& X3 = X4
& in(X4,powerset(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(f349,plain,
! [X0,X1] :
( ~ in(powerset(sK6),sK8(sK14(X0,X1)))
| ~ sP5(X0,X1)
| sP3(sK8(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f331,f201]) ).
fof(f331,plain,
! [X0,X1] :
( sP3(sK8(sK14(X0,X1)),X1,X0)
| in(sK8(sK14(X0,X1)),powerset(sK6))
| ~ sP5(X0,X1) ),
inference(resolution,[],[f203,f146]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| set_difference(sK21(X0,X1,X2),singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( set_difference(sK21(X0,X1,X2),singleton(X1)) = X0
& in(sK21(X0,X1,X2),X2) )
| ~ sP1(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f117,f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ? [X3] :
( set_difference(X3,singleton(X1)) = X0
& in(X3,X2) )
=> ( set_difference(sK21(X0,X1,X2),singleton(X1)) = X0
& in(sK21(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ? [X3] :
( set_difference(X3,singleton(X1)) = X0
& in(X3,X2) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f116]) ).
fof(f116,plain,
! [X3,X0,X1] :
( ? [X6] :
( set_difference(X6,singleton(X0)) = X3
& in(X6,X1) )
| ~ sP1(X3,X0,X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| set_difference(sK20(X0,X1,X2),singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ( set_difference(sK20(X0,X1,X2),singleton(X1)) = X0
& in(sK20(X0,X1,X2),X2) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f113,f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ? [X3] :
( set_difference(X3,singleton(X1)) = X0
& in(X3,X2) )
=> ( set_difference(sK20(X0,X1,X2),singleton(X1)) = X0
& in(sK20(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ? [X3] :
( set_difference(X3,singleton(X1)) = X0
& in(X3,X2) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f112]) ).
fof(f112,plain,
! [X4,X0,X1] :
( ? [X5] :
( set_difference(X5,singleton(X0)) = X4
& in(X5,X1) )
| ~ sP2(X4,X0,X1) ),
inference(nnf_transformation,[],[f78]) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| set_difference(sK19(X0,X1,X2),singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f111]) ).
fof(f332,plain,
! [X0,X1] :
( sP3(sK8(sK14(X0,X1)),X1,X0)
| ~ sP5(X0,X1)
| ~ in(sK7,sK9(sK14(X0,X1))) ),
inference(resolution,[],[f203,f272]) ).
fof(f333,plain,
! [X0,X1] :
( sP3(sK8(sK14(X0,X1)),X1,X0)
| ~ sP5(X0,X1)
| in(sK9(sK14(X0,X1)),sK7) ),
inference(resolution,[],[f203,f147]) ).
fof(f338,plain,
! [X2,X0,X1] :
( ~ in(sK14(X2,X1),X0)
| ~ sP5(X2,X1)
| ~ sP3(X0,X1,X2) ),
inference(resolution,[],[f204,f201]) ).
fof(f203,plain,
! [X3,X0,X1] :
( ~ in(X3,sK14(X0,X1))
| sP3(X3,X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f329,plain,
! [X2,X0,X1] :
( ~ in(powerset(X1),sK18(X0,X1,X2))
| ~ sP3(X0,X1,X2) ),
inference(resolution,[],[f210,f201]) ).
fof(f328,plain,
! [X2,X0,X1] :
( ~ in(X2,sK21(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(resolution,[],[f217,f201]) ).
fof(f327,plain,
! [X2,X0,X1] :
( ~ in(X2,sK20(X0,X1,X2))
| ~ sP2(X0,X1,X2) ),
inference(resolution,[],[f215,f201]) ).
fof(f326,plain,
! [X2,X0,X1] :
( ~ in(X2,sK19(X0,X1,X2))
| ~ sP3(X0,X1,X2) ),
inference(resolution,[],[f212,f201]) ).
fof(f210,plain,
! [X2,X0,X1] :
( in(sK18(X0,X1,X2),powerset(X1))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f217,plain,
! [X2,X0,X1] :
( in(sK21(X0,X1,X2),X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f215,plain,
! [X2,X0,X1] :
( in(sK20(X0,X1,X2),X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f212,plain,
! [X2,X0,X1] :
( in(sK19(X0,X1,X2),X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| sK18(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f111]) ).
