TSTP Solution File: SET654+3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET654+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:20:25 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 97
% Syntax : Number of formulae : 321 ( 41 unt; 0 def)
% Number of atoms : 1372 ( 23 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1807 ( 756 ~; 776 |; 124 &)
% ( 81 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 72 ( 70 usr; 64 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-2 aty)
% Number of variables : 503 ( 441 !; 62 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f526,plain,
$false,
inference(avatar_sat_refutation,[],[f145,f150,f155,f159,f163,f168,f172,f176,f180,f184,f188,f193,f200,f204,f208,f212,f219,f223,f227,f231,f235,f239,f248,f252,f256,f260,f264,f268,f272,f276,f280,f292,f313,f317,f335,f339,f343,f357,f365,f370,f372,f378,f387,f389,f395,f406,f419,f423,f428,f432,f442,f446,f456,f460,f466,f471,f475,f479,f492,f498,f502,f506,f510,f525]) ).
fof(f525,plain,
( ~ spl15_4
| spl15_59 ),
inference(avatar_contradiction_clause,[],[f524]) ).
fof(f524,plain,
( $false
| ~ spl15_4
| spl15_59 ),
inference(resolution,[],[f491,f158]) ).
fof(f158,plain,
( ! [X0] : ilf_type(X0,set_type)
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f157,plain,
( spl15_4
<=> ! [X0] : ilf_type(X0,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f491,plain,
( ~ ilf_type(range_of(sK5),set_type)
| spl15_59 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f489,plain,
( spl15_59
<=> ilf_type(range_of(sK5),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_59])]) ).
fof(f510,plain,
( spl15_63
| ~ spl15_27
| ~ spl15_31 ),
inference(avatar_split_clause,[],[f309,f278,f262,f508]) ).
fof(f508,plain,
( spl15_63
<=> ! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_63])]) ).
fof(f262,plain,
( spl15_27
<=> ! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_27])]) ).
fof(f278,plain,
( spl15_31
<=> ! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).
fof(f309,plain,
( ! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl15_27
| ~ spl15_31 ),
inference(duplicate_literal_removal,[],[f306]) ).
fof(f306,plain,
( ! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl15_27
| ~ spl15_31 ),
inference(resolution,[],[f279,f263]) ).
fof(f263,plain,
( ! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_27 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f279,plain,
( ! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) )
| ~ spl15_31 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f506,plain,
( spl15_62
| ~ spl15_26
| ~ spl15_30 ),
inference(avatar_split_clause,[],[f305,f274,f258,f504]) ).
fof(f504,plain,
( spl15_62
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_62])]) ).
fof(f258,plain,
( spl15_26
<=> ! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_26])]) ).
fof(f274,plain,
( spl15_30
<=> ! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_30])]) ).
fof(f305,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl15_26
| ~ spl15_30 ),
inference(duplicate_literal_removal,[],[f302]) ).
fof(f302,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl15_26
| ~ spl15_30 ),
inference(resolution,[],[f275,f259]) ).
fof(f259,plain,
( ! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_26 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f275,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) )
| ~ spl15_30 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f502,plain,
( spl15_61
| ~ spl15_15
| ~ spl15_27 ),
inference(avatar_split_clause,[],[f294,f262,f206,f500]) ).
fof(f500,plain,
( spl15_61
<=> ! [X0] :
( ilf_type(sK14(power_set(X0)),subset_type(X0))
| ~ ilf_type(sK14(power_set(X0)),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_61])]) ).
fof(f206,plain,
( spl15_15
<=> ! [X0] :
( ilf_type(sK14(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f294,plain,
( ! [X0] :
( ilf_type(sK14(power_set(X0)),subset_type(X0))
| ~ ilf_type(sK14(power_set(X0)),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0)) )
| ~ spl15_15
| ~ spl15_27 ),
inference(resolution,[],[f263,f207]) ).
fof(f207,plain,
( ! [X0] :
( ilf_type(sK14(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) )
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f498,plain,
( spl15_60
| ~ spl15_14
| ~ spl15_23 ),
inference(avatar_split_clause,[],[f282,f246,f202,f496]) ).
