TSTP Solution File: NUN086+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:45:08 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 124
% Syntax : Number of formulae : 416 ( 55 unt; 0 def)
% Number of atoms : 1265 ( 265 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1447 ( 598 ~; 587 |; 150 &)
% ( 93 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 99 ( 97 usr; 94 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-2 aty)
% Number of variables : 657 ( 561 !; 96 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f816,plain,
$false,
inference(avatar_sat_refutation,[],[f113,f117,f121,f125,f129,f133,f137,f141,f145,f149,f153,f157,f168,f172,f176,f180,f186,f191,f195,f200,f205,f209,f213,f223,f227,f231,f236,f241,f246,f250,f258,f262,f266,f270,f274,f298,f303,f307,f311,f315,f320,f325,f333,f337,f341,f348,f352,f356,f360,f374,f378,f382,f386,f398,f403,f407,f411,f415,f442,f455,f470,f474,f489,f496,f500,f507,f511,f527,f532,f537,f541,f571,f583,f587,f601,f605,f610,f614,f635,f639,f658,f662,f673,f678,f706,f710,f714,f755,f759,f763,f784,f788,f810,f815]) ).
fof(f815,plain,
( ~ spl20_1
| ~ spl20_70
| ~ spl20_93 ),
inference(avatar_split_clause,[],[f814,f808,f535,f110]) ).
fof(f110,plain,
( spl20_1
<=> r1(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).
fof(f535,plain,
( spl20_70
<=> ! [X0] : sK19 = sK10(X0,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_70])]) ).
fof(f808,plain,
( spl20_93
<=> ! [X0] :
( ~ r1(sK10(sK19,X0))
| ~ r1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_93])]) ).
fof(f814,plain,
( ~ r1(sK19)
| ~ spl20_70
| ~ spl20_93 ),
inference(duplicate_literal_removal,[],[f812]) ).
fof(f812,plain,
( ~ r1(sK19)
| ~ r1(sK19)
| ~ spl20_70
| ~ spl20_93 ),
inference(superposition,[],[f809,f536]) ).
fof(f536,plain,
( ! [X0] : sK19 = sK10(X0,sK19)
| ~ spl20_70 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f809,plain,
( ! [X0] :
( ~ r1(sK10(sK19,X0))
| ~ r1(X0) )
| ~ spl20_93 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f810,plain,
( ~ spl20_1
| spl20_93
| ~ spl20_43
| ~ spl20_74 ),
inference(avatar_split_clause,[],[f594,f585,f331,f808,f110]) ).
fof(f331,plain,
( spl20_43
<=> ! [X0,X1] :
( ~ r1(X0)
| ~ r1(sK11(X0,X1))
| ~ r1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_43])]) ).
fof(f585,plain,
( spl20_74
<=> ! [X0] : sK10(sK19,X0) = sK11(sK19,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_74])]) ).
fof(f594,plain,
( ! [X0] :
( ~ r1(sK10(sK19,X0))
| ~ r1(sK19)
| ~ r1(X0) )
| ~ spl20_43
| ~ spl20_74 ),
inference(superposition,[],[f332,f586]) ).
fof(f586,plain,
( ! [X0] : sK10(sK19,X0) = sK11(sK19,X0)
| ~ spl20_74 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f332,plain,
( ! [X0,X1] :
( ~ r1(sK11(X0,X1))
| ~ r1(X0)
| ~ r1(X1) )
| ~ spl20_43 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f788,plain,
( spl20_92
| ~ spl20_52
| ~ spl20_58
| ~ spl20_61 ),
inference(avatar_split_clause,[],[f484,f468,f413,f380,f786]) ).
fof(f786,plain,
( spl20_92
<=> ! [X0,X1] :
( sK15(X1,sK0(X0)) = sK14(X1,sK1(X0))
| sK2(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_92])]) ).
fof(f380,plain,
( spl20_52
<=> ! [X0,X1] : sK14(X0,X1) = sK18(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_52])]) ).
fof(f413,plain,
( spl20_58
<=> ! [X0,X1] : sK15(X0,X1) = sK18(X0,sK8(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_58])]) ).
fof(f468,plain,
( spl20_61
<=> ! [X0] :
( sK2(X0) = X0
| sK1(X0) = sK8(sK0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_61])]) ).
fof(f484,plain,
( ! [X0,X1] :
( sK15(X1,sK0(X0)) = sK14(X1,sK1(X0))
| sK2(X0) = X0 )
| ~ spl20_52
| ~ spl20_58
| ~ spl20_61 ),
inference(forward_demodulation,[],[f482,f381]) ).
fof(f381,plain,
( ! [X0,X1] : sK14(X0,X1) = sK18(X0,X1)
| ~ spl20_52 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f482,plain,
( ! [X0,X1] :
( sK15(X1,sK0(X0)) = sK18(X1,sK1(X0))
| sK2(X0) = X0 )
| ~ spl20_58
| ~ spl20_61 ),
inference(superposition,[],[f414,f469]) ).
fof(f469,plain,
( ! [X0] :
( sK1(X0) = sK8(sK0(X0))
| sK2(X0) = X0 )
| ~ spl20_61 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f414,plain,
( ! [X0,X1] : sK15(X0,X1) = sK18(X0,sK8(X1))
| ~ spl20_58 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f784,plain,
( spl20_91
| ~ spl20_51
| ~ spl20_57
| ~ spl20_61 ),
inference(avatar_split_clause,[],[f483,f468,f409,f376,f782]) ).
fof(f782,plain,
( spl20_91
<=> ! [X0,X1] :
( sK11(X1,sK0(X0)) = sK10(X1,sK1(X0))
| sK2(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_91])]) ).
fof(f376,plain,
( spl20_51
<=> ! [X0,X1] : sK10(X0,X1) = sK17(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_51])]) ).
fof(f409,plain,
( spl20_57
<=> ! [X0,X1] : sK11(X0,X1) = sK17(X0,sK8(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_57])]) ).
fof(f483,plain,
( ! [X0,X1] :
( sK11(X1,sK0(X0)) = sK10(X1,sK1(X0))
| sK2(X0) = X0 )
| ~ spl20_51
| ~ spl20_57
| ~ spl20_61 ),
inference(forward_demodulation,[],[f481,f377]) ).
fof(f377,plain,
( ! [X0,X1] : sK10(X0,X1) = sK17(X0,X1)
| ~ spl20_51 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f481,plain,
( ! [X0,X1] :
( sK11(X1,sK0(X0)) = sK17(X1,sK1(X0))
| sK2(X0) = X0 )
| ~ spl20_57
| ~ spl20_61 ),
inference(superposition,[],[f410,f469]) ).
fof(f410,plain,
( ! [X0,X1] : sK11(X0,X1) = sK17(X0,sK8(X1))
| ~ spl20_57 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f763,plain,
( spl20_90
| ~ spl20_29
| ~ spl20_61 ),
inference(avatar_split_clause,[],[f478,f468,f244,f761]) ).
fof(f761,plain,
( spl20_90
<=> ! [X0,X1] :
( r3(X1,sK1(X0),sK15(X1,sK0(X0)))
| sK2(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_90])]) ).
fof(f244,plain,
( spl20_29
<=> ! [X0,X1] : r3(X0,sK8(X1),sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_29])]) ).
fof(f478,plain,
( ! [X0,X1] :
( r3(X1,sK1(X0),sK15(X1,sK0(X0)))
| sK2(X0) = X0 )
| ~ spl20_29
| ~ spl20_61 ),
inference(superposition,[],[f245,f469]) ).
fof(f245,plain,
( ! [X0,X1] : r3(X0,sK8(X1),sK15(X0,X1))
| ~ spl20_29 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f759,plain,
( spl20_89
| ~ spl20_27
| ~ spl20_61 ),
inference(avatar_split_clause,[],[f477,f468,f234,f757]) ).
fof(f757,plain,
( spl20_89
<=> ! [X0,X1] :
( r4(X1,sK1(X0),sK11(X1,sK0(X0)))
| sK2(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_89])]) ).
fof(f234,plain,
( spl20_27
<=> ! [X0,X1] : r4(X0,sK8(X1),sK11(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_27])]) ).
fof(f477,plain,
( ! [X0,X1] :
( r4(X1,sK1(X0),sK11(X1,sK0(X0)))
| sK2(X0) = X0 )
| ~ spl20_27
| ~ spl20_61 ),
inference(superposition,[],[f235,f469]) ).
