TSTP Solution File: RNG050+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 02:40:52 EDT 2024

% Result   : Theorem 0.20s 0.40s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  133
% Syntax   : Number of formulae    :  431 (  62 unt;   0 def)
%            Number of atoms       : 1572 ( 332 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 1985 ( 844   ~; 869   |; 123   &)
%                                         (  99 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  104 ( 102 usr;  95 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-2 aty)
%            Number of variables   :  557 ( 549   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f831,plain,
    $false,
    inference(avatar_sat_refutation,[],[f178,f183,f188,f193,f198,f202,f208,f212,f216,f220,f224,f228,f234,f238,f246,f251,f256,f260,f264,f268,f272,f276,f280,f290,f294,f298,f302,f306,f310,f314,f318,f338,f342,f349,f353,f366,f371,f377,f381,f388,f393,f397,f401,f405,f409,f416,f419,f438,f463,f480,f484,f488,f492,f511,f515,f519,f535,f539,f553,f557,f561,f571,f577,f582,f590,f599,f607,f613,f626,f631,f639,f649,f664,f668,f672,f703,f707,f711,f727,f731,f742,f753,f757,f770,f774,f778,f782,f789,f813,f817,f821,f825,f829,f830]) ).

fof(f830,plain,
    ( ~ spl5_4
    | ~ spl5_12
    | spl5_82 ),
    inference(avatar_split_clause,[],[f783,f739,f226,f190]) ).

fof(f190,plain,
    ( spl5_4
  <=> aScalar0(sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f226,plain,
    ( spl5_12
  <=> ! [X0] :
        ( sdtlseqdt0(X0,X0)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).

fof(f739,plain,
    ( spl5_82
  <=> sdtlseqdt0(sz0z00,sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_82])]) ).

fof(f783,plain,
    ( ~ aScalar0(sz0z00)
    | ~ spl5_12
    | spl5_82 ),
    inference(resolution,[],[f741,f227]) ).

fof(f227,plain,
    ( ! [X0] :
        ( sdtlseqdt0(X0,X0)
        | ~ aScalar0(X0) )
    | ~ spl5_12 ),
    inference(avatar_component_clause,[],[f226]) ).

fof(f741,plain,
    ( ~ sdtlseqdt0(sz0z00,sz0z00)
    | spl5_82 ),
    inference(avatar_component_clause,[],[f739]) ).

fof(f829,plain,
    ( spl5_94
    | ~ spl5_4
    | ~ spl5_55 ),
    inference(avatar_split_clause,[],[f520,f509,f190,f827]) ).

fof(f827,plain,
    ( spl5_94
  <=> ! [X0,X1] :
        ( sdtpldt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(X0,sdtpldt0(X1,sz0z00))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_94])]) ).

fof(f509,plain,
    ( spl5_55
  <=> ! [X2,X0,X1] :
        ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_55])]) ).

fof(f520,plain,
    ( ! [X0,X1] :
        ( sdtpldt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(X0,sdtpldt0(X1,sz0z00))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_4
    | ~ spl5_55 ),
    inference(resolution,[],[f510,f192]) ).

fof(f192,plain,
    ( aScalar0(sz0z00)
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f190]) ).

fof(f510,plain,
    ( ! [X2,X0,X1] :
        ( ~ aScalar0(X2)
        | sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_55 ),
    inference(avatar_component_clause,[],[f509]) ).

fof(f825,plain,
    ( spl5_93
    | ~ spl5_36
    | ~ spl5_54 ),
    inference(avatar_split_clause,[],[f504,f490,f351,f823]) ).

fof(f823,plain,
    ( spl5_93
  <=> ! [X2,X0,X1] :
        ( sdtlseqdt0(X0,X1)
        | ~ sdtlseqdt0(X0,X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X2)
        | ~ aScalar0(X0)
        | sdtlseqdt0(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_93])]) ).

fof(f351,plain,
    ( spl5_36
  <=> ! [X0,X1] :
        ( sdtlseqdt0(X1,X0)
        | sdtlseqdt0(X0,X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).