fof(f496,plain,
( spl15_60
<=> ! [X0] :
( sK9(X0) = ordered_pair(sK7(sK9(X0)),sK8(sK9(X0)))
| ~ ilf_type(sK9(X0),set_type)
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_60])]) ).
fof(f202,plain,
( spl15_14
<=> ! [X0] :
( empty(X0)
| member(sK9(X0),X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f246,plain,
( spl15_23
<=> ! [X4,X0] :
( ordered_pair(sK7(X4),sK8(X4)) = X4
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).
fof(f282,plain,
( ! [X0] :
( sK9(X0) = ordered_pair(sK7(sK9(X0)),sK8(sK9(X0)))
| ~ ilf_type(sK9(X0),set_type)
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl15_14
| ~ spl15_23 ),
inference(resolution,[],[f247,f203]) ).
fof(f203,plain,
( ! [X0] :
( member(sK9(X0),X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f247,plain,
( ! [X0,X4] :
( ~ member(X4,X0)
| ordered_pair(sK7(X4),sK8(X4)) = X4
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) )
| ~ spl15_23 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f492,plain,
( spl15_47
| ~ spl15_59
| ~ spl15_42
| ~ spl15_44 ),
inference(avatar_split_clause,[],[f391,f385,f375,f489,f416]) ).
fof(f416,plain,
( spl15_47
<=> subset(range_of(sK5),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_47])]) ).
fof(f375,plain,
( spl15_42
<=> subset(range_of(sK5),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).
fof(f385,plain,
( spl15_44
<=> ! [X0] :
( subset(X0,sK3)
| ~ ilf_type(X0,set_type)
| ~ subset(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_44])]) ).
fof(f391,plain,
( ~ ilf_type(range_of(sK5),set_type)
| subset(range_of(sK5),sK3)
| ~ spl15_42
| ~ spl15_44 ),
inference(resolution,[],[f386,f377]) ).
fof(f377,plain,
( subset(range_of(sK5),sK2)
| ~ spl15_42 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f386,plain,
( ! [X0] :
( ~ subset(X0,sK2)
| ~ ilf_type(X0,set_type)
| subset(X0,sK3) )
| ~ spl15_44 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f479,plain,
( spl15_58
| ~ spl15_14
| ~ spl15_38 ),
inference(avatar_split_clause,[],[f350,f337,f202,f477]) ).
fof(f477,plain,
( spl15_58
<=> ! [X0,X1] :
( member(sK9(X0),X1)
| ~ ilf_type(sK9(X0),set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_58])]) ).
fof(f337,plain,
( spl15_38
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_38])]) ).
fof(f350,plain,
( ! [X0,X1] :
( member(sK9(X0),X1)
| ~ ilf_type(sK9(X0),set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| empty(X0) )
| ~ spl15_14
| ~ spl15_38 ),
inference(duplicate_literal_removal,[],[f345]) ).
fof(f345,plain,
( ! [X0,X1] :
( member(sK9(X0),X1)
| ~ ilf_type(sK9(X0),set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl15_14
| ~ spl15_38 ),
inference(resolution,[],[f338,f203]) ).
fof(f338,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_38 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f475,plain,
( spl15_57
| ~ spl15_11
| ~ spl15_38 ),
inference(avatar_split_clause,[],[f344,f337,f186,f473]) ).
fof(f473,plain,
( spl15_57
<=> ! [X0,X1] :
( member(sK6(X0),X1)
| ~ ilf_type(sK6(X0),set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_57])]) ).
fof(f186,plain,
( spl15_11
<=> ! [X0] :
( sP0(X0)
| member(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f344,plain,
( ! [X0,X1] :
( member(sK6(X0),X1)
| ~ ilf_type(sK6(X0),set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| sP0(X0) )
| ~ spl15_11
| ~ spl15_38 ),
inference(resolution,[],[f338,f187]) ).