fof(f209,plain,
! [X0,X1] :
( sK16(X0,X1) != sK17(X0,X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( sK16(X0,X1) != sK17(X0,X1)
& sP2(sK17(X0,X1),X1,X0)
& sK15(X0,X1) = sK17(X0,X1)
& sP1(sK16(X0,X1),X1,X0)
& sK15(X0,X1) = sK16(X0,X1) )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f104,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& sP2(X4,X1,X0)
& X2 = X4
& sP1(X3,X1,X0)
& X2 = X3 )
=> ( sK16(X0,X1) != sK17(X0,X1)
& sP2(sK17(X0,X1),X1,X0)
& sK15(X0,X1) = sK17(X0,X1)
& sP1(sK16(X0,X1),X1,X0)
& sK15(X0,X1) = sK16(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& sP2(X4,X1,X0)
& X2 = X4
& sP1(X3,X1,X0)
& X2 = X3 )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f103]) ).
fof(f103,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( X3 != X4
& sP2(X4,X0,X1)
& X2 = X4
& sP1(X3,X0,X1)
& X2 = X3 )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f80]) ).
fof(f207,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| sK15(X0,X1) = sK17(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f205,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| sK15(X0,X1) = sK16(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f325,plain,
! [X0] :
( ~ in(X0,sK8(X0))
| set_difference(sK9(X0),singleton(sK6)) = sK8(X0) ),
inference(resolution,[],[f148,f201]) ).
fof(f148,plain,
! [X2] :
( in(sK8(X2),X2)
| sK8(X2) = set_difference(sK9(X2),singleton(sK6)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f208,plain,
! [X0,X1] :
( sP2(sK17(X0,X1),X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f302,plain,
! [X0] :
( ordinal(sK11(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f175,f157]) ).
fof(f301,plain,
! [X0] :
( ordinal(sK10(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f175,f155]) ).
fof(f324,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| empty(X0)
| ordinal(sK11(X0)) ),
inference(subsumption_resolution,[],[f323,f281]) ).
fof(f323,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| empty(X0)
| ordinal(sK11(X0))
| ~ epsilon_transitive(sK11(X0)) ),
inference(resolution,[],[f296,f182]) ).
fof(f296,plain,
! [X0] :
( epsilon_connected(sK11(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f174,f157]) ).
fof(f322,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| empty(X0)
| ordinal(sK10(X0)) ),
inference(subsumption_resolution,[],[f321,f280]) ).
fof(f321,plain,
! [X0] :
( ~ ordinal(powerset(X0))
| empty(X0)
| ordinal(sK10(X0))
| ~ epsilon_transitive(sK10(X0)) ),
inference(resolution,[],[f295,f182]) ).
fof(f295,plain,
! [X0] :
( epsilon_connected(sK10(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f174,f155]) ).
fof(f281,plain,
! [X0] :
( epsilon_transitive(sK11(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f173,f157]) ).
fof(f280,plain,
! [X0] :
( epsilon_transitive(sK10(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f173,f155]) ).
fof(f306,plain,
! [X0] :
( finite(sK10(X0))
| ~ finite(X0)
| empty(X0) ),
inference(resolution,[],[f160,f155]) ).
fof(f308,plain,
! [X0] :
( finite(sK12(X0))
| ~ finite(X0) ),
inference(resolution,[],[f160,f189]) ).
fof(f305,plain,
( finite(sK7)
| ~ finite(powerset(succ(sK6))) ),
inference(resolution,[],[f160,f145]) ).
fof(f206,plain,
! [X0,X1] :
( sP1(sK16(X0,X1),X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f160,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f175,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) )
| ~ element(X1,X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( element(X1,X0)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f297,plain,
! [X0] :
( epsilon_connected(sK12(X0))
| ~ ordinal(powerset(X0)) ),
inference(resolution,[],[f174,f189]) ).
fof(f174,plain,
! [X0,X1] :
( ~ element(X1,X0)
| epsilon_connected(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f282,plain,
! [X0] :
( epsilon_transitive(sK12(X0))
| ~ ordinal(powerset(X0)) ),
inference(resolution,[],[f173,f189]) ).
fof(f279,plain,
( epsilon_transitive(sK7)
| ~ ordinal(powerset(powerset(succ(sK6)))) ),
inference(resolution,[],[f173,f145]) ).
fof(f173,plain,
! [X0,X1] :
( ~ element(X1,X0)
| epsilon_transitive(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f157,plain,
! [X0] :
( element(sK11(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( finite(sK11(X0))
& ~ empty(sK11(X0))
& element(sK11(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f52,f92]) ).