fof(f235,plain,
( ! [X0,X1] : r4(X0,sK8(X1),sK11(X0,X1))
| ~ spl20_27 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f755,plain,
( spl20_88
| ~ spl20_1
| ~ spl20_48
| ~ spl20_77 ),
inference(avatar_split_clause,[],[f666,f607,f354,f110,f752]) ).
fof(f752,plain,
( spl20_88
<=> r1(sK2(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_88])]) ).
fof(f354,plain,
( spl20_48
<=> ! [X0] :
( r1(sK2(X0))
| ~ r1(sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_48])]) ).
fof(f607,plain,
( spl20_77
<=> sK19 = sK1(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_77])]) ).
fof(f666,plain,
( ~ r1(sK19)
| r1(sK2(sK19))
| ~ spl20_48
| ~ spl20_77 ),
inference(superposition,[],[f355,f609]) ).
fof(f609,plain,
( sK19 = sK1(sK19)
| ~ spl20_77 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f355,plain,
( ! [X0] :
( ~ r1(sK1(X0))
| r1(sK2(X0)) )
| ~ spl20_48 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f714,plain,
( spl20_87
| ~ spl20_58
| ~ spl20_60 ),
inference(avatar_split_clause,[],[f462,f453,f413,f712]) ).
fof(f712,plain,
( spl20_87
<=> ! [X0,X1] : sK15(sK10(sK8(X0),X1),X0) = sK11(sK8(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_87])]) ).
fof(f453,plain,
( spl20_60
<=> ! [X0,X1] : sK11(X0,X1) = sK18(sK10(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_60])]) ).
fof(f462,plain,
( ! [X0,X1] : sK15(sK10(sK8(X0),X1),X0) = sK11(sK8(X0),X1)
| ~ spl20_58
| ~ spl20_60 ),
inference(superposition,[],[f454,f414]) ).
fof(f454,plain,
( ! [X0,X1] : sK11(X0,X1) = sK18(sK10(X0,X1),X0)
| ~ spl20_60 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f710,plain,
( spl20_86
| ~ spl20_52
| ~ spl20_56
| ~ spl20_58 ),
inference(avatar_split_clause,[],[f438,f413,f405,f380,f708]) ).
fof(f708,plain,
( spl20_86
<=> ! [X2,X0,X1] : sK15(X2,sK14(X0,X1)) = sK14(X2,sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_86])]) ).
fof(f405,plain,
( spl20_56
<=> ! [X0,X1] : sK15(X0,X1) = sK8(sK14(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_56])]) ).
fof(f438,plain,
( ! [X2,X0,X1] : sK15(X2,sK14(X0,X1)) = sK14(X2,sK15(X0,X1))
| ~ spl20_52
| ~ spl20_56
| ~ spl20_58 ),
inference(forward_demodulation,[],[f434,f381]) ).
fof(f434,plain,
( ! [X2,X0,X1] : sK15(X2,sK14(X0,X1)) = sK18(X2,sK15(X0,X1))
| ~ spl20_56
| ~ spl20_58 ),
inference(superposition,[],[f414,f406]) ).
fof(f406,plain,
( ! [X0,X1] : sK15(X0,X1) = sK8(sK14(X0,X1))
| ~ spl20_56 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f706,plain,
( spl20_85
| ~ spl20_51
| ~ spl20_56
| ~ spl20_57 ),
inference(avatar_split_clause,[],[f433,f409,f405,f376,f704]) ).
fof(f704,plain,
( spl20_85
<=> ! [X2,X0,X1] : sK11(X2,sK14(X0,X1)) = sK10(X2,sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_85])]) ).
fof(f433,plain,
( ! [X2,X0,X1] : sK11(X2,sK14(X0,X1)) = sK10(X2,sK15(X0,X1))
| ~ spl20_51
| ~ spl20_56
| ~ spl20_57 ),
inference(forward_demodulation,[],[f428,f377]) ).
fof(f428,plain,
( ! [X2,X0,X1] : sK11(X2,sK14(X0,X1)) = sK17(X2,sK15(X0,X1))
| ~ spl20_56
| ~ spl20_57 ),
inference(superposition,[],[f410,f406]) ).
fof(f678,plain,
( spl20_84
| ~ spl20_10
| ~ spl20_59 ),
inference(avatar_split_clause,[],[f457,f440,f147,f676]) ).
fof(f676,plain,
( spl20_84
<=> ! [X0] :
( sK1(X0) = sK8(sK0(X0))
| sK2(X0) = sK19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_84])]) ).
fof(f147,plain,
( spl20_10
<=> ! [X1] :
( sK19 = X1
| ~ r1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_10])]) ).
fof(f440,plain,
( spl20_59
<=> ! [X0] :
( r1(sK2(X0))
| sK1(X0) = sK8(sK0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_59])]) ).
fof(f457,plain,
( ! [X0] :
( sK1(X0) = sK8(sK0(X0))
| sK2(X0) = sK19 )
| ~ spl20_10
| ~ spl20_59 ),
inference(resolution,[],[f441,f148]) ).
fof(f148,plain,
( ! [X1] :
( ~ r1(X1)
| sK19 = X1 )
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f441,plain,
( ! [X0] :
( r1(sK2(X0))
| sK1(X0) = sK8(sK0(X0)) )
| ~ spl20_59 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f673,plain,
( spl20_83
| ~ spl20_27
| ~ spl20_56 ),
inference(avatar_split_clause,[],[f426,f405,f234,f671]) ).
fof(f671,plain,
( spl20_83
<=> ! [X2,X0,X1] : r4(X2,sK15(X0,X1),sK11(X2,sK14(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_83])]) ).
fof(f426,plain,
( ! [X2,X0,X1] : r4(X2,sK15(X0,X1),sK11(X2,sK14(X0,X1)))
| ~ spl20_27
| ~ spl20_56 ),
inference(superposition,[],[f235,f406]) ).
fof(f662,plain,
( spl20_82
| ~ spl20_29
| ~ spl20_56 ),
inference(avatar_split_clause,[],[f425,f405,f244,f660]) ).
fof(f660,plain,
( spl20_82
<=> ! [X2,X0,X1] : r3(X2,sK15(X0,X1),sK15(X2,sK14(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_82])]) ).
fof(f425,plain,
( ! [X2,X0,X1] : r3(X2,sK15(X0,X1),sK15(X2,sK14(X0,X1)))
| ~ spl20_29
| ~ spl20_56 ),
inference(superposition,[],[f245,f406]) ).
fof(f658,plain,
( spl20_81
| ~ spl20_49
| ~ spl20_50 ),
inference(avatar_split_clause,[],[f387,f372,f358,f656]) ).
fof(f656,plain,
( spl20_81
<=> ! [X0] :
( sK2(X0) = X0
| sK1(X0) = sK1(sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_81])]) ).
fof(f358,plain,
( spl20_49
<=> ! [X0] :
( r1(X0)
| sK1(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_49])]) ).
fof(f372,plain,
( spl20_50
<=> ! [X0] :
( sK2(X0) = X0
| ~ r1(sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_50])]) ).
fof(f387,plain,
( ! [X0] :
( sK2(X0) = X0
| sK1(X0) = sK1(sK1(X0)) )
| ~ spl20_49
| ~ spl20_50 ),
inference(resolution,[],[f373,f359]) ).
fof(f359,plain,
( ! [X0] :
( r1(X0)
| sK1(X0) = X0 )
| ~ spl20_49 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f373,plain,
( ! [X0] :
( ~ r1(sK1(X0))
| sK2(X0) = X0 )
| ~ spl20_50 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f639,plain,
( spl20_80
| ~ spl20_52
| ~ spl20_60 ),
inference(avatar_split_clause,[],[f461,f453,f380,f637]) ).
fof(f637,plain,
( spl20_80
<=> ! [X0,X1] : sK11(X0,X1) = sK14(sK10(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_80])]) ).
fof(f461,plain,
( ! [X0,X1] : sK11(X0,X1) = sK14(sK10(X0,X1),X0)
| ~ spl20_52
| ~ spl20_60 ),
inference(superposition,[],[f454,f381]) ).
fof(f635,plain,
( spl20_79
| ~ spl20_48
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f364,f358,f354,f633]) ).
fof(f633,plain,
( spl20_79
<=> ! [X0] :
( sK1(X0) = sK1(sK1(X0))
| r1(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_79])]) ).
fof(f364,plain,
( ! [X0] :
( sK1(X0) = sK1(sK1(X0))
| r1(sK2(X0)) )
| ~ spl20_48
| ~ spl20_49 ),
inference(resolution,[],[f359,f355]) ).
