TSTP Solution File: SET959+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET959+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:14:07 EDT 2024
% Result : Theorem 0.17s 0.36s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 70
% Syntax : Number of formulae : 245 ( 27 unt; 0 def)
% Number of atoms : 774 ( 125 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 953 ( 424 ~; 417 |; 38 &)
% ( 62 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 60 ( 58 usr; 57 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 250 ( 211 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f464,plain,
$false,
inference(avatar_sat_refutation,[],[f49,f54,f59,f63,f69,f75,f79,f83,f89,f95,f99,f103,f107,f111,f120,f124,f130,f134,f148,f156,f160,f164,f168,f196,f202,f206,f210,f214,f218,f222,f231,f259,f283,f288,f297,f310,f319,f324,f329,f334,f335,f358,f379,f384,f393,f402,f411,f416,f417,f421,f428,f433,f434,f452,f463]) ).
fof(f463,plain,
( spl9_38
| ~ spl9_37
| ~ spl9_15
| ~ spl9_31 ),
inference(avatar_split_clause,[],[f338,f224,f118,f290,f294]) ).
fof(f294,plain,
( spl9_38
<=> in(sK6(sK0,sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_38])]) ).
fof(f290,plain,
( spl9_37
<=> in(sK6(sK0,sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_37])]) ).
fof(f118,plain,
( spl9_15
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK0)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
fof(f224,plain,
( spl9_31
<=> sK6(sK0,sK1) = unordered_pair(singleton(sK4(sK6(sK0,sK1))),unordered_pair(sK5(sK6(sK0,sK1)),sK4(sK6(sK0,sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).
fof(f338,plain,
( ~ in(sK6(sK0,sK1),sK0)
| in(sK6(sK0,sK1),sK1)
| ~ spl9_15
| ~ spl9_31 ),
inference(superposition,[],[f119,f226]) ).
fof(f226,plain,
( sK6(sK0,sK1) = unordered_pair(singleton(sK4(sK6(sK0,sK1))),unordered_pair(sK5(sK6(sK0,sK1)),sK4(sK6(sK0,sK1))))
| ~ spl9_31 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f119,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK0)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK1) )
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f452,plain,
( spl9_38
| ~ spl9_37
| ~ spl9_15
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f234,f228,f118,f290,f294]) ).
fof(f228,plain,
( spl9_32
<=> sK6(sK0,sK1) = unordered_pair(singleton(sK2(sK6(sK0,sK1))),unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_32])]) ).
fof(f234,plain,
( ~ in(sK6(sK0,sK1),sK0)
| in(sK6(sK0,sK1),sK1)
| ~ spl9_15
| ~ spl9_32 ),
inference(superposition,[],[f119,f230]) ).
fof(f230,plain,
( sK6(sK0,sK1) = unordered_pair(singleton(sK2(sK6(sK0,sK1))),unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))
| ~ spl9_32 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f434,plain,
( ~ spl9_37
| spl9_1
| ~ spl9_18
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f355,f294,f132,f46,f290]) ).
fof(f46,plain,
( spl9_1
<=> sK0 = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f132,plain,
( spl9_18
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
fof(f355,plain,
( sK0 = sK1
| ~ in(sK6(sK0,sK1),sK0)
| ~ spl9_18
| ~ spl9_38 ),
inference(resolution,[],[f295,f133]) ).
fof(f133,plain,
( ! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| X0 = X1
| ~ in(sK6(X0,X1),X0) )
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f295,plain,
( in(sK6(sK0,sK1),sK1)
| ~ spl9_38 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f433,plain,
( ~ spl9_56
| ~ spl9_12
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f423,f307,f101,f430]) ).
fof(f430,plain,
( spl9_56
<=> in(sK1,sK6(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_56])]) ).
fof(f101,plain,
( spl9_12
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f307,plain,
( spl9_40
<=> in(sK6(sK1,sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_40])]) ).
fof(f423,plain,
( ~ in(sK1,sK6(sK1,sK0))
| ~ spl9_12
| ~ spl9_40 ),
inference(resolution,[],[f308,f102]) ).
fof(f102,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f308,plain,
( in(sK6(sK1,sK0),sK1)
| ~ spl9_40 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f428,plain,
( ~ spl9_55
| ~ spl9_12
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f420,f303,f101,f425]) ).
fof(f425,plain,
( spl9_55
<=> in(sK0,sK6(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_55])]) ).
fof(f303,plain,
( spl9_39
<=> in(sK6(sK1,sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_39])]) ).
fof(f420,plain,
( ~ in(sK0,sK6(sK1,sK0))
| ~ spl9_12
| ~ spl9_39 ),
inference(resolution,[],[f305,f102]) ).
fof(f305,plain,
( in(sK6(sK1,sK0),sK0)
| ~ spl9_39 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f421,plain,
( spl9_40
| ~ spl9_39
| ~ spl9_15
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f262,f252,f118,f303,f307]) ).
fof(f252,plain,
( spl9_33
<=> sK6(sK1,sK0) = unordered_pair(singleton(sK2(sK6(sK1,sK0))),unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
fof(f262,plain,
( ~ in(sK6(sK1,sK0),sK0)
| in(sK6(sK1,sK0),sK1)
| ~ spl9_15
| ~ spl9_33 ),
inference(superposition,[],[f119,f254]) ).
