TSTP Solution File: NUM404+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 08:26:30 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 54
% Syntax : Number of formulae : 312 ( 51 unt; 0 def)
% Number of atoms : 930 ( 76 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 975 ( 357 ~; 420 |; 152 &)
% ( 19 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 9 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 376 ( 342 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f486,plain,
$false,
inference(avatar_sat_refutation,[],[f229,f246,f260,f375,f456,f480,f483,f485]) ).
fof(f485,plain,
( ~ spl19_4
| ~ spl19_6 ),
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f484,plain,
( $false
| ~ spl19_4
| ~ spl19_6 ),
inference(global_subsumption,[],[f128,f130,f134,f161,f160,f159,f127,f135,f136,f137,f177,f178,f179,f180,f181,f182,f183,f185,f186,f187,f188,f201,f202,f203,f204,f206,f163,f125,f126,f138,f139,f144,f145,f146,f162,f143,f210,f211,f174,f212,f213,f216,f147,f151,f236,f152,f154,f250,f155,f166,f266,f167,f267,f268,f156,f269,f157,f158,f164,f171,f276,f172,f173,f277,f150,f165,f294,f169,f298,f297,f300,f299,f292,f302,f301,f170,f308,f311,f296,f168,f316,f288,f317,f289,f318,f290,f319,f314,f320,f321,f322,f323,f324,f176,f327,f325,f330,f328,f329,f331,f335,f334,f175,f338,f339,f332,f336,f342,f347,f348,f349,f350,f341,f361,f362,f366,f360,f140,f416,f379,f417,f386,f423,f392,f424,f396,f425,f403,f429,f431,f409,f326,f437,f438,f439,f337,f444,f445,f446,f447,f448,f449,f450,f421,f263,f259,f153,f467,f468,f469,f462,f470,f466,f453,f472,f295,f474,f477,f457,f271,f245]) ).
fof(f245,plain,
( epsilon_transitive(sK0)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f243,plain,
( spl19_4
<=> epsilon_transitive(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
fof(f271,plain,
~ ordinal(sK0),
inference(duplicate_literal_removal,[],[f270]) ).
fof(f270,plain,
( ~ ordinal(sK0)
| ~ ordinal(sK0) ),
inference(resolution,[],[f266,f126]) ).
fof(f457,plain,
( ordinal(sK0)
| ~ epsilon_transitive(sK0)
| ~ spl19_6 ),
inference(resolution,[],[f259,f147]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ in(X1,X0)
| in(X1,sK0) ),
inference(resolution,[],[f474,f168]) ).
fof(f474,plain,
! [X0] :
( subset(X0,sK0)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f473]) ).
fof(f473,plain,
! [X0] :
( subset(X0,sK0)
| ~ ordinal(X0)
| subset(X0,sK0) ),
inference(resolution,[],[f295,f308]) ).
fof(f295,plain,
! [X0,X1] :
( ordinal(sK5(X0,X1))
| subset(X0,X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f169,f164]) ).
fof(f472,plain,
! [X0] :
( ~ empty(sK3(X0))
| epsilon_connected(X0)
| ~ empty(sK2(X0)) ),
inference(resolution,[],[f453,f146]) ).
fof(f453,plain,
! [X0] :
( ~ ordinal(sK2(X0))
| epsilon_connected(X0)
| ~ empty(sK3(X0)) ),
inference(resolution,[],[f421,f146]) ).
fof(f466,plain,
! [X2,X0,X1] :
( sK5(X1,X2) = X0
| in(X0,sK5(X1,X2))
| in(sK5(X1,X2),X0)
| ~ in(X0,X1)
| ~ epsilon_connected(X1)
| subset(X1,X2) ),
inference(resolution,[],[f153,f169]) ).
fof(f470,plain,
! [X0,X1] :
( sK4(X1) = X0
| in(X0,sK4(X1))
| in(sK4(X1),X0)
| ~ in(X0,X1)
| ~ epsilon_connected(X1) ),
inference(subsumption_resolution,[],[f465,f174]) ).