fof(f92,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK11(X0))
& ~ empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f155,plain,
! [X0] :
( element(sK10(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ~ empty(sK10(X0))
& element(sK10(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f51,f90]) ).
fof(f90,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK10(X0))
& element(sK10(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f276,plain,
! [X0] :
( ~ in(X0,sK8(X0))
| in(sK8(X0),powerset(sK6)) ),
inference(resolution,[],[f146,f201]) ).
fof(f275,plain,
! [X0] :
( ~ in(powerset(sK6),sK8(X0))
| in(sK8(X0),X0) ),
inference(resolution,[],[f146,f201]) ).
fof(f278,plain,
~ in(powerset(sK6),sK8(powerset(sK6))),
inference(resolution,[],[f277,f201]) ).
fof(f277,plain,
in(sK8(powerset(sK6)),powerset(sK6)),
inference(factoring,[],[f146]) ).
fof(f146,plain,
! [X2] :
( in(sK8(X2),powerset(sK6))
| in(sK8(X2),X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f274,plain,
! [X0] :
( ~ in(sK7,sK9(X0))
| ~ in(X0,sK8(X0)) ),
inference(resolution,[],[f272,f201]) ).
fof(f273,plain,
! [X0] :
( ~ in(X0,sK8(X0))
| in(sK9(X0),sK7) ),
inference(resolution,[],[f147,f201]) ).
fof(f272,plain,
! [X0] :
( in(sK8(X0),X0)
| ~ in(sK7,sK9(X0)) ),
inference(resolution,[],[f147,f201]) ).
fof(f147,plain,
! [X2] :
( in(sK9(X2),sK7)
| in(sK8(X2),X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f201,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f200,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_difference(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f188,plain,
! [X0] :
( sP0(X0)
| ~ natural(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( sP0(X0)
| ~ natural(X0)
| ~ ordinal(X0) ),
inference(definition_folding,[],[f68,f75]) ).
fof(f75,plain,
! [X0] :
( ( natural(succ(X0))
& ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f68,plain,
! [X0] :
( ( natural(succ(X0))
& ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ natural(X0)
| ~ ordinal(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( natural(succ(X0))
& ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ natural(X0)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ( natural(X0)
& ordinal(X0) )
=> ( natural(succ(X0))
& ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_arytm_3) ).
fof(f182,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ordinal(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f191,plain,
! [X0] : element(sK13(X0),powerset(X0)),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( finite(sK13(X0))
& natural(sK13(X0))
& ordinal(sK13(X0))
& epsilon_connected(sK13(X0))
& epsilon_transitive(sK13(X0))
& function(sK13(X0))
& relation(sK13(X0))
& empty(sK13(X0))
& element(sK13(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f45,f97]) ).
fof(f97,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK13(X0))
& natural(sK13(X0))
& ordinal(sK13(X0))
& epsilon_connected(sK13(X0))
& epsilon_transitive(sK13(X0))
& function(sK13(X0))
& relation(sK13(X0))
& empty(sK13(X0))
& element(sK13(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f3]) ).
fof(f3,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f189,plain,
! [X0] : element(sK12(X0),powerset(X0)),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( empty(sK12(X0))
& element(sK12(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f27,f95]) ).
fof(f95,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK12(X0))
& element(sK12(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f187,plain,
! [X0] :
( natural(succ(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ( natural(succ(X0))
& ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f186,plain,
! [X0] :
( ordinal(succ(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f185,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f172,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f171,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f170,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f159,plain,
! [X0] :
( finite(sK11(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f158,plain,
! [X0] :
( ~ empty(sK11(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f156,plain,
! [X0] :
( ~ empty(sK10(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f145,plain,
element(sK7,powerset(powerset(succ(sK6)))),
inference(cnf_transformation,[],[f89]) ).
fof(f256,plain,
! [X0] :
( natural(X0)
| ~ empty(X0) ),
inference(global_subsumption,[],[f149,f148,f147,f146,f145,f144,f150,f151,f152,f154,f153,f156,f155,f159,f158,f157,f160,f162,f166,f165,f164,f172,f171,f170,f169,f255,f175,f174,f173,f179]) ).
fof(f258,plain,
! [X0] : ordinal(sK12(X0)),
inference(resolution,[],[f166,f190]) ).