fof(f614,plain,
( spl20_78
| ~ spl20_52
| ~ spl20_58 ),
inference(avatar_split_clause,[],[f435,f413,f380,f612]) ).
fof(f612,plain,
( spl20_78
<=> ! [X0,X1] : sK15(X0,X1) = sK14(X0,sK8(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_78])]) ).
fof(f435,plain,
( ! [X0,X1] : sK15(X0,X1) = sK14(X0,sK8(X1))
| ~ spl20_52
| ~ spl20_58 ),
inference(superposition,[],[f414,f381]) ).
fof(f610,plain,
( spl20_77
| ~ spl20_3
| ~ spl20_37
| ~ spl20_45
| ~ spl20_60
| ~ spl20_65
| ~ spl20_70 ),
inference(avatar_split_clause,[],[f551,f535,f498,f453,f339,f301,f119,f607]) ).
fof(f119,plain,
( spl20_3
<=> ! [X0] : r1(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_3])]) ).
fof(f301,plain,
( spl20_37
<=> ! [X0] : sK4(X0) = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_37])]) ).
fof(f339,plain,
( spl20_45
<=> ! [X0] : sK18(X0,sK19) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_45])]) ).
fof(f498,plain,
( spl20_65
<=> ! [X0] :
( sK11(X0,sK19) = sK1(sK11(X0,sK19))
| ~ r1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_65])]) ).
fof(f551,plain,
( sK19 = sK1(sK19)
| ~ spl20_3
| ~ spl20_37
| ~ spl20_45
| ~ spl20_60
| ~ spl20_65
| ~ spl20_70 ),
inference(forward_demodulation,[],[f550,f536]) ).
fof(f550,plain,
( sK10(sK19,sK19) = sK1(sK10(sK19,sK19))
| ~ spl20_3
| ~ spl20_37
| ~ spl20_45
| ~ spl20_60
| ~ spl20_65 ),
inference(forward_demodulation,[],[f549,f460]) ).
fof(f460,plain,
( ! [X0] : sK10(sK19,X0) = sK11(sK19,X0)
| ~ spl20_45
| ~ spl20_60 ),
inference(superposition,[],[f454,f340]) ).
fof(f340,plain,
( ! [X0] : sK18(X0,sK19) = X0
| ~ spl20_45 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f549,plain,
( sK11(sK19,sK19) = sK1(sK11(sK19,sK19))
| ~ spl20_3
| ~ spl20_37
| ~ spl20_65 ),
inference(forward_demodulation,[],[f545,f302]) ).
fof(f302,plain,
( ! [X0] : sK4(X0) = sK19
| ~ spl20_37 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f545,plain,
( ! [X0] : sK11(sK4(X0),sK19) = sK1(sK11(sK4(X0),sK19))
| ~ spl20_3
| ~ spl20_65 ),
inference(resolution,[],[f499,f120]) ).
fof(f120,plain,
( ! [X0] : r1(sK4(X0))
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f499,plain,
( ! [X0] :
( ~ r1(X0)
| sK11(X0,sK19) = sK1(sK11(X0,sK19)) )
| ~ spl20_65 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f605,plain,
( spl20_76
| ~ spl20_51
| ~ spl20_57 ),
inference(avatar_split_clause,[],[f429,f409,f376,f603]) ).
fof(f603,plain,
( spl20_76
<=> ! [X0,X1] : sK11(X0,X1) = sK10(X0,sK8(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_76])]) ).
fof(f429,plain,
( ! [X0,X1] : sK11(X0,X1) = sK10(X0,sK8(X1))
| ~ spl20_51
| ~ spl20_57 ),
inference(superposition,[],[f410,f377]) ).
fof(f601,plain,
( spl20_75
| ~ spl20_42
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f368,f358,f323,f599]) ).
fof(f599,plain,
( spl20_75
<=> ! [X0,X1] : sK15(X0,X1) = sK1(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_75])]) ).
fof(f323,plain,
( spl20_42
<=> ! [X0,X1] : ~ r1(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_42])]) ).
fof(f368,plain,
( ! [X0,X1] : sK15(X0,X1) = sK1(sK15(X0,X1))
| ~ spl20_42
| ~ spl20_49 ),
inference(resolution,[],[f359,f324]) ).
fof(f324,plain,
( ! [X0,X1] : ~ r1(sK15(X0,X1))
| ~ spl20_42 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f587,plain,
( spl20_74
| ~ spl20_45
| ~ spl20_60 ),
inference(avatar_split_clause,[],[f460,f453,f339,f585]) ).
fof(f583,plain,
( spl20_73
| ~ spl20_10
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f363,f358,f147,f581]) ).
fof(f581,plain,
( spl20_73
<=> ! [X0] :
( sK1(X0) = X0
| sK19 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_73])]) ).
fof(f363,plain,
( ! [X0] :
( sK1(X0) = X0
| sK19 = X0 )
| ~ spl20_10
| ~ spl20_49 ),
inference(resolution,[],[f359,f148]) ).
fof(f571,plain,
( spl20_72
| ~ spl20_13
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f365,f358,f166,f569]) ).
fof(f569,plain,
( spl20_72
<=> ! [X0] : sK8(X0) = sK1(sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_72])]) ).
fof(f166,plain,
( spl20_13
<=> ! [X0] : ~ r1(sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_13])]) ).
fof(f365,plain,
( ! [X0] : sK8(X0) = sK1(sK8(X0))
| ~ spl20_13
| ~ spl20_49 ),
inference(resolution,[],[f359,f167]) ).
fof(f167,plain,
( ! [X0] : ~ r1(sK8(X0))
| ~ spl20_13 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f541,plain,
( spl20_71
| ~ spl20_45
| ~ spl20_52 ),
inference(avatar_split_clause,[],[f392,f380,f339,f539]) ).
fof(f539,plain,
( spl20_71
<=> ! [X0] : sK14(X0,sK19) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_71])]) ).
fof(f392,plain,
( ! [X0] : sK14(X0,sK19) = X0
| ~ spl20_45
| ~ spl20_52 ),
inference(superposition,[],[f381,f340]) ).
fof(f537,plain,
( spl20_70
| ~ spl20_44
| ~ spl20_51 ),
inference(avatar_split_clause,[],[f388,f376,f335,f535]) ).
fof(f335,plain,
( spl20_44
<=> ! [X0] : sK19 = sK17(X0,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_44])]) ).
fof(f388,plain,
( ! [X0] : sK19 = sK10(X0,sK19)
| ~ spl20_44
| ~ spl20_51 ),
inference(superposition,[],[f377,f336]) ).
fof(f336,plain,
( ! [X0] : sK19 = sK17(X0,sK19)
| ~ spl20_44 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f532,plain,
( spl20_69
| ~ spl20_36
| ~ spl20_61 ),
inference(avatar_split_clause,[],[f479,f468,f296,f530]) ).
fof(f530,plain,
( spl20_69
<=> ! [X2,X0,X1] :
( ~ r2(X1,sK1(X0))
| ~ r1(X2)
| ~ r1(sK11(X2,sK0(X0)))
| ~ r1(X1)
| sK2(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_69])]) ).
fof(f296,plain,
( spl20_36
<=> ! [X2,X0,X1] :
( ~ r1(sK11(X0,X1))
| ~ r1(X0)
| ~ r2(X2,sK8(X1))
| ~ r1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_36])]) ).
fof(f479,plain,
( ! [X2,X0,X1] :
( ~ r2(X1,sK1(X0))
| ~ r1(X2)
| ~ r1(sK11(X2,sK0(X0)))
| ~ r1(X1)
| sK2(X0) = X0 )
| ~ spl20_36
| ~ spl20_61 ),
inference(superposition,[],[f297,f469]) ).
fof(f297,plain,
( ! [X2,X0,X1] :
( ~ r2(X2,sK8(X1))
| ~ r1(X0)
| ~ r1(sK11(X0,X1))
| ~ r1(X2) )
| ~ spl20_36 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f527,plain,
( spl20_68
| ~ spl20_12
| ~ spl20_39 ),
inference(avatar_split_clause,[],[f328,f309,f155,f525]) ).
fof(f525,plain,
( spl20_68
<=> ! [X0] : r3(X0,sK19,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_68])]) ).
fof(f155,plain,
( spl20_12
<=> ! [X0] : r3(X0,sK7(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_12])]) ).
fof(f309,plain,
( spl20_39
<=> ! [X0] : sK7(X0) = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_39])]) ).