fof(f490,plain,
    ( spl5_54
  <=> ! [X2,X0,X1] :
        ( sdtlseqdt0(X0,X2)
        | ~ sdtlseqdt0(X1,X2)
        | ~ sdtlseqdt0(X0,X1)
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_54])]) ).

fof(f504,plain,
    ( ! [X2,X0,X1] :
        ( sdtlseqdt0(X0,X1)
        | ~ sdtlseqdt0(X0,X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X2)
        | ~ aScalar0(X0)
        | sdtlseqdt0(X1,X2) )
    | ~ spl5_36
    | ~ spl5_54 ),
    inference(duplicate_literal_removal,[],[f501]) ).

fof(f501,plain,
    ( ! [X2,X0,X1] :
        ( sdtlseqdt0(X0,X1)
        | ~ sdtlseqdt0(X0,X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X2)
        | ~ aScalar0(X0)
        | sdtlseqdt0(X1,X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X2) )
    | ~ spl5_36
    | ~ spl5_54 ),
    inference(resolution,[],[f491,f352]) ).

fof(f352,plain,
    ( ! [X0,X1] :
        ( sdtlseqdt0(X1,X0)
        | sdtlseqdt0(X0,X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_36 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f491,plain,
    ( ! [X2,X0,X1] :
        ( ~ sdtlseqdt0(X1,X2)
        | sdtlseqdt0(X0,X2)
        | ~ sdtlseqdt0(X0,X1)
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_54 ),
    inference(avatar_component_clause,[],[f490]) ).

fof(f821,plain,
    ( spl5_92
    | ~ spl5_11
    | ~ spl5_45 ),
    inference(avatar_split_clause,[],[f467,f403,f222,f819]) ).

fof(f819,plain,
    ( spl5_92
  <=> ! [X0,X1] :
        ( sdtasdt0(smndt0(X0),smndt0(X1)) = smndt0(sdtasdt0(X0,smndt0(X1)))
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_92])]) ).

fof(f222,plain,
    ( spl5_11
  <=> ! [X0] :
        ( aScalar0(smndt0(X0))
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).

fof(f403,plain,
    ( spl5_45
  <=> ! [X0,X1] :
        ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_45])]) ).

fof(f467,plain,
    ( ! [X0,X1] :
        ( sdtasdt0(smndt0(X0),smndt0(X1)) = smndt0(sdtasdt0(X0,smndt0(X1)))
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) )
    | ~ spl5_11
    | ~ spl5_45 ),
    inference(resolution,[],[f404,f223]) ).

fof(f223,plain,
    ( ! [X0] :
        ( aScalar0(smndt0(X0))
        | ~ aScalar0(X0) )
    | ~ spl5_11 ),
    inference(avatar_component_clause,[],[f222]) ).

fof(f404,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X1)
        | smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
        | ~ aScalar0(X0) )
    | ~ spl5_45 ),
    inference(avatar_component_clause,[],[f403]) ).

fof(f817,plain,
    ( spl5_91
    | ~ spl5_11
    | ~ spl5_44 ),
    inference(avatar_split_clause,[],[f457,f399,f222,f815]) ).

fof(f815,plain,
    ( spl5_91
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,smndt0(smndt0(X1))) = smndt0(sdtasdt0(X0,smndt0(X1)))
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_91])]) ).

fof(f399,plain,
    ( spl5_44
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).

fof(f457,plain,
    ( ! [X0,X1] :
        ( sdtasdt0(X0,smndt0(smndt0(X1))) = smndt0(sdtasdt0(X0,smndt0(X1)))
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) )
    | ~ spl5_11
    | ~ spl5_44 ),
    inference(resolution,[],[f400,f223]) ).

fof(f400,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X1)
        | sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
        | ~ aScalar0(X0) )
    | ~ spl5_44 ),
    inference(avatar_component_clause,[],[f399]) ).

fof(f813,plain,
    ( spl5_90
    | ~ spl5_11
    | ~ spl5_43 ),
    inference(avatar_split_clause,[],[f451,f395,f222,f811]) ).

fof(f811,plain,
    ( spl5_90
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X0),smndt0(smndt0(X1)))
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_90])]) ).