fof(f263,plain,
ordinal(sK32),
inference(resolution,[],[f166,f248]) ).
fof(f261,plain,
ordinal(sK28),
inference(resolution,[],[f166,f235]) ).
fof(f260,plain,
ordinal(sK23),
inference(resolution,[],[f166,f221]) ).
fof(f166,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f165,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f164,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f162,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f199,plain,
! [X0] : finite(sK13(X0)),
inference(cnf_transformation,[],[f98]) ).
fof(f198,plain,
! [X0] : natural(sK13(X0)),
inference(cnf_transformation,[],[f98]) ).
fof(f197,plain,
! [X0] : ordinal(sK13(X0)),
inference(cnf_transformation,[],[f98]) ).
fof(f196,plain,
! [X0] : epsilon_connected(sK13(X0)),
inference(cnf_transformation,[],[f98]) ).
fof(f195,plain,
! [X0] : epsilon_transitive(sK13(X0)),
inference(cnf_transformation,[],[f98]) ).
fof(f192,plain,
! [X0] : empty(sK13(X0)),
inference(cnf_transformation,[],[f98]) ).
fof(f190,plain,
! [X0] : empty(sK12(X0)),
inference(cnf_transformation,[],[f96]) ).
fof(f154,plain,
! [X0] : finite(singleton(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( finite(singleton(X0))
& ~ empty(singleton(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
fof(f152,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f151,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f150,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f252,plain,
ordinal(sK33),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ordinal(sK33)
& epsilon_connected(sK33)
& epsilon_transitive(sK33) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f23,f142]) ).
fof(f142,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK33)
& epsilon_connected(sK33)
& epsilon_transitive(sK33) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f251,plain,
epsilon_connected(sK33),
inference(cnf_transformation,[],[f143]) ).
fof(f250,plain,
epsilon_transitive(sK33),
inference(cnf_transformation,[],[f143]) ).
fof(f248,plain,
empty(sK32),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( function(sK32)
& empty(sK32)
& relation(sK32) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f7,f140]) ).
fof(f140,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK32)
& empty(sK32)
& relation(sK32) ) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f246,plain,
ordinal(sK31),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( ordinal(sK31)
& epsilon_connected(sK31)
& epsilon_transitive(sK31)
& empty(sK31)
& function(sK31)
& relation(sK31) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f48,f138]) ).
fof(f138,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK31)
& epsilon_connected(sK31)
& epsilon_transitive(sK31)
& empty(sK31)
& function(sK31)
& relation(sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f5,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f245,plain,
epsilon_connected(sK31),
inference(cnf_transformation,[],[f139]) ).
fof(f244,plain,
epsilon_transitive(sK31),
inference(cnf_transformation,[],[f139]) ).
fof(f243,plain,
empty(sK31),
inference(cnf_transformation,[],[f139]) ).
fof(f235,plain,
empty(sK28),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( relation(sK28)
& empty(sK28) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f9,f132]) ).
fof(f132,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK28)
& empty(sK28) ) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f234,plain,
natural(sK27),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( natural(sK27)
& ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& ~ empty(sK27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f12,f130]) ).
fof(f130,plain,
( ? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( natural(sK27)
& ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& ~ empty(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f12,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f233,plain,
ordinal(sK27),
inference(cnf_transformation,[],[f131]) ).
fof(f232,plain,
epsilon_connected(sK27),
inference(cnf_transformation,[],[f131]) ).
fof(f231,plain,
epsilon_transitive(sK27),
inference(cnf_transformation,[],[f131]) ).
fof(f230,plain,
~ empty(sK27),
inference(cnf_transformation,[],[f131]) ).
fof(f229,plain,
ordinal(sK26),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& ~ empty(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f25,f128]) ).
fof(f128,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& ~ empty(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f228,plain,
epsilon_connected(sK26),
inference(cnf_transformation,[],[f129]) ).
fof(f227,plain,
epsilon_transitive(sK26),
inference(cnf_transformation,[],[f129]) ).
fof(f226,plain,
~ empty(sK26),
inference(cnf_transformation,[],[f129]) ).
fof(f224,plain,
~ empty(sK25),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
( relation(sK25)
& ~ empty(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f11,f126]) ).
fof(f126,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK25)
& ~ empty(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f11,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f223,plain,
finite(sK24),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
( finite(sK24)
& ~ empty(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f14,f124]) ).