fof(f465,plain,
! [X0,X1] :
( sK4(X1) = X0
| in(X0,sK4(X1))
| in(sK4(X1),X0)
| ~ in(X0,X1)
| ~ epsilon_connected(X1)
| empty(X1) ),
inference(resolution,[],[f153,f292]) ).
fof(f462,plain,
! [X0,X1] :
( sK1(X1) = X0
| in(X0,sK1(X1))
| in(sK1(X1),X0)
| ~ in(X0,X1)
| ~ epsilon_connected(X1)
| epsilon_transitive(X1) ),
inference(resolution,[],[f153,f151]) ).
fof(f469,plain,
! [X2,X0,X1] :
( X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ in(X0,X2)
| in(X2,X1)
| X1 = X2
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(subsumption_resolution,[],[f460,f139]) ).
fof(f460,plain,
! [X2,X0,X1] :
( X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ in(X0,X2)
| ~ epsilon_connected(X2)
| in(X2,X1)
| X1 = X2
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(resolution,[],[f153,f140]) ).
fof(f468,plain,
! [X2,X0,X1] :
( X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ in(X0,X2)
| in(X2,X1)
| X1 = X2
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(subsumption_resolution,[],[f459,f139]) ).
fof(f459,plain,
! [X2,X0,X1] :
( X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ in(X0,X2)
| ~ epsilon_connected(X2)
| in(X2,X1)
| X1 = X2
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(resolution,[],[f153,f140]) ).
fof(f467,plain,
( ! [X0,X1] :
( X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ in(X0,sK0)
| ~ ordinal(X1) )
| ~ spl19_6 ),
inference(subsumption_resolution,[],[f458,f259]) ).
fof(f458,plain,
! [X0,X1] :
( X0 = X1
| in(X0,X1)
| in(X1,X0)
| ~ in(X0,sK0)
| ~ epsilon_connected(sK0)
| ~ ordinal(X1) ),
inference(resolution,[],[f153,f126]) ).
fof(f153,plain,
! [X3,X0,X4] :
( ~ in(X4,X0)
| X3 = X4
| in(X3,X4)
| in(X4,X3)
| ~ in(X3,X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( ~ in(sK3(X0),sK2(X0))
& sK2(X0) != sK3(X0)
& ~ in(sK2(X0),sK3(X0))
& in(sK3(X0),X0)
& in(sK2(X0),X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f87,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
=> ( ~ in(sK3(X0),sK2(X0))
& sK2(X0) != sK3(X0)
& ~ in(sK2(X0),sK3(X0))
& in(sK3(X0),X0)
& in(sK2(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f259,plain,
( epsilon_connected(sK0)
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f257,plain,
( spl19_6
<=> epsilon_connected(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
fof(f263,plain,
( epsilon_connected(sK0)
| ordinal(sK3(sK0)) ),
inference(resolution,[],[f155,f125]) ).
fof(f421,plain,
! [X0] :
( ~ ordinal(sK3(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f420,f157]) ).
fof(f420,plain,
! [X0] :
( sK2(X0) = sK3(X0)
| ~ ordinal(sK2(X0))
| ~ ordinal(sK3(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f390,f158]) ).
fof(f390,plain,
! [X0] :
( in(sK3(X0),sK2(X0))
| sK2(X0) = sK3(X0)
| ~ ordinal(sK2(X0))
| ~ ordinal(sK3(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f140,f156]) ).
fof(f450,plain,
! [X0,X1] :
( element(sK5(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) ),
inference(resolution,[],[f337,f169]) ).
fof(f449,plain,
! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) ),
inference(resolution,[],[f337,f292]) ).
fof(f448,plain,
! [X0] :
( element(sK3(sK4(powerset(X0))),X0)
| epsilon_connected(sK4(powerset(X0))) ),
inference(resolution,[],[f337,f155]) ).
fof(f447,plain,
! [X0] :
( element(sK2(sK4(powerset(X0))),X0)
| epsilon_connected(sK4(powerset(X0))) ),
inference(resolution,[],[f337,f154]) ).