fof(f187,plain,
( ! [X0] :
( member(sK6(X0),X0)
| sP0(X0) )
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f471,plain,
( spl15_56
| ~ spl15_13
| ~ spl15_33 ),
inference(avatar_split_clause,[],[f318,f311,f198,f469]) ).
fof(f469,plain,
( spl15_56
<=> ! [X0,X1] :
( ilf_type(sK13(cross_product(X0,X1)),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_56])]) ).
fof(f198,plain,
( spl15_13
<=> ! [X0] :
( ilf_type(sK13(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
fof(f311,plain,
( spl15_33
<=> ! [X0,X1,X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_33])]) ).
fof(f318,plain,
( ! [X0,X1] :
( ilf_type(sK13(cross_product(X0,X1)),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) )
| ~ spl15_13
| ~ spl15_33 ),
inference(resolution,[],[f312,f199]) ).
fof(f199,plain,
( ! [X0] :
( ilf_type(sK13(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f312,plain,
( ! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_33 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f466,plain,
( spl15_55
| ~ spl15_16
| ~ spl15_24 ),
inference(avatar_split_clause,[],[f286,f250,f210,f464]) ).
fof(f464,plain,
( spl15_55
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK11(X0,X1),set_type)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_55])]) ).
fof(f210,plain,
( spl15_16
<=> ! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
fof(f250,plain,
( spl15_24
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| member(sK11(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).
fof(f286,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK11(X0,X1),set_type)
| ~ empty(X0) )
| ~ spl15_16
| ~ spl15_24 ),
inference(duplicate_literal_removal,[],[f285]) ).
fof(f285,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK11(X0,X1),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl15_16
| ~ spl15_24 ),
inference(resolution,[],[f251,f211]) ).
fof(f211,plain,
( ! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f251,plain,
( ! [X0,X1] :
( member(sK11(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_24 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f460,plain,
( spl15_54
| ~ spl15_13
| ~ spl15_22 ),
inference(avatar_split_clause,[],[f244,f237,f198,f458]) ).
fof(f458,plain,
( spl15_54
<=> ! [X0,X1] :
( relation_like(sK13(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_54])]) ).
fof(f237,plain,
( spl15_22
<=> ! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_22])]) ).
fof(f244,plain,
( ! [X0,X1] :
( relation_like(sK13(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) )
| ~ spl15_13
| ~ spl15_22 ),
inference(resolution,[],[f238,f199]) ).
fof(f238,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_22 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f456,plain,
( spl15_53
| ~ spl15_16
| ~ spl15_20 ),
inference(avatar_split_clause,[],[f241,f229,f210,f454]) ).
fof(f454,plain,
( spl15_53
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(X0,X1),set_type)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_53])]) ).
fof(f229,plain,
( spl15_20
<=> ! [X0,X1] :
( subset(X0,X1)
| member(sK10(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_20])]) ).
fof(f241,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(X0,X1),set_type)
| ~ empty(X0) )
| ~ spl15_16
| ~ spl15_20 ),
inference(duplicate_literal_removal,[],[f240]) ).
fof(f240,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(X0,X1),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl15_16
| ~ spl15_20 ),
inference(resolution,[],[f230,f211]) ).
fof(f230,plain,
( ! [X0,X1] :
( member(sK10(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_20 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f446,plain,
( spl15_52
| ~ spl15_22
| ~ spl15_34 ),
inference(avatar_split_clause,[],[f321,f315,f237,f444]) ).
fof(f444,plain,
( spl15_52
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_52])]) ).
fof(f315,plain,
( spl15_34
<=> ! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_34])]) ).
fof(f321,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0) )
| ~ spl15_22
| ~ spl15_34 ),
inference(duplicate_literal_removal,[],[f320]) ).
fof(f320,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl15_22
| ~ spl15_34 ),
inference(resolution,[],[f316,f238]) ).
fof(f316,plain,
( ! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_34 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f442,plain,
( spl15_51
| ~ spl15_15
| ~ spl15_30 ),
inference(avatar_split_clause,[],[f304,f274,f206,f440]) ).