fof(f328,plain,
( ! [X0] : r3(X0,sK19,X0)
| ~ spl20_12
| ~ spl20_39 ),
inference(superposition,[],[f156,f310]) ).
fof(f310,plain,
( ! [X0] : sK7(X0) = sK19
| ~ spl20_39 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f156,plain,
( ! [X0] : r3(X0,sK7(X0),X0)
| ~ spl20_12 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f511,plain,
( spl20_67
| ~ spl20_36
| ~ spl20_56 ),
inference(avatar_split_clause,[],[f424,f405,f296,f509]) ).
fof(f509,plain,
( spl20_67
<=> ! [X0,X3,X2,X1] :
( ~ r2(X2,sK15(X0,X1))
| ~ r1(X3)
| ~ r1(sK11(X3,sK14(X0,X1)))
| ~ r1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_67])]) ).
fof(f424,plain,
( ! [X2,X3,X0,X1] :
( ~ r2(X2,sK15(X0,X1))
| ~ r1(X3)
| ~ r1(sK11(X3,sK14(X0,X1)))
| ~ r1(X2) )
| ~ spl20_36
| ~ spl20_56 ),
inference(superposition,[],[f297,f406]) ).
fof(f507,plain,
( spl20_66
| ~ spl20_20
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f366,f358,f198,f505]) ).
fof(f505,plain,
( spl20_66
<=> ! [X2,X0,X1] :
( sK10(X0,X1) = sK1(sK10(X0,X1))
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_66])]) ).
fof(f198,plain,
( spl20_20
<=> ! [X2,X0,X1] :
( ~ r1(sK10(X0,X1))
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_20])]) ).
fof(f366,plain,
( ! [X2,X0,X1] :
( sK10(X0,X1) = sK1(sK10(X0,X1))
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r1(X2) )
| ~ spl20_20
| ~ spl20_49 ),
inference(resolution,[],[f359,f199]) ).
fof(f199,plain,
( ! [X2,X0,X1] :
( ~ r1(sK10(X0,X1))
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r1(X2) )
| ~ spl20_20 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f500,plain,
( spl20_65
| ~ spl20_3
| ~ spl20_37
| ~ spl20_54 ),
inference(avatar_split_clause,[],[f449,f396,f301,f119,f498]) ).
fof(f396,plain,
( spl20_54
<=> ! [X0,X1] :
( sK11(X0,X1) = sK1(sK11(X0,X1))
| ~ r1(X0)
| ~ r1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_54])]) ).
fof(f449,plain,
( ! [X0] :
( sK11(X0,sK19) = sK1(sK11(X0,sK19))
| ~ r1(X0) )
| ~ spl20_3
| ~ spl20_37
| ~ spl20_54 ),
inference(forward_demodulation,[],[f445,f302]) ).
fof(f445,plain,
( ! [X0,X1] :
( ~ r1(X0)
| sK11(X0,sK4(X1)) = sK1(sK11(X0,sK4(X1))) )
| ~ spl20_3
| ~ spl20_54 ),
inference(resolution,[],[f397,f120]) ).
fof(f397,plain,
( ! [X0,X1] :
( ~ r1(X1)
| ~ r1(X0)
| sK11(X0,X1) = sK1(sK11(X0,X1)) )
| ~ spl20_54 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f496,plain,
( spl20_64
| ~ spl20_32
| ~ spl20_35 ),
inference(avatar_split_clause,[],[f291,f272,f260,f494]) ).
fof(f494,plain,
( spl20_64
<=> ! [X0,X1] :
( sK0(X1) = X0
| ~ r2(X0,sK1(X1))
| sK2(X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_64])]) ).
fof(f260,plain,
( spl20_32
<=> ! [X0] :
( r2(sK0(X0),sK1(X0))
| sK2(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_32])]) ).
fof(f272,plain,
( spl20_35
<=> ! [X0,X1,X3] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_35])]) ).
fof(f291,plain,
( ! [X0,X1] :
( sK0(X1) = X0
| ~ r2(X0,sK1(X1))
| sK2(X1) = X1 )
| ~ spl20_32
| ~ spl20_35 ),
inference(resolution,[],[f273,f261]) ).
fof(f261,plain,
( ! [X0] :
( r2(sK0(X0),sK1(X0))
| sK2(X0) = X0 )
| ~ spl20_32 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f273,plain,
( ! [X3,X0,X1] :
( ~ r2(X1,X3)
| X0 = X1
| ~ r2(X0,X3) )
| ~ spl20_35 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f489,plain,
( spl20_63
| ~ spl20_24
| ~ spl20_35 ),
inference(avatar_split_clause,[],[f292,f272,f221,f487]) ).
fof(f487,plain,
( spl20_63
<=> ! [X0,X1] :
( sK0(X1) = X0
| ~ r2(X0,sK1(X1))
| r1(sK2(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_63])]) ).
fof(f221,plain,
( spl20_24
<=> ! [X0] :
( r2(sK0(X0),sK1(X0))
| r1(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_24])]) ).
fof(f292,plain,
( ! [X0,X1] :
( sK0(X1) = X0
| ~ r2(X0,sK1(X1))
| r1(sK2(X1)) )
| ~ spl20_24
| ~ spl20_35 ),
inference(resolution,[],[f273,f222]) ).
fof(f222,plain,
( ! [X0] :
( r2(sK0(X0),sK1(X0))
| r1(sK2(X0)) )
| ~ spl20_24 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f474,plain,
( spl20_62
| ~ spl20_23
| ~ spl20_35 ),
inference(avatar_split_clause,[],[f290,f272,f211,f472]) ).
fof(f472,plain,
( spl20_62
<=> ! [X2,X0,X1] :
( sK14(X1,X2) = X0
| ~ r2(X0,sK15(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_62])]) ).
fof(f211,plain,
( spl20_23
<=> ! [X0,X1] : r2(sK14(X0,X1),sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_23])]) ).
fof(f290,plain,
( ! [X2,X0,X1] :
( sK14(X1,X2) = X0
| ~ r2(X0,sK15(X1,X2)) )
| ~ spl20_23
| ~ spl20_35 ),
inference(resolution,[],[f273,f212]) ).
fof(f212,plain,
( ! [X0,X1] : r2(sK14(X0,X1),sK15(X0,X1))
| ~ spl20_23 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f470,plain,
( spl20_61
| ~ spl20_22
| ~ spl20_32 ),
inference(avatar_split_clause,[],[f275,f260,f207,f468]) ).
fof(f207,plain,
( spl20_22
<=> ! [X2,X0] :
( sK8(X0) = X2
| ~ r2(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_22])]) ).
fof(f275,plain,
( ! [X0] :
( sK2(X0) = X0
| sK1(X0) = sK8(sK0(X0)) )
| ~ spl20_22
| ~ spl20_32 ),
inference(resolution,[],[f261,f208]) ).
fof(f208,plain,
( ! [X2,X0] :
( ~ r2(X0,X2)
| sK8(X0) = X2 )
| ~ spl20_22 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f455,plain,
( spl20_60
| ~ spl20_30
| ~ spl20_34 ),
inference(avatar_split_clause,[],[f285,f268,f248,f453]) ).
fof(f248,plain,
( spl20_30
<=> ! [X0,X1] : r3(sK10(X0,X1),X0,sK11(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_30])]) ).
fof(f268,plain,
( spl20_34
<=> ! [X0,X1,X3] :
( sK18(X0,X1) = X3
| ~ r3(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_34])]) ).
fof(f285,plain,
( ! [X0,X1] : sK11(X0,X1) = sK18(sK10(X0,X1),X0)
| ~ spl20_30
| ~ spl20_34 ),
inference(resolution,[],[f269,f249]) ).
fof(f249,plain,
( ! [X0,X1] : r3(sK10(X0,X1),X0,sK11(X0,X1))
| ~ spl20_30 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f269,plain,
( ! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK18(X0,X1) = X3 )
| ~ spl20_34 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f442,plain,
( spl20_59
| ~ spl20_22
| ~ spl20_24 ),
inference(avatar_split_clause,[],[f251,f221,f207,f440]) ).
fof(f251,plain,
( ! [X0] :
( r1(sK2(X0))
| sK1(X0) = sK8(sK0(X0)) )
| ~ spl20_22
| ~ spl20_24 ),
inference(resolution,[],[f222,f208]) ).
fof(f415,plain,
( spl20_58
| ~ spl20_29
| ~ spl20_34 ),
inference(avatar_split_clause,[],[f284,f268,f244,f413]) ).