fof(f254,plain,
( sK6(sK1,sK0) = unordered_pair(singleton(sK2(sK6(sK1,sK0))),unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f417,plain,
( spl9_1
| spl9_39
| ~ spl9_17
| spl9_40 ),
inference(avatar_split_clause,[],[f314,f307,f128,f303,f46]) ).
fof(f128,plain,
( spl9_17
<=> ! [X0,X1] :
( X0 = X1
| in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
fof(f314,plain,
( in(sK6(sK1,sK0),sK0)
| sK0 = sK1
| ~ spl9_17
| spl9_40 ),
inference(resolution,[],[f309,f129]) ).
fof(f129,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0)
| X0 = X1 )
| ~ spl9_17 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f309,plain,
( ~ in(sK6(sK1,sK0),sK1)
| spl9_40 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f416,plain,
( ~ spl9_54
| ~ spl9_12
| ~ spl9_37 ),
inference(avatar_split_clause,[],[f370,f290,f101,f413]) ).
fof(f413,plain,
( spl9_54
<=> in(sK0,sK6(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_54])]) ).
fof(f370,plain,
( ~ in(sK0,sK6(sK0,sK1))
| ~ spl9_12
| ~ spl9_37 ),
inference(resolution,[],[f292,f102]) ).
fof(f292,plain,
( in(sK6(sK0,sK1),sK0)
| ~ spl9_37 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f411,plain,
( ~ spl9_52
| spl9_53
| ~ spl9_13
| ~ spl9_15
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f274,f252,f118,f105,f408,f404]) ).
fof(f404,plain,
( spl9_52
<=> in(unordered_pair(sK6(sK1,sK0),singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_52])]) ).
fof(f408,plain,
( spl9_53
<=> in(unordered_pair(sK6(sK1,sK0),singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_53])]) ).
fof(f105,plain,
( spl9_13
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f274,plain,
( in(unordered_pair(sK6(sK1,sK0),singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))),sK1)
| ~ in(unordered_pair(sK6(sK1,sK0),singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))),sK0)
| ~ spl9_13
| ~ spl9_15
| ~ spl9_33 ),
inference(forward_demodulation,[],[f273,f106]) ).
fof(f106,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f273,plain,
( ~ in(unordered_pair(sK6(sK1,sK0),singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))),sK0)
| in(unordered_pair(singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)),sK1)
| ~ spl9_13
| ~ spl9_15
| ~ spl9_33 ),
inference(forward_demodulation,[],[f265,f106]) ).
fof(f265,plain,
( ~ in(unordered_pair(singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)),sK0)
| in(unordered_pair(singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)),sK1)
| ~ spl9_15
| ~ spl9_33 ),
inference(superposition,[],[f119,f254]) ).
fof(f402,plain,
( ~ spl9_50
| spl9_51
| ~ spl9_13
| ~ spl9_15
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f246,f228,f118,f105,f399,f395]) ).
fof(f395,plain,
( spl9_50
<=> in(unordered_pair(sK6(sK0,sK1),singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
fof(f399,plain,
( spl9_51
<=> in(unordered_pair(sK6(sK0,sK1),singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_51])]) ).
fof(f246,plain,
( in(unordered_pair(sK6(sK0,sK1),singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))),sK1)
| ~ in(unordered_pair(sK6(sK0,sK1),singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))),sK0)
| ~ spl9_13
| ~ spl9_15
| ~ spl9_32 ),
inference(forward_demodulation,[],[f245,f106]) ).
fof(f245,plain,
( ~ in(unordered_pair(sK6(sK0,sK1),singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))),sK0)
| in(unordered_pair(singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)),sK1)
| ~ spl9_13
| ~ spl9_15
| ~ spl9_32 ),
inference(forward_demodulation,[],[f237,f106]) ).
fof(f237,plain,
( ~ in(unordered_pair(singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)),sK0)
| in(unordered_pair(singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)),sK1)
| ~ spl9_15
| ~ spl9_32 ),
inference(superposition,[],[f119,f230]) ).
fof(f393,plain,
( ~ spl9_48
| spl9_49
| ~ spl9_10
| ~ spl9_13
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f270,f252,f105,f93,f390,f386]) ).
fof(f386,plain,
( spl9_48
<=> in(unordered_pair(sK6(sK1,sK0),singleton(singleton(sK2(sK6(sK1,sK0))))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_48])]) ).
fof(f390,plain,
( spl9_49
<=> in(unordered_pair(sK6(sK1,sK0),singleton(singleton(sK2(sK6(sK1,sK0))))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_49])]) ).
fof(f93,plain,
( spl9_10
<=> ! [X2,X3] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f270,plain,
( in(unordered_pair(sK6(sK1,sK0),singleton(singleton(sK2(sK6(sK1,sK0))))),sK0)
| ~ in(unordered_pair(sK6(sK1,sK0),singleton(singleton(sK2(sK6(sK1,sK0))))),sK1)
| ~ spl9_10
| ~ spl9_13
| ~ spl9_33 ),
inference(forward_demodulation,[],[f269,f106]) ).
fof(f269,plain,
( ~ in(unordered_pair(sK6(sK1,sK0),singleton(singleton(sK2(sK6(sK1,sK0))))),sK1)
| in(unordered_pair(singleton(singleton(sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)),sK0)
| ~ spl9_10
| ~ spl9_13
| ~ spl9_33 ),
inference(forward_demodulation,[],[f263,f106]) ).