fof(f440,plain,
( spl15_51
<=> ! [X0] :
( member(sK14(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(sK14(X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).
fof(f304,plain,
( ! [X0] :
( member(sK14(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(sK14(X0),set_type) )
| ~ spl15_15
| ~ spl15_30 ),
inference(duplicate_literal_removal,[],[f303]) ).
fof(f303,plain,
( ! [X0] :
( member(sK14(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(sK14(X0),set_type)
| ~ ilf_type(X0,set_type)
| empty(X0) )
| ~ spl15_15
| ~ spl15_30 ),
inference(resolution,[],[f275,f207]) ).
fof(f432,plain,
( spl15_50
| ~ spl15_17
| ~ spl15_29 ),
inference(avatar_split_clause,[],[f301,f270,f217,f430]) ).
fof(f430,plain,
( spl15_50
<=> ! [X0,X1] :
( subset(range_of(sK12(X0,X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).
fof(f217,plain,
( spl15_17
<=> ! [X0,X1] :
( ilf_type(sK12(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_17])]) ).
fof(f270,plain,
( spl15_29
<=> ! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_29])]) ).
fof(f301,plain,
( ! [X0,X1] :
( subset(range_of(sK12(X0,X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl15_17
| ~ spl15_29 ),
inference(duplicate_literal_removal,[],[f300]) ).
fof(f300,plain,
( ! [X0,X1] :
( subset(range_of(sK12(X0,X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_17
| ~ spl15_29 ),
inference(resolution,[],[f271,f218]) ).
fof(f218,plain,
( ! [X0,X1] :
( ilf_type(sK12(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_17 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f271,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| subset(range_of(X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_29 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f428,plain,
( spl15_49
| ~ spl15_17
| ~ spl15_28 ),
inference(avatar_split_clause,[],[f298,f266,f217,f426]) ).
fof(f426,plain,
( spl15_49
<=> ! [X0,X1] :
( subset(domain_of(sK12(X0,X1)),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).
fof(f266,plain,
( spl15_28
<=> ! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_28])]) ).
fof(f298,plain,
( ! [X0,X1] :
( subset(domain_of(sK12(X0,X1)),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl15_17
| ~ spl15_28 ),
inference(duplicate_literal_removal,[],[f297]) ).
fof(f297,plain,
( ! [X0,X1] :
( subset(domain_of(sK12(X0,X1)),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_17
| ~ spl15_28 ),
inference(resolution,[],[f267,f218]) ).
fof(f267,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| subset(domain_of(X2),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_28 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f423,plain,
( spl15_48
| ~ spl15_11
| ~ spl15_16 ),
inference(avatar_split_clause,[],[f213,f210,f186,f421]) ).
fof(f421,plain,
( spl15_48
<=> ! [X0] :
( ~ ilf_type(sK6(X0),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_48])]) ).
fof(f213,plain,
( ! [X0] :
( ~ ilf_type(sK6(X0),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) )
| ~ spl15_11
| ~ spl15_16 ),
inference(resolution,[],[f211,f187]) ).
fof(f419,plain,
( ~ spl15_47
| ~ spl15_43
| spl15_3
| ~ spl15_45 ),
inference(avatar_split_clause,[],[f396,f393,f152,f381,f416]) ).
fof(f381,plain,
( spl15_43
<=> ilf_type(sK3,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).
fof(f152,plain,
( spl15_3
<=> ilf_type(sK5,relation_type(sK4,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f393,plain,
( spl15_45
<=> ! [X0] :
( ~ subset(range_of(sK5),X0)
| ~ ilf_type(X0,set_type)
| ilf_type(sK5,relation_type(sK4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_45])]) ).
fof(f396,plain,
( ~ ilf_type(sK3,set_type)
| ~ subset(range_of(sK5),sK3)
| spl15_3
| ~ spl15_45 ),
inference(resolution,[],[f394,f154]) ).