fof(f395,plain,
    ( spl5_43
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).

fof(f451,plain,
    ( ! [X0,X1] :
        ( sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X0),smndt0(smndt0(X1)))
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) )
    | ~ spl5_11
    | ~ spl5_43 ),
    inference(resolution,[],[f396,f223]) ).

fof(f396,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X1)
        | sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
        | ~ aScalar0(X0) )
    | ~ spl5_43 ),
    inference(avatar_component_clause,[],[f395]) ).

fof(f789,plain,
    ( spl5_89
    | ~ spl5_11
    | ~ spl5_49 ),
    inference(avatar_split_clause,[],[f442,f436,f222,f787]) ).

fof(f787,plain,
    ( spl5_89
  <=> ! [X0,X1] :
        ( ~ aScalar0(X0)
        | sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X1),X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_89])]) ).

fof(f436,plain,
    ( spl5_49
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_49])]) ).

fof(f442,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X0)
        | sdtasdt0(X0,smndt0(X1)) = sdtasdt0(smndt0(X1),X0)
        | ~ aScalar0(X1) )
    | ~ spl5_11
    | ~ spl5_49 ),
    inference(resolution,[],[f437,f223]) ).

fof(f437,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X1)
        | ~ aScalar0(X0)
        | sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
    | ~ spl5_49 ),
    inference(avatar_component_clause,[],[f436]) ).

fof(f782,plain,
    ( spl5_88
    | ~ spl5_11
    | ~ spl5_48 ),
    inference(avatar_split_clause,[],[f433,f414,f222,f780]) ).

fof(f780,plain,
    ( spl5_88
  <=> ! [X0,X1] :
        ( ~ aScalar0(X0)
        | sdtpldt0(X0,smndt0(X1)) = sdtpldt0(smndt0(X1),X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_88])]) ).

fof(f414,plain,
    ( spl5_48
  <=> ! [X0,X1] :
        ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_48])]) ).

fof(f433,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X0)
        | sdtpldt0(X0,smndt0(X1)) = sdtpldt0(smndt0(X1),X0)
        | ~ aScalar0(X1) )
    | ~ spl5_11
    | ~ spl5_48 ),
    inference(resolution,[],[f415,f223]) ).

fof(f415,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X1)
        | ~ aScalar0(X0)
        | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
    | ~ spl5_48 ),
    inference(avatar_component_clause,[],[f414]) ).

fof(f778,plain,
    ( spl5_87
    | ~ spl5_8
    | ~ spl5_35 ),
    inference(avatar_split_clause,[],[f357,f347,f210,f776]) ).

fof(f776,plain,
    ( spl5_87
  <=> ! [X0] :
        ( sz00 = aDimensionOf0(X0)
        | aDimensionOf0(X0) = szszuzczcdt0(sK4(aDimensionOf0(X0)))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_87])]) ).

fof(f210,plain,
    ( spl5_8
  <=> ! [X0] :
        ( aNaturalNumber0(aDimensionOf0(X0))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

fof(f347,plain,
    ( spl5_35
  <=> ! [X0] :
        ( szszuzczcdt0(sK4(X0)) = X0
        | sz00 = X0
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).

fof(f357,plain,
    ( ! [X0] :
        ( sz00 = aDimensionOf0(X0)
        | aDimensionOf0(X0) = szszuzczcdt0(sK4(aDimensionOf0(X0)))
        | ~ aVector0(X0) )
    | ~ spl5_8
    | ~ spl5_35 ),
    inference(resolution,[],[f348,f211]) ).

fof(f211,plain,
    ( ! [X0] :
        ( aNaturalNumber0(aDimensionOf0(X0))
        | ~ aVector0(X0) )
    | ~ spl5_8 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f348,plain,
    ( ! [X0] :
        ( ~ aNaturalNumber0(X0)
        | sz00 = X0
        | szszuzczcdt0(sK4(X0)) = X0 )
    | ~ spl5_35 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f774,plain,
    ( spl5_86
    | ~ spl5_10
    | ~ spl5_35 ),
    inference(avatar_split_clause,[],[f356,f347,f218,f772]) ).