fof(f284,plain,
( ! [X0,X1] : sK15(X0,X1) = sK18(X0,sK8(X1))
| ~ spl20_29
| ~ spl20_34 ),
inference(resolution,[],[f269,f245]) ).
fof(f411,plain,
( spl20_57
| ~ spl20_27
| ~ spl20_33 ),
inference(avatar_split_clause,[],[f280,f264,f234,f409]) ).
fof(f264,plain,
( spl20_33
<=> ! [X0,X1,X3] :
( sK17(X0,X1) = X3
| ~ r4(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_33])]) ).
fof(f280,plain,
( ! [X0,X1] : sK11(X0,X1) = sK17(X0,sK8(X1))
| ~ spl20_27
| ~ spl20_33 ),
inference(resolution,[],[f265,f235]) ).
fof(f265,plain,
( ! [X3,X0,X1] :
( ~ r4(X0,X1,X3)
| sK17(X0,X1) = X3 )
| ~ spl20_33 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f407,plain,
( spl20_56
| ~ spl20_22
| ~ spl20_23 ),
inference(avatar_split_clause,[],[f218,f211,f207,f405]) ).
fof(f218,plain,
( ! [X0,X1] : sK15(X0,X1) = sK8(sK14(X0,X1))
| ~ spl20_22
| ~ spl20_23 ),
inference(resolution,[],[f212,f208]) ).
fof(f403,plain,
( spl20_55
| ~ spl20_10
| ~ spl20_21 ),
inference(avatar_split_clause,[],[f214,f203,f147,f401]) ).
fof(f401,plain,
( spl20_55
<=> ! [X0] :
( sK1(X0) = X0
| sK2(X0) = sK19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_55])]) ).
fof(f203,plain,
( spl20_21
<=> ! [X0] :
( sK1(X0) = X0
| r1(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_21])]) ).
fof(f214,plain,
( ! [X0] :
( sK1(X0) = X0
| sK2(X0) = sK19 )
| ~ spl20_10
| ~ spl20_21 ),
inference(resolution,[],[f204,f148]) ).
fof(f204,plain,
( ! [X0] :
( r1(sK2(X0))
| sK1(X0) = X0 )
| ~ spl20_21 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f398,plain,
( spl20_54
| ~ spl20_43
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f367,f358,f331,f396]) ).
fof(f367,plain,
( ! [X0,X1] :
( sK11(X0,X1) = sK1(sK11(X0,X1))
| ~ r1(X0)
| ~ r1(X1) )
| ~ spl20_43
| ~ spl20_49 ),
inference(resolution,[],[f359,f332]) ).
fof(f386,plain,
( spl20_53
| ~ spl20_7
| ~ spl20_35 ),
inference(avatar_split_clause,[],[f287,f272,f135,f384]) ).
fof(f384,plain,
( spl20_53
<=> ! [X0,X1] :
( X0 = X1
| ~ r2(X0,sK8(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_53])]) ).
fof(f135,plain,
( spl20_7
<=> ! [X0] : r2(X0,sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_7])]) ).
fof(f287,plain,
( ! [X0,X1] :
( X0 = X1
| ~ r2(X0,sK8(X1)) )
| ~ spl20_7
| ~ spl20_35 ),
inference(resolution,[],[f273,f136]) ).
fof(f136,plain,
( ! [X0] : r2(X0,sK8(X0))
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f382,plain,
( spl20_52
| ~ spl20_15
| ~ spl20_34 ),
inference(avatar_split_clause,[],[f282,f268,f174,f380]) ).
fof(f174,plain,
( spl20_15
<=> ! [X0,X1] : r3(X0,X1,sK14(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_15])]) ).
fof(f282,plain,
( ! [X0,X1] : sK14(X0,X1) = sK18(X0,X1)
| ~ spl20_15
| ~ spl20_34 ),
inference(resolution,[],[f269,f175]) ).
fof(f175,plain,
( ! [X0,X1] : r3(X0,X1,sK14(X0,X1))
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f378,plain,
( spl20_51
| ~ spl20_14
| ~ spl20_33 ),
inference(avatar_split_clause,[],[f278,f264,f170,f376]) ).
fof(f170,plain,
( spl20_14
<=> ! [X0,X1] : r4(X0,X1,sK10(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_14])]) ).
fof(f278,plain,
( ! [X0,X1] : sK10(X0,X1) = sK17(X0,X1)
| ~ spl20_14
| ~ spl20_33 ),
inference(resolution,[],[f265,f171]) ).
fof(f171,plain,
( ! [X0,X1] : r4(X0,X1,sK10(X0,X1))
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f374,plain,
( spl20_50
| ~ spl20_11
| ~ spl20_32 ),
inference(avatar_split_clause,[],[f276,f260,f151,f372]) ).
fof(f151,plain,
( spl20_11
<=> ! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_11])]) ).
fof(f276,plain,
( ! [X0] :
( sK2(X0) = X0
| ~ r1(sK1(X0)) )
| ~ spl20_11
| ~ spl20_32 ),
inference(resolution,[],[f261,f152]) ).
fof(f152,plain,
( ! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) )
| ~ spl20_11 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f360,plain,
( spl20_49
| ~ spl20_21
| ~ spl20_25 ),
inference(avatar_split_clause,[],[f254,f225,f203,f358]) ).
fof(f225,plain,
( spl20_25
<=> ! [X0] :
( sK1(X0) = X0
| sK2(X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_25])]) ).
fof(f254,plain,
( ! [X0] :
( r1(X0)
| sK1(X0) = X0 )
| ~ spl20_21
| ~ spl20_25 ),
inference(duplicate_literal_removal,[],[f253]) ).
fof(f253,plain,
( ! [X0] :
( r1(X0)
| sK1(X0) = X0
| sK1(X0) = X0 )
| ~ spl20_21
| ~ spl20_25 ),
inference(superposition,[],[f204,f226]) ).
fof(f226,plain,
( ! [X0] :
( sK2(X0) = X0
| sK1(X0) = X0 )
| ~ spl20_25 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f356,plain,
( spl20_48
| ~ spl20_11
| ~ spl20_24 ),
inference(avatar_split_clause,[],[f252,f221,f151,f354]) ).
fof(f252,plain,
( ! [X0] :
( r1(sK2(X0))
| ~ r1(sK1(X0)) )
| ~ spl20_11
| ~ spl20_24 ),
inference(resolution,[],[f222,f152]) ).
fof(f352,plain,
( spl20_47
| ~ spl20_9
| ~ spl20_22 ),
inference(avatar_split_clause,[],[f217,f207,f143,f350]) ).
fof(f350,plain,
( spl20_47
<=> ! [X0,X1] : sK8(X0) = sK16(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_47])]) ).
fof(f143,plain,
( spl20_9
<=> ! [X0,X1] : r2(X1,sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_9])]) ).
fof(f217,plain,
( ! [X0,X1] : sK8(X0) = sK16(X1,X0)
| ~ spl20_9
| ~ spl20_22 ),
inference(resolution,[],[f208,f144]) ).
fof(f144,plain,
( ! [X0,X1] : r2(X1,sK16(X0,X1))
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f348,plain,
( spl20_46
| ~ spl20_8
| ~ spl20_22 ),
inference(avatar_split_clause,[],[f216,f207,f139,f346]) ).
fof(f346,plain,
( spl20_46
<=> ! [X0,X1] : sK8(X0) = sK12(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_46])]) ).
fof(f139,plain,
( spl20_8
<=> ! [X0,X1] : r2(X1,sK12(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_8])]) ).
fof(f216,plain,
( ! [X0,X1] : sK8(X0) = sK12(X1,X0)
| ~ spl20_8
| ~ spl20_22 ),
inference(resolution,[],[f208,f140]) ).
fof(f140,plain,
( ! [X0,X1] : r2(X1,sK12(X0,X1))
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f341,plain,
( spl20_45
| ~ spl20_4
| ~ spl20_10
| ~ spl20_12
| ~ spl20_34 ),
inference(avatar_split_clause,[],[f286,f268,f155,f147,f123,f339]) ).
fof(f123,plain,
( spl20_4
<=> ! [X0] : r1(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_4])]) ).
fof(f286,plain,
( ! [X0] : sK18(X0,sK19) = X0
| ~ spl20_4
| ~ spl20_10
| ~ spl20_12
| ~ spl20_34 ),
inference(forward_demodulation,[],[f281,f160]) ).