fof(f263,plain,
( ~ in(unordered_pair(singleton(singleton(sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)),sK1)
| in(unordered_pair(singleton(singleton(sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)),sK0)
| ~ spl9_10
| ~ spl9_33 ),
inference(superposition,[],[f94,f254]) ).
fof(f94,plain,
( ! [X2,X3] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK0) )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f384,plain,
( ~ spl9_47
| ~ spl9_12
| ~ spl9_38 ),
inference(avatar_split_clause,[],[f357,f294,f101,f381]) ).
fof(f381,plain,
( spl9_47
<=> in(sK1,sK6(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_47])]) ).
fof(f357,plain,
( ~ in(sK1,sK6(sK0,sK1))
| ~ spl9_12
| ~ spl9_38 ),
inference(resolution,[],[f295,f102]) ).
fof(f379,plain,
( ~ spl9_45
| spl9_46
| ~ spl9_10
| ~ spl9_13
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f242,f228,f105,f93,f376,f372]) ).
fof(f372,plain,
( spl9_45
<=> in(unordered_pair(sK6(sK0,sK1),singleton(singleton(sK2(sK6(sK0,sK1))))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_45])]) ).
fof(f376,plain,
( spl9_46
<=> in(unordered_pair(sK6(sK0,sK1),singleton(singleton(sK2(sK6(sK0,sK1))))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_46])]) ).
fof(f242,plain,
( in(unordered_pair(sK6(sK0,sK1),singleton(singleton(sK2(sK6(sK0,sK1))))),sK0)
| ~ in(unordered_pair(sK6(sK0,sK1),singleton(singleton(sK2(sK6(sK0,sK1))))),sK1)
| ~ spl9_10
| ~ spl9_13
| ~ spl9_32 ),
inference(forward_demodulation,[],[f241,f106]) ).
fof(f241,plain,
( ~ in(unordered_pair(sK6(sK0,sK1),singleton(singleton(sK2(sK6(sK0,sK1))))),sK1)
| in(unordered_pair(singleton(singleton(sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)),sK0)
| ~ spl9_10
| ~ spl9_13
| ~ spl9_32 ),
inference(forward_demodulation,[],[f235,f106]) ).
fof(f235,plain,
( ~ in(unordered_pair(singleton(singleton(sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)),sK1)
| in(unordered_pair(singleton(singleton(sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)),sK0)
| ~ spl9_10
| ~ spl9_32 ),
inference(superposition,[],[f94,f230]) ).
fof(f358,plain,
( spl9_37
| ~ spl9_38
| ~ spl9_19
| ~ spl9_31 ),
inference(avatar_split_clause,[],[f337,f224,f146,f294,f290]) ).
fof(f146,plain,
( spl9_19
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK1)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
fof(f337,plain,
( ~ in(sK6(sK0,sK1),sK1)
| in(sK6(sK0,sK1),sK0)
| ~ spl9_19
| ~ spl9_31 ),
inference(superposition,[],[f147,f226]) ).
fof(f147,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK1)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK0) )
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f335,plain,
( spl9_1
| spl9_37
| ~ spl9_17
| spl9_38 ),
inference(avatar_split_clause,[],[f301,f294,f128,f290,f46]) ).
fof(f301,plain,
( in(sK6(sK0,sK1),sK0)
| sK0 = sK1
| ~ spl9_17
| spl9_38 ),
inference(resolution,[],[f296,f129]) ).
fof(f296,plain,
( ~ in(sK6(sK0,sK1),sK1)
| spl9_38 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f334,plain,
( ~ spl9_44
| ~ spl9_13
| ~ spl9_24
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f278,f252,f194,f105,f331]) ).
fof(f331,plain,
( spl9_44
<=> empty(unordered_pair(sK6(sK1,sK0),singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_44])]) ).
fof(f194,plain,
( spl9_24
<=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
fof(f278,plain,
( ~ empty(unordered_pair(sK6(sK1,sK0),singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))))
| ~ spl9_13
| ~ spl9_24
| ~ spl9_33 ),
inference(forward_demodulation,[],[f268,f106]) ).
fof(f268,plain,
( ~ empty(unordered_pair(singleton(unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)))
| ~ spl9_24
| ~ spl9_33 ),
inference(superposition,[],[f195,f254]) ).
fof(f195,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f329,plain,
( ~ spl9_43
| ~ spl9_13
| ~ spl9_24
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f250,f228,f194,f105,f326]) ).
fof(f326,plain,
( spl9_43
<=> empty(unordered_pair(sK6(sK0,sK1),singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_43])]) ).
fof(f250,plain,
( ~ empty(unordered_pair(sK6(sK0,sK1),singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))))
| ~ spl9_13
| ~ spl9_24
| ~ spl9_32 ),
inference(forward_demodulation,[],[f240,f106]) ).
fof(f240,plain,
( ~ empty(unordered_pair(singleton(unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)))
| ~ spl9_24
| ~ spl9_32 ),
inference(superposition,[],[f195,f230]) ).
fof(f324,plain,
( ~ spl9_42
| ~ spl9_13
| ~ spl9_16
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f275,f252,f122,f105,f321]) ).