fof(f154,plain,
( ~ ilf_type(sK5,relation_type(sK4,sK3))
| spl15_3 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f394,plain,
( ! [X0] :
( ilf_type(sK5,relation_type(sK4,X0))
| ~ ilf_type(X0,set_type)
| ~ subset(range_of(sK5),X0) )
| ~ spl15_45 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f406,plain,
( spl15_46
| ~ spl15_24
| ~ spl15_25 ),
inference(avatar_split_clause,[],[f288,f254,f250,f404]) ).
fof(f404,plain,
( spl15_46
<=> ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_46])]) ).
fof(f254,plain,
( spl15_25
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_25])]) ).
fof(f288,plain,
( ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl15_24
| ~ spl15_25 ),
inference(duplicate_literal_removal,[],[f287]) ).
fof(f287,plain,
( ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_24
| ~ spl15_25 ),
inference(resolution,[],[f255,f251]) ).
fof(f255,plain,
( ! [X0,X1] :
( ~ member(sK11(X0,X1),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_25 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f395,plain,
( ~ spl15_36
| ~ spl15_35
| spl15_45
| ~ spl15_2
| ~ spl15_41 ),
inference(avatar_split_clause,[],[f366,f363,f147,f393,f324,f328]) ).
fof(f328,plain,
( spl15_36
<=> ilf_type(sK2,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).
fof(f324,plain,
( spl15_35
<=> ilf_type(sK4,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_35])]) ).
fof(f147,plain,
( spl15_2
<=> ilf_type(sK5,relation_type(sK4,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f363,plain,
( spl15_41
<=> ! [X0,X3,X2,X1] :
( ilf_type(X3,relation_type(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_41])]) ).
fof(f366,plain,
( ! [X0] :
( ~ subset(range_of(sK5),X0)
| ilf_type(sK5,relation_type(sK4,X0))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK2,set_type) )
| ~ spl15_2
| ~ spl15_41 ),
inference(resolution,[],[f364,f149]) ).
fof(f149,plain,
( ilf_type(sK5,relation_type(sK4,sK2))
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f364,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X2,X0))
| ~ subset(range_of(X3),X1)
| ilf_type(X3,relation_type(X2,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_41 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f389,plain,
( ~ spl15_4
| spl15_43 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f388,plain,
( $false
| ~ spl15_4
| spl15_43 ),
inference(resolution,[],[f383,f158]) ).
fof(f383,plain,
( ~ ilf_type(sK3,set_type)
| spl15_43 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f387,plain,
( ~ spl15_36
| ~ spl15_43
| spl15_44
| ~ spl15_1
| ~ spl15_39 ),
inference(avatar_split_clause,[],[f351,f341,f142,f385,f381,f328]) ).
fof(f142,plain,
( spl15_1
<=> subset(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f341,plain,
( spl15_39
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_39])]) ).
fof(f351,plain,
( ! [X0] :
( subset(X0,sK3)
| ~ subset(X0,sK2)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_1
| ~ spl15_39 ),
inference(resolution,[],[f342,f144]) ).
fof(f144,plain,
( subset(sK2,sK3)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f342,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl15_39 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f378,plain,
( ~ spl15_35
| ~ spl15_36
| spl15_42
| ~ spl15_2
| ~ spl15_29 ),
inference(avatar_split_clause,[],[f299,f270,f147,f375,f328,f324]) ).
fof(f299,plain,
( subset(range_of(sK5),sK2)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK4,set_type)
| ~ spl15_2
| ~ spl15_29 ),
inference(resolution,[],[f271,f149]) ).
fof(f372,plain,
( ~ spl15_4
| spl15_36 ),
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f371,plain,
( $false
| ~ spl15_4
| spl15_36 ),
inference(resolution,[],[f330,f158]) ).
fof(f330,plain,
( ~ ilf_type(sK2,set_type)
| spl15_36 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f370,plain,
( ~ spl15_4
| spl15_35 ),
inference(avatar_contradiction_clause,[],[f369]) ).
fof(f369,plain,
( $false
| ~ spl15_4
| spl15_35 ),
inference(resolution,[],[f326,f158]) ).