fof(f124,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK24)
& ~ empty(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f14,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f222,plain,
~ empty(sK24),
inference(cnf_transformation,[],[f125]) ).
fof(f221,plain,
empty(sK23),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
empty(sK23),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f28,f122]) ).
fof(f122,plain,
( ? [X0] : empty(X0)
=> empty(sK23) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f220,plain,
~ empty(sK22),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
~ empty(sK22),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f29,f120]) ).
fof(f120,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK22) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f144,plain,
ordinal(sK6),
inference(cnf_transformation,[],[f89]) ).
fof(f257,plain,
! [X0] : ~ empty(succ(X0)),
inference(global_subsumption,[],[f149,f148,f147,f146,f145,f144,f150,f151,f152,f154,f153,f156,f155,f159,f158,f157,f160,f162,f166,f165,f164,f172,f171,f170,f169,f255,f175,f174,f173,f179,f256,f182,f187,f186,f185,f184,f183]) ).
fof(f183,plain,
! [X0] :
( ~ empty(succ(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f179,plain,
! [X0] :
( natural(X0)
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( ordinal(X0)
& empty(X0) )
=> ( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_arytm_3) ).
fof(f255,plain,
! [X0] : ~ empty(succ(X0)),
inference(global_subsumption,[],[f149,f148,f147,f146,f145,f144,f150,f151,f152,f154,f153,f156,f155,f159,f158,f157,f160,f162,f166,f165,f164,f172,f171,f170,f169]) ).
fof(f169,plain,
! [X0] :
( ~ empty(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f153,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f531,plain,
( spl34_7
| ~ spl34_9 ),
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f530,plain,
( $false
| spl34_7
| ~ spl34_9 ),
inference(global_subsumption,[],[f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f348,f370,f334,f371,f335,f373,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f368,f446,f447,f448,f449,f411,f458,f372,f469,f470,f471,f472,f473,f474,f475,f374,f505,f462,f525,f459,f386]) ).
fof(f386,plain,
( sK8(sK14(sK7,sK6)) != sK18(sK8(sK14(sK7,sK6)),sK6,sK7)
| spl34_7 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f529,plain,
( spl34_7
| ~ spl34_9 ),
inference(avatar_contradiction_clause,[],[f528]) ).
fof(f528,plain,
( $false
| spl34_7
| ~ spl34_9 ),
inference(global_subsumption,[],[f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f348,f370,f334,f371,f335,f373,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f386,f368,f446,f447,f448,f449,f411,f458,f372,f469,f470,f471,f472,f473,f474,f475,f374,f505,f462,f525,f459]) ).
fof(f527,plain,
( ~ spl34_5
| spl34_7
| ~ spl34_9
| spl34_13 ),
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f526,plain,
( $false
| ~ spl34_5
| spl34_7
| ~ spl34_9
| spl34_13 ),
inference(global_subsumption,[],[f525,f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f348,f370,f334,f371,f335,f373,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f379,f386,f361,f405,f368,f446,f447,f448,f449,f372,f469,f470,f471,f472,f473,f474,f475,f495,f502,f504,f374,f505,f520]) ).
fof(f520,plain,
( sK8(sK14(sK7,sK6)) = sK18(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_5
| spl34_13 ),
inference(subsumption_resolution,[],[f501,f361]) ).
fof(f501,plain,
( ~ sP5(sK7,sK6)
| sK8(sK14(sK7,sK6)) = sK18(sK8(sK14(sK7,sK6)),sK6,sK7)
| spl34_13 ),
inference(resolution,[],[f495,f341]) ).
fof(f504,plain,
( ~ in(sK14(sK7,sK6),sK8(sK14(sK7,sK6)))
| spl34_13 ),
inference(resolution,[],[f502,f201]) ).
fof(f502,plain,
( in(sK8(sK14(sK7,sK6)),sK14(sK7,sK6))
| spl34_13 ),
inference(resolution,[],[f495,f147]) ).
fof(f495,plain,
( ~ in(sK9(sK14(sK7,sK6)),sK7)
| spl34_13 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f493,plain,
( spl34_13
<=> in(sK9(sK14(sK7,sK6)),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_13])]) ).
fof(f405,plain,
( set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)) = sK8(sK14(sK7,sK6))
| sK8(sK14(sK7,sK6)) = sK18(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_5 ),
inference(resolution,[],[f361,f369]) ).