fof(f446,plain,
! [X0] :
( element(sK1(sK4(powerset(X0))),X0)
| epsilon_transitive(sK4(powerset(X0))) ),
inference(resolution,[],[f337,f151]) ).
fof(f445,plain,
! [X0,X1] :
( element(X0,X1)
| in(sK4(powerset(X1)),X0)
| sK4(powerset(X1)) = X0
| ~ ordinal(X0)
| ~ ordinal(sK4(powerset(X1))) ),
inference(resolution,[],[f337,f140]) ).
fof(f444,plain,
! [X0,X1] :
( element(X0,X1)
| in(sK4(powerset(X1)),X0)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0) ),
inference(resolution,[],[f337,f140]) ).
fof(f337,plain,
! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| element(X0,X1) ),
inference(resolution,[],[f175,f162]) ).
fof(f439,plain,
! [X0,X1] :
( ~ in(X0,sK3(powerset(X1)))
| ~ empty(X1)
| epsilon_connected(powerset(X1)) ),
inference(resolution,[],[f326,f290]) ).
fof(f438,plain,
! [X0,X1] :
( ~ in(X0,sK2(powerset(X1)))
| ~ empty(X1)
| epsilon_connected(powerset(X1)) ),
inference(resolution,[],[f326,f289]) ).
fof(f437,plain,
! [X0,X1] :
( ~ in(X0,sK1(powerset(X1)))
| ~ empty(X1)
| epsilon_transitive(powerset(X1)) ),
inference(resolution,[],[f326,f288]) ).
fof(f326,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) ),
inference(resolution,[],[f176,f172]) ).
fof(f409,plain,
! [X0,X1] :
( in(X0,sK5(X1,X0))
| sK5(X1,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK5(X1,X0))
| subset(X1,X0) ),
inference(resolution,[],[f140,f170]) ).
fof(f431,plain,
! [X0] :
( ~ ordinal(sK2(X0))
| ~ ordinal(sK3(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f430,f157]) ).
fof(f430,plain,
! [X0] :
( sK2(X0) = sK3(X0)
| ~ ordinal(sK2(X0))
| ~ ordinal(sK3(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f408,f156]) ).
fof(f408,plain,
! [X0] :
( in(sK2(X0),sK3(X0))
| sK2(X0) = sK3(X0)
| ~ ordinal(sK2(X0))
| ~ ordinal(sK3(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f140,f158]) ).
fof(f429,plain,
! [X0] :
( ~ ordinal(sK3(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f428,f157]) ).
fof(f428,plain,
! [X0] :
( sK2(X0) = sK3(X0)
| ~ ordinal(sK3(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f407,f158]) ).
fof(f407,plain,
! [X0] :
( in(sK3(X0),sK2(X0))
| sK2(X0) = sK3(X0)
| ~ ordinal(sK3(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f140,f156]) ).
fof(f403,plain,
! [X0,X1] :
( in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| in(X1,X0) ),
inference(resolution,[],[f140,f314]) ).
fof(f425,plain,
! [X0,X1] :
( in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f402,f334]) ).
fof(f402,plain,
! [X0,X1] :
( in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(resolution,[],[f140,f325]) ).
fof(f396,plain,
! [X0,X1] :
( in(powerset(X0),X1)
| powerset(X0) = X1
| ~ ordinal(powerset(X0))
| ~ ordinal(X1)
| subset(X1,X0) ),
inference(resolution,[],[f140,f277]) ).
fof(f424,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f395,f146]) ).
fof(f395,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(resolution,[],[f140,f174]) ).
fof(f392,plain,
! [X0,X1] :
( in(X0,sK5(X1,X0))
| sK5(X1,X0) = X0
| ~ ordinal(sK5(X1,X0))
| ~ ordinal(X0)
| subset(X1,X0) ),
inference(resolution,[],[f140,f170]) ).
fof(f423,plain,
! [X0] :
( ~ ordinal(sK3(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f422,f157]) ).
fof(f422,plain,
! [X0] :
( sK2(X0) = sK3(X0)
| ~ ordinal(sK3(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(subsumption_resolution,[],[f391,f156]) ).