fof(f772,plain,
    ( spl5_86
  <=> ! [X0] :
        ( sz00 = szszuzczcdt0(X0)
        | szszuzczcdt0(X0) = szszuzczcdt0(sK4(szszuzczcdt0(X0)))
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_86])]) ).

fof(f218,plain,
    ( spl5_10
  <=> ! [X0] :
        ( aNaturalNumber0(szszuzczcdt0(X0))
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).

fof(f356,plain,
    ( ! [X0] :
        ( sz00 = szszuzczcdt0(X0)
        | szszuzczcdt0(X0) = szszuzczcdt0(sK4(szszuzczcdt0(X0)))
        | ~ aNaturalNumber0(X0) )
    | ~ spl5_10
    | ~ spl5_35 ),
    inference(resolution,[],[f348,f219]) ).

fof(f219,plain,
    ( ! [X0] :
        ( aNaturalNumber0(szszuzczcdt0(X0))
        | ~ aNaturalNumber0(X0) )
    | ~ spl5_10 ),
    inference(avatar_component_clause,[],[f218]) ).

fof(f770,plain,
    ( spl5_85
    | ~ spl5_17
    | ~ spl5_39 ),
    inference(avatar_split_clause,[],[f382,f375,f249,f768]) ).

fof(f768,plain,
    ( spl5_85
  <=> ! [X0,X1] :
        ( ~ aNaturalNumber0(X0)
        | sdtlbdtrb0(X1,X0) = sdtlbdtrb0(sziznziztdt0(X1),X0)
        | ~ sP1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_85])]) ).

fof(f249,plain,
    ( spl5_17
  <=> ! [X0] :
        ( sP0(X0,sziznziztdt0(X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).

fof(f375,plain,
    ( spl5_39
  <=> ! [X0,X1,X3] :
        ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
        | ~ aNaturalNumber0(X3)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).

fof(f382,plain,
    ( ! [X0,X1] :
        ( ~ aNaturalNumber0(X0)
        | sdtlbdtrb0(X1,X0) = sdtlbdtrb0(sziznziztdt0(X1),X0)
        | ~ sP1(X1) )
    | ~ spl5_17
    | ~ spl5_39 ),
    inference(resolution,[],[f376,f250]) ).

fof(f250,plain,
    ( ! [X0] :
        ( sP0(X0,sziznziztdt0(X0))
        | ~ sP1(X0) )
    | ~ spl5_17 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f376,plain,
    ( ! [X3,X0,X1] :
        ( ~ sP0(X0,X1)
        | ~ aNaturalNumber0(X3)
        | sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
    | ~ spl5_39 ),
    inference(avatar_component_clause,[],[f375]) ).

fof(f757,plain,
    ( spl5_84
    | ~ spl5_64 ),
    inference(avatar_split_clause,[],[f578,f575,f755]) ).

fof(f755,plain,
    ( spl5_84
  <=> ! [X0] :
        ( sP0(X0,X0)
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X0))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_84])]) ).

fof(f575,plain,
    ( spl5_64
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_64])]) ).

fof(f578,plain,
    ( ! [X0] :
        ( sP0(X0,X0)
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X0))
        | ~ aVector0(X0) )
    | ~ spl5_64 ),
    inference(equality_resolution,[],[f576]) ).

fof(f576,plain,
    ( ! [X0,X1] :
        ( sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
        | sP0(X0,X1)
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) )
    | ~ spl5_64 ),
    inference(avatar_component_clause,[],[f575]) ).

fof(f753,plain,
    ( spl5_83
    | ~ spl5_4
    | ~ spl5_45 ),
    inference(avatar_split_clause,[],[f464,f403,f190,f751]) ).

fof(f751,plain,
    ( spl5_83
  <=> ! [X0] :
        ( sdtasdt0(smndt0(X0),sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_83])]) ).

fof(f464,plain,
    ( ! [X0] :
        ( sdtasdt0(smndt0(X0),sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
        | ~ aScalar0(X0) )
    | ~ spl5_4
    | ~ spl5_45 ),
    inference(resolution,[],[f404,f192]) ).