fof(f326,plain,
( ~ ilf_type(sK4,set_type)
| spl15_35 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f365,plain,
spl15_41,
inference(avatar_split_clause,[],[f131,f363]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f357,plain,
spl15_40,
inference(avatar_split_clause,[],[f124,f355]) ).
fof(f355,plain,
( spl15_40
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).
fof(f124,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f81,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f343,plain,
spl15_39,
inference(avatar_split_clause,[],[f130,f341]) ).
fof(f130,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f339,plain,
spl15_38,
inference(avatar_split_clause,[],[f120,f337]) ).
fof(f120,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK10(X0,X1),X1)
& member(sK10(X0,X1),X0)
& ilf_type(sK10(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f77,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK10(X0,X1),X1)
& member(sK10(X0,X1),X0)
& ilf_type(sK10(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f335,plain,
( ~ spl15_35
| ~ spl15_36
| spl15_37
| ~ spl15_2
| ~ spl15_28 ),
inference(avatar_split_clause,[],[f296,f266,f147,f332,f328,f324]) ).
fof(f332,plain,
( spl15_37
<=> subset(domain_of(sK5),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).
fof(f296,plain,
( subset(domain_of(sK5),sK4)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK4,set_type)
| ~ spl15_2
| ~ spl15_28 ),
inference(resolution,[],[f267,f149]) ).
fof(f317,plain,
spl15_34,
inference(avatar_split_clause,[],[f119,f315]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f313,plain,
spl15_33,
inference(avatar_split_clause,[],[f118,f311]) ).
fof(f118,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f292,plain,
( spl15_32
| ~ spl15_4
| ~ spl15_12 ),
inference(avatar_split_clause,[],[f194,f191,f157,f290]) ).
fof(f290,plain,
( spl15_32
<=> ! [X0] :
( relation_like(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_32])]) ).
fof(f191,plain,
( spl15_12
<=> ! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f194,plain,
( ! [X0] :
( relation_like(X0)
| ~ empty(X0) )
| ~ spl15_4
| ~ spl15_12 ),
inference(resolution,[],[f192,f158]) ).
fof(f192,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| relation_like(X0)
| ~ empty(X0) )
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f280,plain,
spl15_31,
inference(avatar_split_clause,[],[f137,f278]) ).
fof(f137,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f276,plain,
spl15_30,
inference(avatar_split_clause,[],[f136,f274]) ).
fof(f136,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f272,plain,
spl15_29,
inference(avatar_split_clause,[],[f133,f270]) ).
fof(f133,plain,
! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f268,plain,
spl15_28,
inference(avatar_split_clause,[],[f132,f266]) ).
fof(f132,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f264,plain,
spl15_27,
inference(avatar_split_clause,[],[f129,f262]) ).
fof(f129,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f260,plain,
spl15_26,
inference(avatar_split_clause,[],[f128,f258]) ).
fof(f128,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f256,plain,
spl15_25,
inference(avatar_split_clause,[],[f127,f254]) ).
fof(f127,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f252,plain,
spl15_24,
inference(avatar_split_clause,[],[f126,f250]) ).
fof(f126,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK11(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f248,plain,
spl15_23,
inference(avatar_split_clause,[],[f108,f246]) ).
fof(f108,plain,
! [X0,X4] :
( ordered_pair(sK7(X4),sK8(X4)) = X4
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK6(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK6(X0),X0)
& ilf_type(sK6(X0),set_type) ) )
& ( ! [X4] :
( ( ordered_pair(sK7(X4),sK8(X4)) = X4
& ilf_type(sK8(X4),set_type)
& ilf_type(sK7(X4),set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f67,f70,f69,f68]) ).
fof(f68,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) )
=> ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK6(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK6(X0),X0)
& ilf_type(sK6(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
=> ( ? [X6] :
( ordered_pair(sK7(X4),X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(sK7(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X4] :
( ? [X6] :
( ordered_pair(sK7(X4),X6) = X4
& ilf_type(X6,set_type) )
=> ( ordered_pair(sK7(X4),sK8(X4)) = X4
& ilf_type(sK8(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( sP0(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f239,plain,
spl15_22,
inference(avatar_split_clause,[],[f134,f237]) ).