fof(f321,plain,
( spl9_42
<=> empty(unordered_pair(sK6(sK1,sK0),singleton(singleton(sK2(sK6(sK1,sK0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
fof(f122,plain,
( spl9_16
<=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
fof(f275,plain,
( ~ empty(unordered_pair(sK6(sK1,sK0),singleton(singleton(sK2(sK6(sK1,sK0))))))
| ~ spl9_13
| ~ spl9_16
| ~ spl9_33 ),
inference(forward_demodulation,[],[f266,f106]) ).
fof(f266,plain,
( ~ empty(unordered_pair(singleton(singleton(sK2(sK6(sK1,sK0)))),sK6(sK1,sK0)))
| ~ spl9_16
| ~ spl9_33 ),
inference(superposition,[],[f123,f254]) ).
fof(f123,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
| ~ spl9_16 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f319,plain,
( ~ spl9_41
| ~ spl9_13
| ~ spl9_16
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f247,f228,f122,f105,f316]) ).
fof(f316,plain,
( spl9_41
<=> empty(unordered_pair(sK6(sK0,sK1),singleton(singleton(sK2(sK6(sK0,sK1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_41])]) ).
fof(f247,plain,
( ~ empty(unordered_pair(sK6(sK0,sK1),singleton(singleton(sK2(sK6(sK0,sK1))))))
| ~ spl9_13
| ~ spl9_16
| ~ spl9_32 ),
inference(forward_demodulation,[],[f238,f106]) ).
fof(f238,plain,
( ~ empty(unordered_pair(singleton(singleton(sK2(sK6(sK0,sK1)))),sK6(sK0,sK1)))
| ~ spl9_16
| ~ spl9_32 ),
inference(superposition,[],[f123,f230]) ).
fof(f310,plain,
( spl9_39
| ~ spl9_40
| ~ spl9_19
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f261,f252,f146,f307,f303]) ).
fof(f261,plain,
( ~ in(sK6(sK1,sK0),sK1)
| in(sK6(sK1,sK0),sK0)
| ~ spl9_19
| ~ spl9_33 ),
inference(superposition,[],[f147,f254]) ).
fof(f297,plain,
( spl9_37
| ~ spl9_38
| ~ spl9_19
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f233,f228,f146,f294,f290]) ).
fof(f233,plain,
( ~ in(sK6(sK0,sK1),sK1)
| in(sK6(sK0,sK1),sK0)
| ~ spl9_19
| ~ spl9_32 ),
inference(superposition,[],[f147,f230]) ).
fof(f288,plain,
( ~ spl9_36
| ~ spl9_24
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f260,f252,f194,f285]) ).
fof(f285,plain,
( spl9_36
<=> empty(sK6(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_36])]) ).
fof(f260,plain,
( ~ empty(sK6(sK1,sK0))
| ~ spl9_24
| ~ spl9_33 ),
inference(superposition,[],[f195,f254]) ).
fof(f283,plain,
( ~ spl9_35
| ~ spl9_24
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f232,f228,f194,f280]) ).
fof(f280,plain,
( spl9_35
<=> empty(sK6(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_35])]) ).
fof(f232,plain,
( ~ empty(sK6(sK0,sK1))
| ~ spl9_24
| ~ spl9_32 ),
inference(superposition,[],[f195,f230]) ).
fof(f259,plain,
( spl9_33
| spl9_34
| spl9_1
| ~ spl9_6
| ~ spl9_21 ),
inference(avatar_split_clause,[],[f176,f158,f73,f46,f256,f252]) ).
fof(f256,plain,
( spl9_34
<=> sK6(sK1,sK0) = unordered_pair(singleton(sK4(sK6(sK1,sK0))),unordered_pair(sK5(sK6(sK1,sK0)),sK4(sK6(sK1,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_34])]) ).
fof(f73,plain,
( spl9_6
<=> ! [X4] :
( unordered_pair(singleton(sK2(X4)),unordered_pair(sK3(X4),sK2(X4))) = X4
| ~ in(X4,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f158,plain,
( spl9_21
<=> ! [X0] :
( in(sK6(X0,sK0),X0)
| sK0 = X0
| sK6(X0,sK0) = unordered_pair(singleton(sK4(sK6(X0,sK0))),unordered_pair(sK5(sK6(X0,sK0)),sK4(sK6(X0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
fof(f176,plain,
( sK0 = sK1
| sK6(sK1,sK0) = unordered_pair(singleton(sK4(sK6(sK1,sK0))),unordered_pair(sK5(sK6(sK1,sK0)),sK4(sK6(sK1,sK0))))
| sK6(sK1,sK0) = unordered_pair(singleton(sK2(sK6(sK1,sK0))),unordered_pair(sK3(sK6(sK1,sK0)),sK2(sK6(sK1,sK0))))
| ~ spl9_6
| ~ spl9_21 ),
inference(resolution,[],[f159,f74]) ).
fof(f74,plain,
( ! [X4] :
( ~ in(X4,sK1)
| unordered_pair(singleton(sK2(X4)),unordered_pair(sK3(X4),sK2(X4))) = X4 )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f159,plain,
( ! [X0] :
( in(sK6(X0,sK0),X0)
| sK0 = X0
| sK6(X0,sK0) = unordered_pair(singleton(sK4(sK6(X0,sK0))),unordered_pair(sK5(sK6(X0,sK0)),sK4(sK6(X0,sK0)))) )
| ~ spl9_21 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f231,plain,
( spl9_31
| spl9_32
| spl9_1
| ~ spl9_7
| ~ spl9_20 ),
inference(avatar_split_clause,[],[f171,f154,f77,f46,f228,f224]) ).