fof(f391,plain,
! [X0] :
( in(sK2(X0),sK3(X0))
| sK2(X0) = sK3(X0)
| ~ ordinal(sK3(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f140,f158]) ).
fof(f386,plain,
! [X0,X1] :
( in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(X1)
| ~ ordinal(sK4(powerset(X0)))
| in(X1,X0) ),
inference(resolution,[],[f140,f314]) ).
fof(f417,plain,
! [X0,X1] :
( in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f385,f334]) ).
fof(f385,plain,
! [X0,X1] :
( in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(X1)
| ~ ordinal(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f140,f325]) ).
fof(f379,plain,
! [X0,X1] :
( in(powerset(X0),X1)
| powerset(X0) = X1
| ~ ordinal(X1)
| ~ ordinal(powerset(X0))
| subset(X1,X0) ),
inference(resolution,[],[f140,f277]) ).
fof(f416,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f378,f146]) ).
fof(f378,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(resolution,[],[f140,f174]) ).
fof(f140,plain,
! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f360,plain,
( ~ in(powerset(empty_set),empty_set)
| empty(powerset(empty_set)) ),
inference(superposition,[],[f302,f341]) ).
fof(f366,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(resolution,[],[f362,f165]) ).
fof(f362,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[],[f162,f341]) ).
fof(f361,plain,
( in(empty_set,powerset(empty_set))
| empty(powerset(empty_set)) ),
inference(superposition,[],[f292,f341]) ).
fof(f341,plain,
empty_set = sK4(powerset(empty_set)),
inference(resolution,[],[f336,f127]) ).
fof(f350,plain,
empty_set = sK4(powerset(empty_set)),
inference(forward_demodulation,[],[f346,f213]) ).
fof(f346,plain,
empty_set = sK4(powerset(sK18)),
inference(resolution,[],[f336,f206]) ).
fof(f349,plain,
empty_set = sK4(powerset(empty_set)),
inference(forward_demodulation,[],[f345,f212]) ).
fof(f345,plain,
empty_set = sK4(powerset(sK17)),
inference(resolution,[],[f336,f201]) ).
fof(f348,plain,
empty_set = sK4(powerset(empty_set)),
inference(forward_demodulation,[],[f344,f211]) ).
fof(f344,plain,
empty_set = sK4(powerset(sK11)),
inference(resolution,[],[f336,f188]) ).
fof(f347,plain,
empty_set = sK4(powerset(empty_set)),
inference(forward_demodulation,[],[f343,f210]) ).
fof(f343,plain,
empty_set = sK4(powerset(sK7)),
inference(resolution,[],[f336,f178]) ).
fof(f342,plain,
! [X0] :
( empty_set = sK4(powerset(sK4(powerset(X0))))
| ~ empty(X0) ),
inference(resolution,[],[f336,f331]) ).
fof(f336,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK4(powerset(X0)) ),
inference(resolution,[],[f331,f143]) ).
fof(f332,plain,
! [X0,X1] :
( subset(sK4(powerset(X0)),X1)
| ~ empty(X0) ),
inference(resolution,[],[f325,f169]) ).
fof(f339,plain,
! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ in(X2,powerset(X1)) ),
inference(resolution,[],[f175,f167]) ).
fof(f338,plain,
! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ),
inference(resolution,[],[f175,f172]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f334,plain,
! [X0] :
( ordinal(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f333,f328]) ).
fof(f333,plain,
! [X0] :
( ~ empty(X0)
| ordinal(sK4(powerset(X0)))
| ~ epsilon_transitive(sK4(powerset(X0))) ),
inference(resolution,[],[f329,f147]) ).
fof(f335,plain,
! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ empty(X1) ),
inference(resolution,[],[f331,f173]) ).
fof(f331,plain,
! [X0] :
( empty(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f325,f292]) ).
fof(f329,plain,
! [X0] :
( epsilon_connected(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f325,f154]) ).
fof(f328,plain,
! [X0] :
( epsilon_transitive(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f325,f151]) ).