fof(f160,plain,
( ! [X0] : sK7(X0) = sK19
| ~ spl20_4
| ~ spl20_10 ),
inference(resolution,[],[f148,f124]) ).
fof(f124,plain,
( ! [X0] : r1(sK7(X0))
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f281,plain,
( ! [X0] : sK18(X0,sK7(X0)) = X0
| ~ spl20_12
| ~ spl20_34 ),
inference(resolution,[],[f269,f156]) ).
fof(f337,plain,
( spl20_44
| ~ spl20_17
| ~ spl20_33 ),
inference(avatar_split_clause,[],[f277,f264,f184,f335]) ).
fof(f184,plain,
( spl20_17
<=> ! [X0] : r4(X0,sK19,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_17])]) ).
fof(f277,plain,
( ! [X0] : sK19 = sK17(X0,sK19)
| ~ spl20_17
| ~ spl20_33 ),
inference(resolution,[],[f265,f185]) ).
fof(f185,plain,
( ! [X0] : r4(X0,sK19,sK19)
| ~ spl20_17 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f333,plain,
( spl20_43
| ~ spl20_7
| ~ spl20_36 ),
inference(avatar_split_clause,[],[f299,f296,f135,f331]) ).
fof(f299,plain,
( ! [X0,X1] :
( ~ r1(X0)
| ~ r1(sK11(X0,X1))
| ~ r1(X1) )
| ~ spl20_7
| ~ spl20_36 ),
inference(resolution,[],[f297,f136]) ).
fof(f325,plain,
( spl20_42
| ~ spl20_11
| ~ spl20_23 ),
inference(avatar_split_clause,[],[f219,f211,f151,f323]) ).
fof(f219,plain,
( ! [X0,X1] : ~ r1(sK15(X0,X1))
| ~ spl20_11
| ~ spl20_23 ),
inference(resolution,[],[f212,f152]) ).
fof(f320,plain,
( spl20_41
| ~ spl20_9
| ~ spl20_11 ),
inference(avatar_split_clause,[],[f164,f151,f143,f318]) ).
fof(f318,plain,
( spl20_41
<=> ! [X0,X1] : ~ r1(sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_41])]) ).
fof(f164,plain,
( ! [X0,X1] : ~ r1(sK16(X0,X1))
| ~ spl20_9
| ~ spl20_11 ),
inference(resolution,[],[f152,f144]) ).
fof(f315,plain,
( spl20_40
| ~ spl20_8
| ~ spl20_11 ),
inference(avatar_split_clause,[],[f163,f151,f139,f313]) ).
fof(f313,plain,
( spl20_40
<=> ! [X0,X1] : ~ r1(sK12(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_40])]) ).
fof(f163,plain,
( ! [X0,X1] : ~ r1(sK12(X0,X1))
| ~ spl20_8
| ~ spl20_11 ),
inference(resolution,[],[f152,f140]) ).
fof(f311,plain,
( spl20_39
| ~ spl20_4
| ~ spl20_10 ),
inference(avatar_split_clause,[],[f160,f147,f123,f309]) ).
fof(f307,plain,
( spl20_38
| ~ spl20_2
| ~ spl20_10 ),
inference(avatar_split_clause,[],[f159,f147,f115,f305]) ).
fof(f305,plain,
( spl20_38
<=> ! [X0] : sK5(X0) = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_38])]) ).
fof(f115,plain,
( spl20_2
<=> ! [X0] : r1(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).
fof(f159,plain,
( ! [X0] : sK5(X0) = sK19
| ~ spl20_2
| ~ spl20_10 ),
inference(resolution,[],[f148,f116]) ).
fof(f116,plain,
( ! [X0] : r1(sK5(X0))
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f303,plain,
( spl20_37
| ~ spl20_3
| ~ spl20_10 ),
inference(avatar_split_clause,[],[f158,f147,f119,f301]) ).
fof(f158,plain,
( ! [X0] : sK4(X0) = sK19
| ~ spl20_3
| ~ spl20_10 ),
inference(resolution,[],[f148,f120]) ).
fof(f298,plain,
( spl20_36
| ~ spl20_5
| ~ spl20_27 ),
inference(avatar_split_clause,[],[f237,f234,f127,f296]) ).
fof(f127,plain,
( spl20_5
<=> ! [X4,X3,X2,X1] :
( ~ r1(X1)
| ~ r4(X3,X2,X1)
| ~ r1(X3)
| ~ r2(X4,X2)
| ~ r1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_5])]) ).
fof(f237,plain,
( ! [X2,X0,X1] :
( ~ r1(sK11(X0,X1))
| ~ r1(X0)
| ~ r2(X2,sK8(X1))
| ~ r1(X2) )
| ~ spl20_5
| ~ spl20_27 ),
inference(resolution,[],[f235,f128]) ).
fof(f128,plain,
( ! [X2,X3,X1,X4] :
( ~ r4(X3,X2,X1)
| ~ r1(X1)
| ~ r1(X3)
| ~ r2(X4,X2)
| ~ r1(X4) )
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f274,plain,
spl20_35,
inference(avatar_split_clause,[],[f101,f272]) ).
fof(f101,plain,
! [X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X2 != X3
| ~ r2(X0,X3) ) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X25,X26] :
( X25 = X26
| ! [X27] :
( ~ r2(X26,X27)
| ! [X28] :
( X27 != X28
| ~ r2(X25,X28) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).
fof(f270,plain,
spl20_34,
inference(avatar_split_clause,[],[f88,f268]) ).
fof(f88,plain,
! [X3,X0,X1] :
( sK18(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X3] :
( ( sK18(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK18(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f24,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) )
=> ! [X3] :
( ( sK18(X0,X1) = X3
& r3(X0,X1,X3) )
| ( sK18(X0,X1) != X3
& ~ r3(X0,X1,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r3(X0,X1,X3) )
| ( X2 != X3
& ~ r3(X0,X1,X3) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X5,X6] :
? [X7] :
! [X8] :
( ( X7 = X8
& r3(X5,X6,X8) )
| ( X7 != X8
& ~ r3(X5,X6,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f266,plain,
spl20_33,
inference(avatar_split_clause,[],[f84,f264]) ).
fof(f84,plain,
! [X3,X0,X1] :
( sK17(X0,X1) = X3
| ~ r4(X0,X1,X3) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X3] :
( ( sK17(X0,X1) = X3
& r4(X0,X1,X3) )
| ( sK17(X0,X1) != X3
& ~ r4(X0,X1,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f23,f48]) ).
fof(f48,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| ( X2 != X3
& ~ r4(X0,X1,X3) ) )
=> ! [X3] :
( ( sK17(X0,X1) = X3
& r4(X0,X1,X3) )
| ( sK17(X0,X1) != X3
& ~ r4(X0,X1,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X2 = X3
& r4(X0,X1,X3) )
| ( X2 != X3
& ~ r4(X0,X1,X3) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X9,X10] :
? [X11] :
! [X12] :
( ( X11 = X12
& r4(X9,X10,X12) )
| ( X11 != X12
& ~ r4(X9,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f262,plain,
spl20_32,
inference(avatar_split_clause,[],[f56,f260]) ).
fof(f56,plain,
! [X0] :
( r2(sK0(X0),sK1(X0))
| sK2(X0) = X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ( sK1(X0) = X0
& r2(sK0(X0),sK1(X0)) )
| ( sK2(X0) = X0
& r1(sK2(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f27,f26]) ).
fof(f26,plain,
! [X0] :
( ? [X1,X2] :
( X0 = X2
& r2(X1,X2) )
=> ( sK1(X0) = X0
& r2(sK0(X0),sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ? [X3] :
( X0 = X3
& r1(X3) )
=> ( sK2(X0) = X0
& r1(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0] :
( ? [X1,X2] :
( X0 = X2
& r2(X1,X2) )
| ? [X3] :
( X0 = X3
& r1(X3) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X36] :
( ? [X38,X39] :
( X36 = X39
& r2(X38,X39) )
| ? [X37] :
( X36 = X37
& r1(X37) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6a) ).
fof(f258,plain,
( spl20_31
| ~ spl20_5
| ~ spl20_18 ),
inference(avatar_split_clause,[],[f201,f189,f127,f256]) ).
fof(f256,plain,
( spl20_31
<=> ! [X2,X0,X1] :
( ~ r1(sK17(X0,X1))
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_31])]) ).
fof(f189,plain,
( spl20_18
<=> ! [X0,X1] : r4(X0,X1,sK17(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_18])]) ).