fof(f379,plain,
( set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)) = sK8(sK14(sK7,sK6))
| sK8(sK14(sK7,sK6)) = sK18(sK8(sK14(sK7,sK6)),sK6,sK7)
| ~ spl34_5 ),
inference(resolution,[],[f369,f361]) ).
fof(f524,plain,
( ~ spl34_5
| spl34_7
| ~ spl34_8
| spl34_13 ),
inference(avatar_contradiction_clause,[],[f523]) ).
fof(f523,plain,
( $false
| ~ spl34_5
| spl34_7
| ~ spl34_8
| spl34_13 ),
inference(global_subsumption,[],[f457,f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f348,f370,f334,f371,f335,f373,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f379,f386,f361,f405,f368,f446,f447,f448,f449,f372,f469,f470,f471,f472,f473,f474,f475,f495,f502,f504,f374,f505,f520]) ).
fof(f457,plain,
( ! [X0] :
( sP3(sK8(sK14(sK7,sK6)),sK6,X0)
| ~ in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ in(sK9(sK14(sK7,sK6)),X0) )
| ~ spl34_8 ),
inference(forward_demodulation,[],[f431,f391]) ).
fof(f391,plain,
( set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)) = sK8(sK14(sK7,sK6))
| ~ spl34_8 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f389,plain,
( spl34_8
<=> set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)) = sK8(sK14(sK7,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_8])]) ).
fof(f431,plain,
( ! [X0] :
( ~ in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ in(sK9(sK14(sK7,sK6)),X0)
| sP3(set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)),sK6,X0) )
| ~ spl34_8 ),
inference(superposition,[],[f254,f391]) ).
fof(f522,plain,
( ~ spl34_5
| spl34_7
| spl34_13 ),
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f521,plain,
( $false
| ~ spl34_5
| spl34_7
| spl34_13 ),
inference(global_subsumption,[],[f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f348,f370,f334,f371,f335,f373,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f379,f386,f361,f405,f368,f446,f447,f448,f449,f372,f469,f470,f471,f472,f473,f474,f475,f495,f502,f504,f374,f505,f520]) ).
fof(f519,plain,
( ~ spl34_7
| ~ spl34_9
| spl34_13
| ~ spl34_14 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f518,plain,
( $false
| ~ spl34_7
| ~ spl34_9
| spl34_13
| ~ spl34_14 ),
inference(subsumption_resolution,[],[f517,f460]) ).
fof(f517,plain,
( ~ in(sK8(sK14(sK7,sK6)),powerset(sK6))
| spl34_13
| ~ spl34_14 ),
inference(subsumption_resolution,[],[f516,f502]) ).
fof(f513,plain,
( ~ spl34_9
| spl34_15 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f512,plain,
( $false
| ~ spl34_9
| spl34_15 ),
inference(subsumption_resolution,[],[f511,f411]) ).
fof(f511,plain,
( ~ sP3(sK8(sK14(sK7,sK6)),sK6,sK7)
| spl34_15 ),
inference(resolution,[],[f509,f212]) ).
fof(f509,plain,
( ~ in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),sK7)
| spl34_15 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f507,plain,
( spl34_15
<=> in(sK19(sK8(sK14(sK7,sK6)),sK6,sK7),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_15])]) ).
fof(f510,plain,
( ~ spl34_15
| spl34_14
| ~ spl34_9 ),
inference(avatar_split_clause,[],[f462,f410,f497,f507]) ).
fof(f499,plain,
( ~ spl34_13
| spl34_14
| ~ spl34_8 ),
inference(avatar_split_clause,[],[f430,f389,f497,f493]) ).
fof(f430,plain,
( ! [X0] :
( sK8(X0) != sK8(sK14(sK7,sK6))
| ~ in(sK9(sK14(sK7,sK6)),sK7)
| ~ in(sK8(X0),powerset(sK6))
| ~ in(sK8(X0),X0) )
| ~ spl34_8 ),
inference(superposition,[],[f149,f391]) ).
fof(f456,plain,
( ~ spl34_5
| ~ spl34_8
| spl34_9 ),
inference(avatar_contradiction_clause,[],[f455]) ).
fof(f455,plain,
( $false
| ~ spl34_5
| ~ spl34_8
| spl34_9 ),
inference(subsumption_resolution,[],[f452,f427]) ).