fof(f330,plain,
! [X0] :
( ~ empty(X0)
| epsilon_connected(sK4(powerset(X0))) ),
inference(resolution,[],[f325,f155]) ).
fof(f325,plain,
! [X0,X1] :
( ~ in(X1,sK4(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f176,f162]) ).
fof(f327,plain,
! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ in(X2,powerset(X0)) ),
inference(resolution,[],[f176,f167]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f324,plain,
! [X0,X1] :
( in(sK5(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) ),
inference(resolution,[],[f314,f169]) ).
fof(f323,plain,
! [X0] :
( in(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) ),
inference(resolution,[],[f314,f292]) ).
fof(f322,plain,
! [X0] :
( in(sK3(sK4(powerset(X0))),X0)
| epsilon_connected(sK4(powerset(X0))) ),
inference(resolution,[],[f314,f155]) ).
fof(f321,plain,
! [X0] :
( in(sK2(sK4(powerset(X0))),X0)
| epsilon_connected(sK4(powerset(X0))) ),
inference(resolution,[],[f314,f154]) ).
fof(f320,plain,
! [X0] :
( in(sK1(sK4(powerset(X0))),X0)
| epsilon_transitive(sK4(powerset(X0))) ),
inference(resolution,[],[f314,f151]) ).
fof(f314,plain,
! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| in(X0,X1) ),
inference(resolution,[],[f168,f276]) ).
fof(f319,plain,
! [X0,X1] :
( epsilon_connected(powerset(X0))
| ~ in(X1,sK3(powerset(X0)))
| in(X1,X0) ),
inference(resolution,[],[f290,f168]) ).
fof(f290,plain,
! [X0] :
( subset(sK3(powerset(X0)),X0)
| epsilon_connected(powerset(X0)) ),
inference(resolution,[],[f277,f155]) ).
fof(f318,plain,
! [X0,X1] :
( epsilon_connected(powerset(X0))
| ~ in(X1,sK2(powerset(X0)))
| in(X1,X0) ),
inference(resolution,[],[f289,f168]) ).
fof(f289,plain,
! [X0] :
( subset(sK2(powerset(X0)),X0)
| epsilon_connected(powerset(X0)) ),
inference(resolution,[],[f277,f154]) ).
fof(f317,plain,
! [X0,X1] :
( epsilon_transitive(powerset(X0))
| ~ in(X1,sK1(powerset(X0)))
| in(X1,X0) ),
inference(resolution,[],[f288,f168]) ).
fof(f288,plain,
! [X0] :
( subset(sK1(powerset(X0)),X0)
| epsilon_transitive(powerset(X0)) ),
inference(resolution,[],[f277,f151]) ).
fof(f316,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(resolution,[],[f168,f150]) ).
fof(f168,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f95,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f95,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,[],[f94]) ).
fof(f94,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,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f296,plain,
! [X0,X1] :
( ~ in(X0,sK5(X0,X1))
| subset(X0,X1) ),
inference(resolution,[],[f169,f166]) ).
fof(f311,plain,
! [X0] :
( ~ empty(sK5(X0,sK0))
| subset(X0,sK0) ),
inference(resolution,[],[f308,f146]) ).
fof(f308,plain,
! [X0] :
( ~ ordinal(sK5(X0,sK0))
| subset(X0,sK0) ),
inference(resolution,[],[f170,f126]) ).
fof(f170,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f301,plain,
! [X0] :
( ordinal(sK4(X0))
| empty(X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f292,f164]) ).
fof(f302,plain,
! [X0] :
( ~ in(X0,sK4(X0))
| empty(X0) ),
inference(resolution,[],[f292,f166]) ).
fof(f292,plain,
! [X0] :
( in(sK4(X0),X0)
| empty(X0) ),
inference(resolution,[],[f165,f162]) ).
fof(f299,plain,
! [X0] :
( ordinal(sK5(sK0,X0))
| subset(sK0,X0) ),
inference(resolution,[],[f169,f125]) ).
fof(f300,plain,
! [X0] :
( ~ empty(sK1(X0))
| epsilon_transitive(X0) ),
inference(resolution,[],[f297,f152]) ).