fof(f77,plain,
( spl9_7
<=> ! [X7] :
( unordered_pair(singleton(sK4(X7)),unordered_pair(sK5(X7),sK4(X7))) = X7
| ~ in(X7,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f154,plain,
( spl9_20
<=> ! [X0] :
( in(sK6(X0,sK1),X0)
| sK1 = X0
| sK6(X0,sK1) = unordered_pair(singleton(sK2(sK6(X0,sK1))),unordered_pair(sK3(sK6(X0,sK1)),sK2(sK6(X0,sK1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
fof(f171,plain,
( sK0 = sK1
| sK6(sK0,sK1) = unordered_pair(singleton(sK2(sK6(sK0,sK1))),unordered_pair(sK3(sK6(sK0,sK1)),sK2(sK6(sK0,sK1))))
| sK6(sK0,sK1) = unordered_pair(singleton(sK4(sK6(sK0,sK1))),unordered_pair(sK5(sK6(sK0,sK1)),sK4(sK6(sK0,sK1))))
| ~ spl9_7
| ~ spl9_20 ),
inference(resolution,[],[f155,f78]) ).
fof(f78,plain,
( ! [X7] :
( ~ in(X7,sK0)
| unordered_pair(singleton(sK4(X7)),unordered_pair(sK5(X7),sK4(X7))) = X7 )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f155,plain,
( ! [X0] :
( in(sK6(X0,sK1),X0)
| sK1 = X0
| sK6(X0,sK1) = unordered_pair(singleton(sK2(sK6(X0,sK1))),unordered_pair(sK3(sK6(X0,sK1)),sK2(sK6(X0,sK1)))) )
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f222,plain,
( spl9_30
| ~ spl9_12
| ~ spl9_23 ),
inference(avatar_split_clause,[],[f190,f166,f101,f220]) ).
fof(f220,plain,
( spl9_30
<=> ! [X0] :
( sK0 = X0
| sK6(sK0,X0) = unordered_pair(singleton(sK4(sK6(sK0,X0))),unordered_pair(sK5(sK6(sK0,X0)),sK4(sK6(sK0,X0))))
| ~ in(X0,sK6(sK0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
fof(f166,plain,
( spl9_23
<=> ! [X0] :
( in(sK6(sK0,X0),X0)
| sK0 = X0
| sK6(sK0,X0) = unordered_pair(singleton(sK4(sK6(sK0,X0))),unordered_pair(sK5(sK6(sK0,X0)),sK4(sK6(sK0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
fof(f190,plain,
( ! [X0] :
( sK0 = X0
| sK6(sK0,X0) = unordered_pair(singleton(sK4(sK6(sK0,X0))),unordered_pair(sK5(sK6(sK0,X0)),sK4(sK6(sK0,X0))))
| ~ in(X0,sK6(sK0,X0)) )
| ~ spl9_12
| ~ spl9_23 ),
inference(resolution,[],[f167,f102]) ).
fof(f167,plain,
( ! [X0] :
( in(sK6(sK0,X0),X0)
| sK0 = X0
| sK6(sK0,X0) = unordered_pair(singleton(sK4(sK6(sK0,X0))),unordered_pair(sK5(sK6(sK0,X0)),sK4(sK6(sK0,X0)))) )
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f218,plain,
( spl9_29
| ~ spl9_12
| ~ spl9_22 ),
inference(avatar_split_clause,[],[f184,f162,f101,f216]) ).
fof(f216,plain,
( spl9_29
<=> ! [X0] :
( sK1 = X0
| sK6(sK1,X0) = unordered_pair(singleton(sK2(sK6(sK1,X0))),unordered_pair(sK3(sK6(sK1,X0)),sK2(sK6(sK1,X0))))
| ~ in(X0,sK6(sK1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
fof(f162,plain,
( spl9_22
<=> ! [X0] :
( in(sK6(sK1,X0),X0)
| sK1 = X0
| sK6(sK1,X0) = unordered_pair(singleton(sK2(sK6(sK1,X0))),unordered_pair(sK3(sK6(sK1,X0)),sK2(sK6(sK1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
fof(f184,plain,
( ! [X0] :
( sK1 = X0
| sK6(sK1,X0) = unordered_pair(singleton(sK2(sK6(sK1,X0))),unordered_pair(sK3(sK6(sK1,X0)),sK2(sK6(sK1,X0))))
| ~ in(X0,sK6(sK1,X0)) )
| ~ spl9_12
| ~ spl9_22 ),
inference(resolution,[],[f163,f102]) ).
fof(f163,plain,
( ! [X0] :
( in(sK6(sK1,X0),X0)
| sK1 = X0
| sK6(sK1,X0) = unordered_pair(singleton(sK2(sK6(sK1,X0))),unordered_pair(sK3(sK6(sK1,X0)),sK2(sK6(sK1,X0)))) )
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f214,plain,
( spl9_28
| ~ spl9_12
| ~ spl9_21 ),
inference(avatar_split_clause,[],[f178,f158,f101,f212]) ).