fof(f427,plain,
( in(sK9(sK14(sK7,sK6)),sK7)
| ~ spl34_5
| spl34_9 ),
inference(subsumption_resolution,[],[f421,f361]) ).
fof(f421,plain,
( ~ sP5(sK7,sK6)
| in(sK9(sK14(sK7,sK6)),sK7)
| spl34_9 ),
inference(resolution,[],[f412,f333]) ).
fof(f412,plain,
( ~ sP3(sK8(sK14(sK7,sK6)),sK6,sK7)
| spl34_9 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f452,plain,
( ~ in(sK9(sK14(sK7,sK6)),sK7)
| ~ spl34_5
| ~ spl34_8
| spl34_9 ),
inference(resolution,[],[f435,f412]) ).
fof(f435,plain,
( ! [X0] :
( sP3(sK8(sK14(sK7,sK6)),sK6,X0)
| ~ in(sK9(sK14(sK7,sK6)),X0) )
| ~ spl34_5
| ~ spl34_8
| spl34_9 ),
inference(forward_demodulation,[],[f434,f391]) ).
fof(f434,plain,
( ! [X0] :
( ~ in(sK9(sK14(sK7,sK6)),X0)
| sP3(set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)),sK6,X0) )
| ~ spl34_5
| ~ spl34_8
| spl34_9 ),
inference(subsumption_resolution,[],[f431,f425]) ).
fof(f425,plain,
( in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ spl34_5
| spl34_9 ),
inference(subsumption_resolution,[],[f419,f361]) ).
fof(f419,plain,
( in(sK8(sK14(sK7,sK6)),powerset(sK6))
| ~ sP5(sK7,sK6)
| spl34_9 ),
inference(resolution,[],[f412,f331]) ).
fof(f444,plain,
( ~ spl34_11
| spl34_12
| ~ spl34_8 ),
inference(avatar_split_clause,[],[f432,f389,f441,f437]) ).
fof(f437,plain,
( spl34_11
<=> finite(sK9(sK14(sK7,sK6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_11])]) ).
fof(f441,plain,
( spl34_12
<=> finite(sK8(sK14(sK7,sK6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_12])]) ).
fof(f432,plain,
( finite(sK8(sK14(sK7,sK6)))
| ~ finite(sK9(sK14(sK7,sK6)))
| ~ spl34_8 ),
inference(superposition,[],[f200,f391]) ).
fof(f424,plain,
( ~ spl34_5
| spl34_8
| spl34_9 ),
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f423,plain,
( $false
| ~ spl34_5
| spl34_8
| spl34_9 ),
inference(subsumption_resolution,[],[f422,f390]) ).
fof(f390,plain,
( set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)) != sK8(sK14(sK7,sK6))
| spl34_8 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f422,plain,
( set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)) = sK8(sK14(sK7,sK6))
| ~ spl34_5
| spl34_9 ),
inference(subsumption_resolution,[],[f418,f361]) ).
fof(f418,plain,
( ~ sP5(sK7,sK6)
| set_difference(sK9(sK14(sK7,sK6)),singleton(sK6)) = sK8(sK14(sK7,sK6))
| spl34_9 ),
inference(resolution,[],[f412,f330]) ).
fof(f417,plain,
( ~ spl34_9
| ~ spl34_10
| ~ spl34_7 ),
inference(avatar_split_clause,[],[f407,f385,f414,f410]) ).
fof(f414,plain,
( spl34_10
<=> in(powerset(sK6),sK8(sK14(sK7,sK6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_10])]) ).
fof(f404,plain,
~ spl34_6,
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f403,plain,
( $false
| ~ spl34_6 ),
inference(global_subsumption,[],[f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f368,f348,f370,f334,f371,f372,f335,f373,f374,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f365,f393,f394,f396,f395,f399,f402]) ).
fof(f402,plain,
( sP2(sK15(sK7,sK6),sK6,sK7)
| ~ spl34_6 ),
inference(subsumption_resolution,[],[f398,f365]) ).
fof(f398,plain,
( sP2(sK15(sK7,sK6),sK6,sK7)
| ~ sP4(sK7,sK6)
| ~ spl34_6 ),
inference(superposition,[],[f208,f395]) ).
fof(f399,plain,
( sK16(sK7,sK6) != sK15(sK7,sK6)
| ~ spl34_6 ),
inference(subsumption_resolution,[],[f397,f365]) ).