fof(f201,plain,
( ! [X2,X0,X1] :
( ~ r1(sK17(X0,X1))
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r1(X2) )
| ~ spl20_5
| ~ spl20_18 ),
inference(resolution,[],[f190,f128]) ).
fof(f190,plain,
( ! [X0,X1] : r4(X0,X1,sK17(X0,X1))
| ~ spl20_18 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f250,plain,
spl20_30,
inference(avatar_split_clause,[],[f95,f248]) ).
fof(f95,plain,
! [X0,X1] : r3(sK10(X0,X1),X0,sK11(X0,X1)),
inference(definition_unfolding,[],[f75,f74]) ).
fof(f74,plain,
! [X0,X1] : sK9(X0,X1) = sK11(X0,X1),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( r4(X0,X1,sK10(X0,X1))
& r3(sK10(X0,X1),X0,sK9(X0,X1))
& sK9(X0,X1) = sK11(X0,X1)
& r4(X0,sK12(X0,X1),sK11(X0,X1))
& r2(X1,sK12(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f21,f41,f40,f39,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK9(X0,X1)) )
& ? [X4] :
( sK9(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0,X1] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK9(X0,X1)) )
=> ( r4(X0,X1,sK10(X0,X1))
& r3(sK10(X0,X1),X0,sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1] :
( ? [X4] :
( sK9(X0,X1) = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK9(X0,X1) = sK11(X0,X1)
& ? [X5] :
( r4(X0,X5,sK11(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X1] :
( ? [X5] :
( r4(X0,X5,sK11(X0,X1))
& r2(X1,X5) )
=> ( r4(X0,sK12(X0,X1),sK11(X0,X1))
& r2(X1,sK12(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X19,X20] :
? [X21] :
( ? [X24] :
( r4(X19,X20,X24)
& r3(X24,X19,X21) )
& ? [X22] :
( X21 = X22
& ? [X23] :
( r4(X19,X23,X22)
& r2(X20,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2a) ).
fof(f75,plain,
! [X0,X1] : r3(sK10(X0,X1),X0,sK9(X0,X1)),
inference(cnf_transformation,[],[f42]) ).
fof(f246,plain,
( spl20_29
| ~ spl20_9
| ~ spl20_22
| ~ spl20_28 ),
inference(avatar_split_clause,[],[f242,f239,f207,f143,f244]) ).
fof(f239,plain,
( spl20_28
<=> ! [X0,X1] : r3(X0,sK16(X0,X1),sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_28])]) ).
fof(f242,plain,
( ! [X0,X1] : r3(X0,sK8(X1),sK15(X0,X1))
| ~ spl20_9
| ~ spl20_22
| ~ spl20_28 ),
inference(forward_demodulation,[],[f240,f217]) ).
fof(f240,plain,
( ! [X0,X1] : r3(X0,sK16(X0,X1),sK15(X0,X1))
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f241,plain,
spl20_28,
inference(avatar_split_clause,[],[f78,f239]) ).
fof(f78,plain,
! [X0,X1] : r3(X0,sK16(X0,X1),sK15(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( r3(X0,X1,sK14(X0,X1))
& r2(sK14(X0,X1),sK13(X0,X1))
& sK13(X0,X1) = sK15(X0,X1)
& r3(X0,sK16(X0,X1),sK15(X0,X1))
& r2(X1,sK16(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f22,f46,f45,f44,f43]) ).
fof(f43,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) )
=> ( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK13(X0,X1)) )
& ? [X4] :
( sK13(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK13(X0,X1)) )
=> ( r3(X0,X1,sK14(X0,X1))
& r2(sK14(X0,X1),sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X4] :
( sK13(X0,X1) = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) )
=> ( sK13(X0,X1) = sK15(X0,X1)
& ? [X5] :
( r3(X0,X5,sK15(X0,X1))
& r2(X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X5] :
( r3(X0,X5,sK15(X0,X1))
& r2(X1,X5) )
=> ( r3(X0,sK16(X0,X1),sK15(X0,X1))
& r2(X1,sK16(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( X2 = X4
& ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X13,X14] :
? [X15] :
( ? [X18] :
( r3(X13,X14,X18)
& r2(X18,X15) )
& ? [X16] :
( X15 = X16
& ? [X17] :
( r3(X13,X17,X16)
& r2(X14,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f236,plain,
( spl20_27
| ~ spl20_8
| ~ spl20_22
| ~ spl20_26 ),
inference(avatar_split_clause,[],[f232,f229,f207,f139,f234]) ).
fof(f229,plain,
( spl20_26
<=> ! [X0,X1] : r4(X0,sK12(X0,X1),sK11(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_26])]) ).
fof(f232,plain,
( ! [X0,X1] : r4(X0,sK8(X1),sK11(X0,X1))
| ~ spl20_8
| ~ spl20_22
| ~ spl20_26 ),
inference(forward_demodulation,[],[f230,f216]) ).
fof(f230,plain,
( ! [X0,X1] : r4(X0,sK12(X0,X1),sK11(X0,X1))
| ~ spl20_26 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f231,plain,
spl20_26,
inference(avatar_split_clause,[],[f73,f229]) ).
fof(f73,plain,
! [X0,X1] : r4(X0,sK12(X0,X1),sK11(X0,X1)),
inference(cnf_transformation,[],[f42]) ).
fof(f227,plain,
spl20_25,
inference(avatar_split_clause,[],[f58,f225]) ).
fof(f58,plain,
! [X0] :
( sK1(X0) = X0
| sK2(X0) = X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f223,plain,
spl20_24,
inference(avatar_split_clause,[],[f55,f221]) ).
fof(f55,plain,
! [X0] :
( r2(sK0(X0),sK1(X0))
| r1(sK2(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f213,plain,
spl20_23,
inference(avatar_split_clause,[],[f96,f211]) ).
fof(f96,plain,
! [X0,X1] : r2(sK14(X0,X1),sK15(X0,X1)),
inference(definition_unfolding,[],[f80,f79]) ).
fof(f79,plain,
! [X0,X1] : sK13(X0,X1) = sK15(X0,X1),
inference(cnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0,X1] : r2(sK14(X0,X1),sK13(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f209,plain,
spl20_22,
inference(avatar_split_clause,[],[f68,f207]) ).
fof(f68,plain,
! [X2,X0] :
( sK8(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X2] :
( ( sK8(X0) = X2
& r2(X0,X2) )
| ( sK8(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f18,f36]) ).
fof(f36,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) )
=> ! [X2] :
( ( sK8(X0) = X2
& r2(X0,X2) )
| ( sK8(X0) != X2
& ~ r2(X0,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( X3 = X4
& r2(X2,X4) )
| ( X3 != X4
& ~ r2(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f205,plain,
spl20_21,
inference(avatar_split_clause,[],[f57,f203]) ).
fof(f57,plain,
! [X0] :
( sK1(X0) = X0
| r1(sK2(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f200,plain,
( spl20_20
| ~ spl20_5
| ~ spl20_14 ),
inference(avatar_split_clause,[],[f196,f170,f127,f198]) ).
fof(f196,plain,
( ! [X2,X0,X1] :
( ~ r1(sK10(X0,X1))
| ~ r1(X0)
| ~ r2(X2,X1)
| ~ r1(X2) )
| ~ spl20_5
| ~ spl20_14 ),
inference(resolution,[],[f171,f128]) ).
fof(f195,plain,
spl20_19,
inference(avatar_split_clause,[],[f105,f193]) ).
fof(f193,plain,
( spl20_19
<=> ! [X0,X1] : r3(X0,X1,sK18(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_19])]) ).
fof(f105,plain,
! [X0,X1] : r3(X0,X1,sK18(X0,X1)),
inference(equality_resolution,[],[f87]) ).
fof(f87,plain,
! [X3,X0,X1] :
( r3(X0,X1,X3)
| sK18(X0,X1) != X3 ),
inference(cnf_transformation,[],[f51]) ).
fof(f191,plain,
spl20_18,
inference(avatar_split_clause,[],[f103,f189]) ).
fof(f103,plain,
! [X0,X1] : r4(X0,X1,sK17(X0,X1)),
inference(equality_resolution,[],[f83]) ).
fof(f83,plain,
! [X3,X0,X1] :
( r4(X0,X1,X3)
| sK17(X0,X1) != X3 ),
inference(cnf_transformation,[],[f49]) ).
fof(f186,plain,
( spl20_17
| ~ spl20_2
| ~ spl20_3
| ~ spl20_10
| ~ spl20_16 ),
inference(avatar_split_clause,[],[f182,f178,f147,f119,f115,f184]) ).