fof(f212,plain,
( spl9_28
<=> ! [X0] :
( sK0 = X0
| sK6(X0,sK0) = unordered_pair(singleton(sK4(sK6(X0,sK0))),unordered_pair(sK5(sK6(X0,sK0)),sK4(sK6(X0,sK0))))
| ~ in(X0,sK6(X0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
fof(f178,plain,
( ! [X0] :
( sK0 = X0
| sK6(X0,sK0) = unordered_pair(singleton(sK4(sK6(X0,sK0))),unordered_pair(sK5(sK6(X0,sK0)),sK4(sK6(X0,sK0))))
| ~ in(X0,sK6(X0,sK0)) )
| ~ spl9_12
| ~ spl9_21 ),
inference(resolution,[],[f159,f102]) ).
fof(f210,plain,
( spl9_27
| ~ spl9_12
| ~ spl9_20 ),
inference(avatar_split_clause,[],[f172,f154,f101,f208]) ).
fof(f208,plain,
( spl9_27
<=> ! [X0] :
( sK1 = X0
| sK6(X0,sK1) = unordered_pair(singleton(sK2(sK6(X0,sK1))),unordered_pair(sK3(sK6(X0,sK1)),sK2(sK6(X0,sK1))))
| ~ in(X0,sK6(X0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
fof(f172,plain,
( ! [X0] :
( sK1 = X0
| sK6(X0,sK1) = unordered_pair(singleton(sK2(sK6(X0,sK1))),unordered_pair(sK3(sK6(X0,sK1)),sK2(sK6(X0,sK1))))
| ~ in(X0,sK6(X0,sK1)) )
| ~ spl9_12
| ~ spl9_20 ),
inference(resolution,[],[f155,f102]) ).
fof(f206,plain,
( spl9_26
| ~ spl9_12
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f140,f128,f101,f204]) ).
fof(f204,plain,
( spl9_26
<=> ! [X0,X1] :
( in(sK6(X0,X1),X1)
| X0 = X1
| ~ in(X0,sK6(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
fof(f140,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X1)
| X0 = X1
| ~ in(X0,sK6(X0,X1)) )
| ~ spl9_12
| ~ spl9_17 ),
inference(resolution,[],[f129,f102]) ).
fof(f202,plain,
( spl9_25
| ~ spl9_12
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f137,f128,f101,f200]) ).
fof(f200,plain,
( spl9_25
<=> ! [X0,X1] :
( in(sK6(X0,X1),X0)
| X0 = X1
| ~ in(X1,sK6(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
fof(f137,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X0)
| X0 = X1
| ~ in(X1,sK6(X0,X1)) )
| ~ spl9_12
| ~ spl9_17 ),
inference(resolution,[],[f129,f102]) ).
fof(f196,plain,
( spl9_24
| ~ spl9_13
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f125,f122,f105,f194]) ).
fof(f125,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ spl9_13
| ~ spl9_16 ),
inference(superposition,[],[f123,f106]) ).
fof(f168,plain,
( spl9_23
| ~ spl9_7
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f139,f128,f77,f166]) ).
fof(f139,plain,
( ! [X0] :
( in(sK6(sK0,X0),X0)
| sK0 = X0
| sK6(sK0,X0) = unordered_pair(singleton(sK4(sK6(sK0,X0))),unordered_pair(sK5(sK6(sK0,X0)),sK4(sK6(sK0,X0)))) )
| ~ spl9_7
| ~ spl9_17 ),
inference(resolution,[],[f129,f78]) ).
fof(f164,plain,
( spl9_22
| ~ spl9_6
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f138,f128,f73,f162]) ).
fof(f138,plain,
( ! [X0] :
( in(sK6(sK1,X0),X0)
| sK1 = X0
| sK6(sK1,X0) = unordered_pair(singleton(sK2(sK6(sK1,X0))),unordered_pair(sK3(sK6(sK1,X0)),sK2(sK6(sK1,X0)))) )
| ~ spl9_6
| ~ spl9_17 ),
inference(resolution,[],[f129,f74]) ).
fof(f160,plain,
( spl9_21
| ~ spl9_7
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f136,f128,f77,f158]) ).
fof(f136,plain,
( ! [X0] :
( in(sK6(X0,sK0),X0)
| sK0 = X0
| sK6(X0,sK0) = unordered_pair(singleton(sK4(sK6(X0,sK0))),unordered_pair(sK5(sK6(X0,sK0)),sK4(sK6(X0,sK0)))) )
| ~ spl9_7
| ~ spl9_17 ),
inference(resolution,[],[f129,f78]) ).
fof(f156,plain,
( spl9_20
| ~ spl9_6
| ~ spl9_17 ),
inference(avatar_split_clause,[],[f135,f128,f73,f154]) ).
fof(f135,plain,
( ! [X0] :
( in(sK6(X0,sK1),X0)
| sK1 = X0
| sK6(X0,sK1) = unordered_pair(singleton(sK2(sK6(X0,sK1))),unordered_pair(sK3(sK6(X0,sK1)),sK2(sK6(X0,sK1)))) )
| ~ spl9_6
| ~ spl9_17 ),
inference(resolution,[],[f129,f74]) ).
fof(f148,plain,
( spl9_19
| ~ spl9_10
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f114,f105,f93,f146]) ).
fof(f114,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK1)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK0) )
| ~ spl9_10
| ~ spl9_13 ),
inference(superposition,[],[f94,f106]) ).
fof(f134,plain,
spl9_18,
inference(avatar_split_clause,[],[f37,f132]) ).
fof(f37,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) )
& ( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f20,f21]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) )
& ( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f130,plain,
spl9_17,
inference(avatar_split_clause,[],[f36,f128]) ).