fof(f297,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[],[f169,f174]) ).
fof(f298,plain,
! [X0,X1] :
( subset(powerset(X0),X1)
| subset(sK5(powerset(X0),X1),X0) ),
inference(resolution,[],[f169,f277]) ).
fof(f169,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f294,plain,
! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ),
inference(resolution,[],[f165,f172]) ).
fof(f165,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f150,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK1(X0),X0)
& in(sK1(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f83,f84]) ).
fof(f84,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK1(X0),X0)
& in(sK1(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f277,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(resolution,[],[f171,f167]) ).
fof(f173,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f172,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f276,plain,
! [X0] : subset(sK4(powerset(X0)),X0),
inference(resolution,[],[f171,f162]) ).
fof(f171,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f164,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f158,plain,
! [X0] :
( ~ in(sK3(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f157,plain,
! [X0] :
( sK2(X0) != sK3(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f269,plain,
! [X0] :
( ~ in(X0,sK3(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f166,f155]) ).
fof(f156,plain,
! [X0] :
( ~ in(sK2(X0),sK3(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f268,plain,
! [X0] :
( ~ in(X0,sK2(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f166,f154]) ).
fof(f267,plain,
! [X0] :
( ~ in(X0,sK1(X0))
| epsilon_transitive(X0) ),
inference(resolution,[],[f166,f151]) ).
fof(f167,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f266,plain,
! [X0] :
( ~ in(sK0,X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f166,f126]) ).
fof(f166,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,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(f155,plain,
! [X0] :
( in(sK3(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f250,plain,
( epsilon_connected(sK0)
| ordinal(sK2(sK0)) ),
inference(resolution,[],[f154,f125]) ).
fof(f154,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f152,plain,
! [X0] :
( ~ subset(sK1(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f236,plain,
( epsilon_transitive(sK0)
| ordinal(sK1(sK0)) ),
inference(resolution,[],[f151,f125]) ).
fof(f151,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f147,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ordinal(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f216,plain,
! [X0] :
( ~ empty(sK0)
| ~ ordinal(X0) ),
inference(resolution,[],[f174,f126]) ).
fof(f213,plain,
empty_set = sK18,
inference(resolution,[],[f143,f206]) ).
fof(f212,plain,
empty_set = sK17,
inference(resolution,[],[f143,f201]) ).
fof(f174,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f211,plain,
empty_set = sK11,
inference(resolution,[],[f143,f188]) ).
fof(f210,plain,
empty_set = sK7,
inference(resolution,[],[f143,f178]) ).
fof(f143,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f162,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f12,f92]) ).
fof(f92,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f12,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f146,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f145,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f144,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f139,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f138,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f126,plain,
! [X1] :
( in(X1,sK0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X1] :
( ( in(X1,sK0)
| ~ ordinal(X1) )
& ( ordinal(X1)
| ~ in(X1,sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f79,f80]) ).
fof(f80,plain,
( ? [X0] :
! [X1] :
( ( in(X1,X0)
| ~ ordinal(X1) )
& ( ordinal(X1)
| ~ in(X1,X0) ) )
=> ! [X1] :
( ( in(X1,sK0)
| ~ ordinal(X1) )
& ( ordinal(X1)
| ~ in(X1,sK0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0] :
! [X1] :
( ( in(X1,X0)
| ~ ordinal(X1) )
& ( ordinal(X1)
| ~ in(X1,X0) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
? [X0] :
! [X1] :
( in(X1,X0)
<=> ordinal(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0] :
~ ! [X1] :
( in(X1,X0)
<=> ordinal(X1) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0] :
~ ! [X1] :
( in(X1,X0)
<=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(f125,plain,
! [X1] :
( ~ in(X1,sK0)
| ordinal(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f163,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f206,plain,
empty(sK18),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( function(sK18)
& empty(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f21,f123]) ).
fof(f123,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK18)
& empty(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f204,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& empty(sK17)
& function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f52,f121]) ).
fof(f121,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& empty(sK17)
& function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f22]) ).