fof(f178,plain,
( spl20_16
<=> ! [X0] : r4(X0,sK5(X0),sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_16])]) ).
fof(f182,plain,
( ! [X0] : r4(X0,sK19,sK19)
| ~ spl20_2
| ~ spl20_3
| ~ spl20_10
| ~ spl20_16 ),
inference(forward_demodulation,[],[f181,f159]) ).
fof(f181,plain,
( ! [X0] : r4(X0,sK5(X0),sK19)
| ~ spl20_3
| ~ spl20_10
| ~ spl20_16 ),
inference(forward_demodulation,[],[f179,f158]) ).
fof(f179,plain,
( ! [X0] : r4(X0,sK5(X0),sK4(X0))
| ~ spl20_16 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f180,plain,
spl20_16,
inference(avatar_split_clause,[],[f94,f178]) ).
fof(f94,plain,
! [X0] : r4(X0,sK5(X0),sK4(X0)),
inference(definition_unfolding,[],[f60,f62]) ).
fof(f62,plain,
! [X0] : sK3(X0) = sK4(X0),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( sK3(X0) = sK4(X0)
& r1(sK4(X0))
& r4(X0,sK5(X0),sK3(X0))
& r1(sK5(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f16,f31,f30,f29]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) )
=> ( ? [X2] :
( sK3(X0) = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,sK3(X0))
& r1(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0] :
( ? [X2] :
( sK3(X0) = X2
& r1(X2) )
=> ( sK3(X0) = sK4(X0)
& r1(sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0] :
( ? [X3] :
( r4(X0,X3,sK3(X0))
& r1(X3) )
=> ( r4(X0,sK5(X0),sK3(X0))
& r1(sK5(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
? [X1] :
( ? [X2] :
( X1 = X2
& r1(X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X32] :
? [X33] :
( ? [X35] :
( X33 = X35
& r1(X35) )
& ? [X34] :
( r4(X32,X34,X33)
& r1(X34) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
fof(f60,plain,
! [X0] : r4(X0,sK5(X0),sK3(X0)),
inference(cnf_transformation,[],[f32]) ).
fof(f176,plain,
spl20_15,
inference(avatar_split_clause,[],[f81,f174]) ).
fof(f81,plain,
! [X0,X1] : r3(X0,X1,sK14(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f172,plain,
spl20_14,
inference(avatar_split_clause,[],[f76,f170]) ).
fof(f76,plain,
! [X0,X1] : r4(X0,X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f42]) ).
fof(f168,plain,
( spl20_13
| ~ spl20_7
| ~ spl20_11 ),
inference(avatar_split_clause,[],[f162,f151,f135,f166]) ).
fof(f162,plain,
( ! [X0] : ~ r1(sK8(X0))
| ~ spl20_7
| ~ spl20_11 ),
inference(resolution,[],[f152,f136]) ).
fof(f157,plain,
spl20_12,
inference(avatar_split_clause,[],[f108,f155]) ).
fof(f108,plain,
! [X0] : r3(X0,sK7(X0),X0),
inference(forward_demodulation,[],[f64,f65]) ).
fof(f65,plain,
! [X0] : sK6(X0) = X0,
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( sK6(X0) = X0
& r3(X0,sK7(X0),sK6(X0))
& r1(sK7(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f17,f34,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) )
=> ( sK6(X0) = X0
& ? [X2] :
( r3(X0,X2,sK6(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK6(X0))
& r1(X2) )
=> ( r3(X0,sK7(X0),sK6(X0))
& r1(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
? [X1] :
( X0 = X1
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X29] :
? [X30] :
( X29 = X30
& ? [X31] :
( r3(X29,X31,X30)
& r1(X31) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f64,plain,
! [X0] : r3(X0,sK7(X0),sK6(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f153,plain,
spl20_11,
inference(avatar_split_clause,[],[f100,f151]) ).
fof(f100,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f70]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X1 != X2
| ~ r1(X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X40,X41] :
( ~ r2(X40,X41)
| ! [X42] :
( X41 != X42
| ~ r1(X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f149,plain,
spl20_10,
inference(avatar_split_clause,[],[f92,f147]) ).
fof(f92,plain,
! [X1] :
( sK19 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X1] :
( ( sK19 = X1
& r1(X1) )
| ( sK19 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1,f52]) ).
fof(f52,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) )
=> ! [X1] :
( ( sK19 = X1
& r1(X1) )
| ( sK19 != X1
& ~ r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f145,plain,
spl20_9,
inference(avatar_split_clause,[],[f77,f143]) ).
fof(f77,plain,
! [X0,X1] : r2(X1,sK16(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f141,plain,
spl20_8,
inference(avatar_split_clause,[],[f72,f139]) ).
fof(f72,plain,
! [X0,X1] : r2(X1,sK12(X0,X1)),
inference(cnf_transformation,[],[f42]) ).
fof(f137,plain,
spl20_7,
inference(avatar_split_clause,[],[f99,f135]) ).
fof(f99,plain,
! [X0] : r2(X0,sK8(X0)),
inference(equality_resolution,[],[f67]) ).
fof(f67,plain,
! [X2,X0] :
( r2(X0,X2)
| sK8(X0) != X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f133,plain,
spl20_6,
inference(avatar_split_clause,[],[f65,f131]) ).
fof(f131,plain,
( spl20_6
<=> ! [X0] : sK6(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_6])]) ).
fof(f129,plain,
spl20_5,
inference(avatar_split_clause,[],[f97,f127]) ).
fof(f97,plain,
! [X2,X3,X1,X4] :
( ~ r1(X1)
| ~ r4(X3,X2,X1)
| ~ r1(X3)
| ~ r2(X4,X2)
| ~ r1(X4) ),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4] :
( X0 != X1
| ~ r1(X1)
| ~ r4(X3,X2,X0)
| ~ r1(X3)
| ~ r2(X4,X2)
| ~ r1(X4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( X0 != X1
| ~ r1(X1) )
| ! [X2] :
( ! [X3] :
( ~ r4(X3,X2,X0)
| ~ r1(X3) )
| ! [X4] :
( ~ r2(X4,X2)
| ~ r1(X4) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ? [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
& ? [X2] :
( ? [X3] :
( r4(X3,X2,X0)
& r1(X3) )
& ? [X4] :
( r2(X4,X2)
& r1(X4) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ? [X16] :
( X16 = X38
& r1(X16) )
& ? [X21] :
( ? [X15] :
( r4(X15,X21,X38)
& r1(X15) )
& ? [X22] :
( r2(X22,X21)
& r1(X22) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38] :
( ? [X16] :
( X16 = X38
& r1(X16) )
& ? [X21] :
( ? [X15] :
( r4(X15,X21,X38)
& r1(X15) )
& ? [X22] :
( r2(X22,X21)
& r1(X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimesoneeqzero) ).
fof(f125,plain,
spl20_4,
inference(avatar_split_clause,[],[f63,f123]) ).
fof(f63,plain,
! [X0] : r1(sK7(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f121,plain,
spl20_3,
inference(avatar_split_clause,[],[f61,f119]) ).
fof(f61,plain,
! [X0] : r1(sK4(X0)),
inference(cnf_transformation,[],[f32]) ).
fof(f117,plain,
spl20_2,
inference(avatar_split_clause,[],[f59,f115]) ).
fof(f59,plain,
! [X0] : r1(sK5(X0)),
inference(cnf_transformation,[],[f32]) ).
fof(f113,plain,
spl20_1,
inference(avatar_split_clause,[],[f107,f110]) ).
fof(f107,plain,
r1(sK19),
inference(equality_resolution,[],[f91]) ).
fof(f91,plain,
! [X1] :
( r1(X1)
| sK19 != X1 ),
inference(cnf_transformation,[],[f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 18:52:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (18977)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (18982)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (18980)WARNING: value z3 for option sas not known
% 0.14/0.37 % (18978)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (18979)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (18980)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (18981)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (18983)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (18984)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (18982)First to succeed.
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (18980)Also succeeded, but the first one will report.
% 0.14/0.38 % (18982)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18977"
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (18982)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (18982)------------------------------
% 0.14/0.39 % (18982)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (18982)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (18982)Memory used [KB]: 1146
% 0.14/0.39 % (18982)Time elapsed: 0.015 s
% 0.14/0.39 % (18982)Instructions burned: 37 (million)
% 0.14/0.39 % (18977)Success in time 0.025 s
%------------------------------------------------------------------------------