fof(f134,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f235,plain,
spl15_21,
inference(avatar_split_clause,[],[f123,f233]) ).
fof(f233,plain,
( spl15_21
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(sK10(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).
fof(f123,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK10(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f231,plain,
spl15_20,
inference(avatar_split_clause,[],[f122,f229]) ).
fof(f122,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK10(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f227,plain,
spl15_19,
inference(avatar_split_clause,[],[f111,f225]) ).
fof(f225,plain,
( spl15_19
<=> ! [X2,X0,X3] :
( sP0(X0)
| ordered_pair(X2,X3) != sK6(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_19])]) ).
fof(f111,plain,
! [X2,X3,X0] :
( sP0(X0)
| ordered_pair(X2,X3) != sK6(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f223,plain,
( spl15_18
| ~ spl15_4
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f189,f166,f157,f221]) ).
fof(f221,plain,
( spl15_18
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_18])]) ).
fof(f166,plain,
( spl15_6
<=> ! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f189,plain,
( ! [X0] : subset(X0,X0)
| ~ spl15_4
| ~ spl15_6 ),
inference(resolution,[],[f167,f158]) ).
fof(f167,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| subset(X0,X0) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f219,plain,
spl15_17,
inference(avatar_split_clause,[],[f135,f217]) ).
fof(f135,plain,
! [X0,X1] :
( ilf_type(sK12(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ilf_type(sK12(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f49,f85]) ).
fof(f85,plain,
! [X0,X1] :
( ? [X2] : ilf_type(X2,relation_type(X1,X0))
=> ilf_type(sK12(X0,X1),relation_type(X1,X0)) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ? [X2] : ilf_type(X2,relation_type(X1,X0))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ? [X2] : ilf_type(X2,relation_type(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f212,plain,
spl15_16,
inference(avatar_split_clause,[],[f113,f210]) ).
fof(f113,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK9(X0),X0)
& ilf_type(sK9(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f73,f74]) ).
fof(f74,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK9(X0),X0)
& ilf_type(sK9(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
fof(f208,plain,
spl15_15,
inference(avatar_split_clause,[],[f139,f206]) ).
fof(f139,plain,
! [X0] :
( ilf_type(sK14(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ilf_type(sK14(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f54,f90]) ).
fof(f90,plain,
! [X0] :
( ? [X1] : ilf_type(X1,member_type(X0))
=> ilf_type(sK14(X0),member_type(X0)) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0] :
( ? [X1] : ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ? [X1] : ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ? [X1] : ilf_type(X1,member_type(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
fof(f204,plain,
spl15_14,
inference(avatar_split_clause,[],[f115,f202]) ).
fof(f115,plain,
! [X0] :
( empty(X0)
| member(sK9(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f200,plain,
spl15_13,
inference(avatar_split_clause,[],[f138,f198]) ).
fof(f138,plain,
! [X0] :
( ilf_type(sK13(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ilf_type(sK13(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f52,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1] : ilf_type(X1,subset_type(X0))
=> ilf_type(sK13(X0),subset_type(X0)) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0] :
( ? [X1] : ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ? [X1] : ilf_type(X1,subset_type(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
fof(f193,plain,
spl15_12,
inference(avatar_split_clause,[],[f140,f191]) ).
fof(f140,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ( ilf_type(X0,set_type)
& empty(X0) )
=> relation_like(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f188,plain,
spl15_11,
inference(avatar_split_clause,[],[f110,f186]) ).
fof(f110,plain,
! [X0] :
( sP0(X0)
| member(sK6(X0),X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f184,plain,
spl15_10,
inference(avatar_split_clause,[],[f105,f182]) ).
fof(f182,plain,
( spl15_10
<=> ! [X0] :
( relation_like(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f105,plain,
! [X0] :
( relation_like(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( ( relation_like(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ relation_like(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( relation_like(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f180,plain,
spl15_9,
inference(avatar_split_clause,[],[f104,f178]) ).