fof(f22,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f203,plain,
epsilon_connected(sK17),
inference(cnf_transformation,[],[f122]) ).
fof(f202,plain,
epsilon_transitive(sK17),
inference(cnf_transformation,[],[f122]) ).
fof(f201,plain,
empty(sK17),
inference(cnf_transformation,[],[f122]) ).
fof(f188,plain,
empty(sK11),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
( relation(sK11)
& empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f19,f109]) ).
fof(f109,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK11)
& empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f187,plain,
ordinal(sK10),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f18,f107]) ).
fof(f107,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f186,plain,
epsilon_connected(sK10),
inference(cnf_transformation,[],[f108]) ).
fof(f185,plain,
epsilon_transitive(sK10),
inference(cnf_transformation,[],[f108]) ).
fof(f183,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f23,f105]) ).
fof(f105,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f182,plain,
ordinal(sK8),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8)
& ~ empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f26,f103]) ).
fof(f103,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8)
& ~ empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f181,plain,
epsilon_connected(sK8),
inference(cnf_transformation,[],[f104]) ).
fof(f180,plain,
epsilon_transitive(sK8),
inference(cnf_transformation,[],[f104]) ).
fof(f179,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f104]) ).
fof(f178,plain,
empty(sK7),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f20,f101]) ).
fof(f101,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f177,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
~ empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f24,f99]) ).
fof(f99,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f137,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f47]) ).
fof(f47,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f15]) ).
fof(f15,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f136,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f49]) ).
fof(f135,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f49]) ).
fof(f127,plain,
empty(empty_set),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f159,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f160,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f161,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f134,plain,
empty(empty_set),
inference(cnf_transformation,[],[f49]) ).
fof(f130,plain,
empty(empty_set),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(pure_predicate_removal,[],[f13]) ).
fof(f13,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f128,plain,
empty(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f483,plain,
( ~ spl19_3
| ~ spl19_6 ),
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f482,plain,
( $false
| ~ spl19_3
| ~ spl19_6 ),
inference(global_subsumption,[],[f128,f130,f134,f161,f160,f159,f127,f135,f136,f137,f177,f178,f179,f180,f181,f182,f183,f185,f186,f187,f188,f201,f202,f203,f204,f206,f163,f125,f126,f138,f139,f144,f145,f146,f162,f143,f210,f211,f174,f212,f213,f216,f147,f151,f236,f241,f152,f154,f250,f155,f166,f266,f167,f267,f268,f156,f269,f157,f158,f164,f171,f276,f172,f173,f277,f150,f165,f294,f169,f298,f297,f300,f299,f292,f302,f301,f170,f308,f311,f296,f168,f316,f288,f317,f289,f318,f290,f319,f314,f320,f321,f322,f323,f324,f176,f327,f325,f330,f328,f329,f331,f335,f334,f175,f338,f339,f332,f336,f342,f347,f348,f349,f350,f341,f361,f362,f366,f360,f140,f416,f379,f417,f386,f423,f392,f424,f396,f425,f403,f429,f431,f409,f326,f437,f438,f439,f337,f444,f445,f446,f447,f448,f449,f450,f421,f263,f259,f153,f467,f468,f469,f462,f470,f466,f453,f472,f295,f474,f477,f478,f457,f481,f271]) ).
fof(f481,plain,
( ordinal(sK0)
| ~ spl19_3
| ~ spl19_6 ),
inference(global_subsumption,[],[f128,f130,f134,f161,f160,f159,f127,f135,f136,f137,f177,f178,f179,f180,f181,f182,f183,f185,f186,f187,f188,f201,f202,f203,f204,f206,f163,f125,f126,f138,f139,f144,f145,f146,f162,f143,f210,f211,f174,f212,f213,f216,f147,f151,f236,f241,f152,f154,f250,f155,f166,f266,f167,f267,f268,f156,f269,f157,f158,f164,f171,f276,f172,f173,f277,f150,f165,f294,f169,f298,f297,f300,f299,f292,f302,f301,f170,f308,f311,f296,f168,f316,f288,f317,f289,f318,f290,f319,f314,f320,f321,f322,f323,f324,f176,f327,f325,f330,f328,f329,f331,f335,f334,f175,f338,f339,f332,f336,f342,f347,f348,f349,f350,f341,f361,f362,f366,f360,f140,f416,f379,f417,f386,f423,f392,f424,f396,f425,f403,f429,f431,f409,f326,f437,f438,f439,f337,f444,f445,f446,f447,f448,f449,f450,f421,f263,f259,f153,f467,f468,f469,f462,f470,f466,f453,f472,f295,f474,f477,f478,f457]) ).