fof(f36,plain,
! [X0,X1] :
( X0 = X1
| in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f124,plain,
( spl9_16
| ~ spl9_13
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f112,f109,f105,f122]) ).
fof(f109,plain,
( spl9_14
<=> ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f112,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
| ~ spl9_13
| ~ spl9_14 ),
inference(forward_demodulation,[],[f110,f106]) ).
fof(f110,plain,
( ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0)))
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f120,plain,
( spl9_15
| ~ spl9_11
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f113,f105,f97,f118]) ).
fof(f97,plain,
( spl9_11
<=> ! [X2,X3] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f113,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK0)
| in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK1) )
| ~ spl9_11
| ~ spl9_13 ),
inference(superposition,[],[f98,f106]) ).
fof(f98,plain,
( ! [X2,X3] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK1) )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f111,plain,
spl9_14,
inference(avatar_split_clause,[],[f44,f109]) ).
fof(f44,plain,
! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(definition_unfolding,[],[f32,f34]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f32,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f107,plain,
spl9_13,
inference(avatar_split_clause,[],[f33,f105]) ).
fof(f33,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f103,plain,
spl9_12,
inference(avatar_split_clause,[],[f35,f101]) ).
fof(f35,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,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(f99,plain,
( spl9_11
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f91,f87,f97]) ).
fof(f87,plain,
( spl9_9
<=> ! [X2,X3] :
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f91,plain,
( ! [X2,X3] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK1) )
| ~ spl9_9 ),
inference(forward_demodulation,[],[f90,f33]) ).
fof(f90,plain,
( ! [X2,X3] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK0) )
| ~ spl9_9 ),
inference(forward_demodulation,[],[f88,f33]) ).
fof(f88,plain,
( ! [X2,X3] :
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK0) )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f95,plain,
( spl9_10
| ~ spl9_8 ),
inference(avatar_split_clause,[],[f85,f81,f93]) ).
fof(f81,plain,
( spl9_8
<=> ! [X2,X3] :
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f85,plain,
( ! [X2,X3] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK0) )
| ~ spl9_8 ),
inference(forward_demodulation,[],[f84,f33]) ).
fof(f84,plain,
( ! [X2,X3] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sK0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK1) )
| ~ spl9_8 ),
inference(forward_demodulation,[],[f82,f33]) ).
fof(f82,plain,
( ! [X2,X3] :
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK1) )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f89,plain,
spl9_9,
inference(avatar_split_clause,[],[f41,f87]) ).
fof(f41,plain,
! [X2,X3] :
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK0) ),
inference(definition_unfolding,[],[f29,f34,f34]) ).
fof(f29,plain,
! [X2,X3] :
( in(ordered_pair(X2,X3),sK1)
| ~ in(ordered_pair(X2,X3),sK0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( sK0 != sK1
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),sK0)
| ~ in(ordered_pair(X2,X3),sK1) )
& ( in(ordered_pair(X2,X3),sK1)
| ~ in(ordered_pair(X2,X3),sK0) ) )
& ! [X4] :
( ordered_pair(sK2(X4),sK3(X4)) = X4
| ~ in(X4,sK1) )
& ! [X7] :
( ordered_pair(sK4(X7),sK5(X7)) = X7
| ~ in(X7,sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f15,f18,f17,f16]) ).
fof(f16,plain,
( ? [X0,X1] :
( X0 != X1
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X1) )
& ! [X7] :
( ? [X8,X9] : ordered_pair(X8,X9) = X7
| ~ in(X7,X0) ) )
=> ( sK0 != sK1
& ! [X3,X2] :
( ( in(ordered_pair(X2,X3),sK0)
| ~ in(ordered_pair(X2,X3),sK1) )
& ( in(ordered_pair(X2,X3),sK1)
| ~ in(ordered_pair(X2,X3),sK0) ) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,sK1) )
& ! [X7] :
( ? [X8,X9] : ordered_pair(X8,X9) = X7
| ~ in(X7,sK0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK2(X4),sK3(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X7] :
( ? [X8,X9] : ordered_pair(X8,X9) = X7
=> ordered_pair(sK4(X7),sK5(X7)) = X7 ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1] :
( X0 != X1
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X1) )
& ! [X7] :
( ? [X8,X9] : ordered_pair(X8,X9) = X7
| ~ in(X7,X0) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
? [X0,X1] :
( X0 != X1
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X1) )
& ! [X7] :
( ? [X8,X9] : ordered_pair(X8,X9) = X7
| ~ in(X7,X0) ) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
? [X0,X1] :
( X0 != X1
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X1) )
& ! [X7] :
( ? [X8,X9] : ordered_pair(X8,X9) = X7
| ~ in(X7,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
~ ! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X4] :
~ ( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X1) )
& ! [X7] :
~ ( ! [X8,X9] : ordered_pair(X8,X9) != X7
& in(X7,X0) ) )
=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X2
& in(X2,X1) )
& ! [X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X2
& in(X2,X0) ) )
=> X0 = X1 ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X2
& in(X2,X1) )
& ! [X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X2
& in(X2,X0) ) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
fof(f83,plain,
spl9_8,
inference(avatar_split_clause,[],[f40,f81]) ).
fof(f40,plain,
! [X2,X3] :
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sK1) ),
inference(definition_unfolding,[],[f30,f34,f34]) ).