fof(f397,plain,
( sK16(sK7,sK6) != sK15(sK7,sK6)
| ~ sP4(sK7,sK6)
| ~ spl34_6 ),
inference(superposition,[],[f209,f395]) ).
fof(f395,plain,
( sK17(sK7,sK6) = sK15(sK7,sK6)
| ~ spl34_6 ),
inference(resolution,[],[f365,f207]) ).
fof(f396,plain,
( sK16(sK7,sK6) = sK15(sK7,sK6)
| ~ spl34_6 ),
inference(resolution,[],[f365,f205]) ).
fof(f394,plain,
( sK17(sK7,sK6) = set_difference(sK20(sK17(sK7,sK6),sK6,sK7),singleton(sK6))
| ~ spl34_6 ),
inference(resolution,[],[f365,f345]) ).
fof(f393,plain,
( sK16(sK7,sK6) = set_difference(sK21(sK16(sK7,sK6),sK6,sK7),singleton(sK6))
| ~ spl34_6 ),
inference(resolution,[],[f365,f346]) ).
fof(f365,plain,
( sP4(sK7,sK6)
| ~ spl34_6 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f363,plain,
( spl34_6
<=> sP4(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_6])]) ).
fof(f401,plain,
~ spl34_6,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f400,plain,
( $false
| ~ spl34_6 ),
inference(global_subsumption,[],[f153,f169,f255,f179,f183,f257,f144,f220,f221,f222,f223,f224,f226,f227,f228,f229,f230,f231,f232,f233,f234,f235,f243,f244,f245,f246,f248,f250,f251,f252,f150,f151,f152,f154,f190,f192,f195,f196,f197,f198,f199,f162,f164,f165,f166,f260,f261,f263,f258,f256,f145,f156,f158,f159,f170,f171,f172,f184,f185,f186,f187,f189,f191,f182,f188,f200,f201,f147,f272,f273,f274,f146,f277,f278,f275,f276,f155,f157,f173,f279,f282,f174,f297,f175,f160,f206,f305,f308,f306,f280,f281,f295,f322,f296,f324,f301,f302,f208,f148,f325,f205,f207,f209,f211,f212,f215,f217,f210,f326,f327,f328,f329,f203,f204,f338,f333,f332,f213,f216,f218,f331,f349,f219,f355,f353,f354,f356,f357,f149,f254,f345,f346,f341,f367,f342,f330,f368,f348,f370,f334,f371,f372,f335,f373,f374,f336,f375,f376,f340,f344,f377,f343,f347,f378,f369,f380,f381,f382,f383,f365,f393,f394,f396,f395,f399]) ).
fof(f392,plain,
( spl34_7
| spl34_8
| ~ spl34_5 ),
inference(avatar_split_clause,[],[f379,f359,f389,f385]) ).
fof(f366,plain,
( spl34_5
| spl34_6 ),
inference(avatar_split_clause,[],[f355,f363,f359]) ).
fof(f318,plain,
( ~ spl34_3
| spl34_4 ),
inference(avatar_split_clause,[],[f305,f315,f311]) ).
fof(f311,plain,
( spl34_3
<=> finite(powerset(succ(sK6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_3])]) ).
fof(f315,plain,
( spl34_4
<=> finite(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_4])]) ).
fof(f292,plain,
( ~ spl34_1
| spl34_2 ),
inference(avatar_split_clause,[],[f279,f289,f285]) ).
fof(f285,plain,
( spl34_1
<=> ordinal(powerset(powerset(succ(sK6)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_1])]) ).
fof(f289,plain,
( spl34_2
<=> epsilon_transitive(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_2])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU298+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 12:00:06 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (29504)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (29507)WARNING: value z3 for option sas not known
% 0.15/0.38 % (29505)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (29508)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (29507)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)
% 0.15/0.38 % (29506)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (29509)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)
% 0.15/0.38 % (29511)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)
% 0.15/0.38 % (29510)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.40 % (29507)First to succeed.
% 0.22/0.41 % (29507)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29504"
% 0.22/0.41 % (29507)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (29507)------------------------------
% 0.22/0.41 % (29507)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41 % (29507)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (29507)Memory used [KB]: 1116
% 0.22/0.41 % (29507)Time elapsed: 0.028 s
% 0.22/0.41 % (29507)Instructions burned: 41 (million)
% 0.22/0.41 % (29504)Success in time 0.045 s
%------------------------------------------------------------------------------