fof(f178,plain,
( spl15_9
<=> ! [X0] :
( sP0(X0)
| ~ relation_like(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f104,plain,
! [X0] :
( sP0(X0)
| ~ relation_like(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f176,plain,
( spl15_8
| ~ spl15_4
| ~ spl15_5 ),
inference(avatar_split_clause,[],[f164,f161,f157,f174]) ).
fof(f174,plain,
( spl15_8
<=> ! [X0] : sP1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f161,plain,
( spl15_5
<=> ! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f164,plain,
( ! [X0] : sP1(X0)
| ~ spl15_4
| ~ spl15_5 ),
inference(resolution,[],[f162,f158]) ).
fof(f162,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| sP1(X0) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f172,plain,
spl15_7,
inference(avatar_split_clause,[],[f102,f170]) ).
fof(f170,plain,
( spl15_7
<=> ! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f102,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(f168,plain,
spl15_6,
inference(avatar_split_clause,[],[f101,f166]) ).
fof(f101,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f163,plain,
spl15_5,
inference(avatar_split_clause,[],[f112,f161]) ).
fof(f112,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f33,f58,f57]) ).
fof(f33,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( relation_like(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
=> ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f159,plain,
spl15_4,
inference(avatar_split_clause,[],[f98,f157]) ).
fof(f98,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f155,plain,
~ spl15_3,
inference(avatar_split_clause,[],[f97,f152]) ).
fof(f97,plain,
~ ilf_type(sK5,relation_type(sK4,sK3)),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( ~ ilf_type(sK5,relation_type(sK4,sK3))
& subset(sK2,sK3)
& ilf_type(sK5,relation_type(sK4,sK2))
& ilf_type(sK4,set_type)
& ilf_type(sK3,set_type)
& ilf_type(sK2,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f27,f63,f62,f61,f60]) ).
fof(f60,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(X0,X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(sK2,X1)
& ilf_type(X3,relation_type(X2,sK2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK2,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(sK2,X1)
& ilf_type(X3,relation_type(X2,sK2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,sK3))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(X2,sK2)) )
& ilf_type(X2,set_type) )
& ilf_type(sK3,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,sK3))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(X2,sK2)) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(X3,relation_type(sK4,sK3))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(sK4,sK2)) )
& ilf_type(sK4,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK4,sK3))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(sK4,sK2)) )
=> ( ~ ilf_type(sK5,relation_type(sK4,sK3))
& subset(sK2,sK3)
& ilf_type(sK5,relation_type(sK4,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(X0,X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(X0,X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
inference(negated_conjecture,[],[f23]) ).
fof(f23,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_16) ).
fof(f150,plain,
spl15_2,
inference(avatar_split_clause,[],[f95,f147]) ).
fof(f95,plain,
ilf_type(sK5,relation_type(sK4,sK2)),
inference(cnf_transformation,[],[f64]) ).
fof(f145,plain,
spl15_1,
inference(avatar_split_clause,[],[f96,f142]) ).
fof(f96,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET654+3 : TPTP v8.2.0. Released v2.2.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 11:05:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (1636)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (1639)WARNING: value z3 for option sas not known
% 0.13/0.36 % (1643)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)
% 0.13/0.36 % (1637)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % (1639)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)
% 0.13/0.36 % (1638)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (1641)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)
% 0.13/0.36 % (1640)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (1642)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)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 % (1641)First to succeed.
% 0.13/0.37 % (1642)Also succeeded, but the first one will report.
% 0.13/0.37 TRYING [3]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 % (1641)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1636"
% 0.13/0.38 TRYING [2]
% 0.13/0.38 % (1641)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (1641)------------------------------
% 0.13/0.38 % (1641)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (1641)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (1641)Memory used [KB]: 1025
% 0.13/0.38 % (1641)Time elapsed: 0.015 s
% 0.13/0.38 % (1641)Instructions burned: 25 (million)
% 0.13/0.38 % (1636)Success in time 0.02 s
%------------------------------------------------------------------------------