fof(f30,plain,
! [X2,X3] :
( in(ordered_pair(X2,X3),sK0)
| ~ in(ordered_pair(X2,X3),sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f79,plain,
( spl9_7
| ~ spl9_5 ),
inference(avatar_split_clause,[],[f71,f67,f77]) ).
fof(f67,plain,
( spl9_5
<=> ! [X7] :
( unordered_pair(unordered_pair(sK4(X7),sK5(X7)),singleton(sK4(X7))) = X7
| ~ in(X7,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f71,plain,
( ! [X7] :
( unordered_pair(singleton(sK4(X7)),unordered_pair(sK5(X7),sK4(X7))) = X7
| ~ in(X7,sK0) )
| ~ spl9_5 ),
inference(forward_demodulation,[],[f70,f33]) ).
fof(f70,plain,
( ! [X7] :
( unordered_pair(singleton(sK4(X7)),unordered_pair(sK4(X7),sK5(X7))) = X7
| ~ in(X7,sK0) )
| ~ spl9_5 ),
inference(forward_demodulation,[],[f68,f33]) ).
fof(f68,plain,
( ! [X7] :
( unordered_pair(unordered_pair(sK4(X7),sK5(X7)),singleton(sK4(X7))) = X7
| ~ in(X7,sK0) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f75,plain,
( spl9_6
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f65,f61,f73]) ).
fof(f61,plain,
( spl9_4
<=> ! [X4] :
( unordered_pair(unordered_pair(sK2(X4),sK3(X4)),singleton(sK2(X4))) = X4
| ~ in(X4,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f65,plain,
( ! [X4] :
( unordered_pair(singleton(sK2(X4)),unordered_pair(sK3(X4),sK2(X4))) = X4
| ~ in(X4,sK1) )
| ~ spl9_4 ),
inference(forward_demodulation,[],[f64,f33]) ).
fof(f64,plain,
( ! [X4] :
( unordered_pair(singleton(sK2(X4)),unordered_pair(sK2(X4),sK3(X4))) = X4
| ~ in(X4,sK1) )
| ~ spl9_4 ),
inference(forward_demodulation,[],[f62,f33]) ).
fof(f62,plain,
( ! [X4] :
( unordered_pair(unordered_pair(sK2(X4),sK3(X4)),singleton(sK2(X4))) = X4
| ~ in(X4,sK1) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f69,plain,
spl9_5,
inference(avatar_split_clause,[],[f43,f67]) ).
fof(f43,plain,
! [X7] :
( unordered_pair(unordered_pair(sK4(X7),sK5(X7)),singleton(sK4(X7))) = X7
| ~ in(X7,sK0) ),
inference(definition_unfolding,[],[f27,f34]) ).
fof(f27,plain,
! [X7] :
( ordered_pair(sK4(X7),sK5(X7)) = X7
| ~ in(X7,sK0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f63,plain,
spl9_4,
inference(avatar_split_clause,[],[f42,f61]) ).
fof(f42,plain,
! [X4] :
( unordered_pair(unordered_pair(sK2(X4),sK3(X4)),singleton(sK2(X4))) = X4
| ~ in(X4,sK1) ),
inference(definition_unfolding,[],[f28,f34]) ).
fof(f28,plain,
! [X4] :
( ordered_pair(sK2(X4),sK3(X4)) = X4
| ~ in(X4,sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f59,plain,
spl9_3,
inference(avatar_split_clause,[],[f39,f56]) ).
fof(f56,plain,
( spl9_3
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f39,plain,
empty(sK8),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f5,f25]) ).
fof(f25,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f5,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f54,plain,
~ spl9_2,
inference(avatar_split_clause,[],[f38,f51]) ).
fof(f51,plain,
( spl9_2
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f38,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
~ empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f6,f23]) ).
fof(f23,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f6,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f49,plain,
~ spl9_1,
inference(avatar_split_clause,[],[f31,f46]) ).
fof(f31,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET959+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 01:39:58 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (31867)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (31870)WARNING: value z3 for option sas not known
% 0.11/0.34 % (31874)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)
% 0.11/0.34 % (31869)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 % (31873)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)
% 0.11/0.34 % (31868)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (31871)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (31870)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)
% 0.11/0.34 % (31872)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)
% 0.17/0.34 TRYING [1]
% 0.17/0.34 TRYING [2]
% 0.17/0.34 TRYING [1]
% 0.17/0.34 TRYING [3]
% 0.17/0.34 TRYING [2]
% 0.17/0.35 TRYING [3]
% 0.17/0.35 % (31872)First to succeed.
% 0.17/0.35 % (31873)Also succeeded, but the first one will report.
% 0.17/0.36 % (31872)Refutation found. Thanks to Tanya!
% 0.17/0.36 % SZS status Theorem for theBenchmark
% 0.17/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.36 % (31872)------------------------------
% 0.17/0.36 % (31872)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.36 % (31872)Termination reason: Refutation
% 0.17/0.36
% 0.17/0.36 % (31872)Memory used [KB]: 991
% 0.17/0.36 % (31872)Time elapsed: 0.015 s
% 0.17/0.36 % (31872)Instructions burned: 26 (million)
% 0.17/0.36 % (31872)------------------------------
% 0.17/0.36 % (31872)------------------------------
% 0.17/0.36 % (31867)Success in time 0.019 s
%------------------------------------------------------------------------------