fof(f478,plain,
( epsilon_transitive(sK0)
| ~ spl19_3 ),
inference(subsumption_resolution,[],[f475,f241]) ).
fof(f475,plain,
( ~ ordinal(sK1(sK0))
| epsilon_transitive(sK0) ),
inference(resolution,[],[f474,f152]) ).
fof(f241,plain,
( ordinal(sK1(sK0))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f239,plain,
( spl19_3
<=> ordinal(sK1(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
fof(f480,plain,
( ~ spl19_3
| spl19_4 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f479,plain,
( $false
| ~ spl19_3
| spl19_4 ),
inference(subsumption_resolution,[],[f478,f244]) ).
fof(f244,plain,
( ~ epsilon_transitive(sK0)
| spl19_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f456,plain,
( ~ spl19_5
| spl19_6 ),
inference(avatar_contradiction_clause,[],[f455]) ).
fof(f455,plain,
( $false
| ~ spl19_5
| spl19_6 ),
inference(subsumption_resolution,[],[f454,f258]) ).
fof(f258,plain,
( ~ epsilon_connected(sK0)
| spl19_6 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f454,plain,
( epsilon_connected(sK0)
| ~ spl19_5
| spl19_6 ),
inference(subsumption_resolution,[],[f452,f255]) ).
fof(f255,plain,
( ordinal(sK2(sK0))
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl19_5
<=> ordinal(sK2(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
fof(f452,plain,
( ~ ordinal(sK2(sK0))
| epsilon_connected(sK0)
| spl19_6 ),
inference(resolution,[],[f421,f265]) ).
fof(f265,plain,
( ordinal(sK3(sK0))
| spl19_6 ),
inference(subsumption_resolution,[],[f263,f258]) ).
fof(f375,plain,
( spl19_7
| ~ spl19_8 ),
inference(avatar_split_clause,[],[f360,f372,f368]) ).
fof(f368,plain,
( spl19_7
<=> empty(powerset(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
fof(f372,plain,
( spl19_8
<=> in(powerset(empty_set),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).
fof(f260,plain,
( spl19_5
| spl19_6 ),
inference(avatar_split_clause,[],[f250,f257,f253]) ).
fof(f246,plain,
( spl19_3
| spl19_4 ),
inference(avatar_split_clause,[],[f236,f243,f239]) ).
fof(f229,plain,
( spl19_1
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f216,f226,f223]) ).
fof(f223,plain,
( spl19_1
<=> ! [X0] : ~ ordinal(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f226,plain,
( spl19_2
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n023.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 14:38:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (10685)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (10688)WARNING: value z3 for option sas not known
% 0.15/0.38 % (10689)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (10687)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 % (10688)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 % (10691)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)
% 0.15/0.38 % (10690)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 % (10686)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (10692)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 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [4]
% 0.15/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [5]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 % (10688)First to succeed.
% 0.22/0.39 TRYING [4]
% 0.22/0.39 TRYING [3]
% 0.22/0.40 TRYING [6]
% 0.22/0.40 % (10688)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10685"
% 0.22/0.40 % (10688)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (10688)------------------------------
% 0.22/0.40 % (10688)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40 % (10688)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (10688)Memory used [KB]: 1015
% 0.22/0.40 % (10688)Time elapsed: 0.018 s
% 0.22/0.40 % (10688)Instructions burned: 26 (million)
% 0.22/0.40 % (10685)Success in time 0.023 s
%------------------------------------------------------------------------------