fof(f742,plain,
    ( ~ spl5_82
    | spl5_1
    | ~ spl5_71 ),
    inference(avatar_split_clause,[],[f687,f628,f175,f739]) ).

fof(f175,plain,
    ( spl5_1
  <=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f628,plain,
    ( spl5_71
  <=> sz0z00 = sdtasasdt0(xs,xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_71])]) ).

fof(f687,plain,
    ( ~ sdtlseqdt0(sz0z00,sz0z00)
    | spl5_1
    | ~ spl5_71 ),
    inference(superposition,[],[f177,f630]) ).

fof(f630,plain,
    ( sz0z00 = sdtasasdt0(xs,xs)
    | ~ spl5_71 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f177,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
    | spl5_1 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f731,plain,
    ( spl5_81
    | ~ spl5_4
    | ~ spl5_16
    | ~ spl5_44 ),
    inference(avatar_split_clause,[],[f459,f399,f243,f190,f729]) ).

fof(f729,plain,
    ( spl5_81
  <=> ! [X0] :
        ( sdtasdt0(X0,sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_81])]) ).

fof(f243,plain,
    ( spl5_16
  <=> sz0z00 = smndt0(sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).

fof(f459,plain,
    ( ! [X0] :
        ( sdtasdt0(X0,sz0z00) = smndt0(sdtasdt0(X0,sz0z00))
        | ~ aScalar0(X0) )
    | ~ spl5_4
    | ~ spl5_16
    | ~ spl5_44 ),
    inference(forward_demodulation,[],[f454,f245]) ).

fof(f245,plain,
    ( sz0z00 = smndt0(sz0z00)
    | ~ spl5_16 ),
    inference(avatar_component_clause,[],[f243]) ).

fof(f454,plain,
    ( ! [X0] :
        ( sdtasdt0(X0,smndt0(sz0z00)) = smndt0(sdtasdt0(X0,sz0z00))
        | ~ aScalar0(X0) )
    | ~ spl5_4
    | ~ spl5_44 ),
    inference(resolution,[],[f400,f192]) ).

fof(f727,plain,
    ( spl5_80
    | ~ spl5_4
    | ~ spl5_16
    | ~ spl5_43 ),
    inference(avatar_split_clause,[],[f453,f395,f243,f190,f725]) ).

fof(f725,plain,
    ( spl5_80
  <=> ! [X0] :
        ( sdtasdt0(X0,sz0z00) = sdtasdt0(smndt0(X0),sz0z00)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_80])]) ).

fof(f453,plain,
    ( ! [X0] :
        ( sdtasdt0(X0,sz0z00) = sdtasdt0(smndt0(X0),sz0z00)
        | ~ aScalar0(X0) )
    | ~ spl5_4
    | ~ spl5_16
    | ~ spl5_43 ),
    inference(forward_demodulation,[],[f448,f245]) ).

fof(f448,plain,
    ( ! [X0] :
        ( sdtasdt0(X0,sz0z00) = sdtasdt0(smndt0(X0),smndt0(sz0z00))
        | ~ aScalar0(X0) )
    | ~ spl5_4
    | ~ spl5_43 ),
    inference(resolution,[],[f396,f192]) ).

fof(f711,plain,
    ( spl5_79
    | ~ spl5_4
    | ~ spl5_49 ),
    inference(avatar_split_clause,[],[f439,f436,f190,f709]) ).

fof(f709,plain,
    ( spl5_79
  <=> ! [X0] :
        ( ~ aScalar0(X0)
        | sdtasdt0(X0,sz0z00) = sdtasdt0(sz0z00,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_79])]) ).

fof(f439,plain,
    ( ! [X0] :
        ( ~ aScalar0(X0)
        | sdtasdt0(X0,sz0z00) = sdtasdt0(sz0z00,X0) )
    | ~ spl5_4
    | ~ spl5_49 ),
    inference(resolution,[],[f437,f192]) ).

fof(f707,plain,
    ( spl5_78
    | ~ spl5_4
    | ~ spl5_48 ),
    inference(avatar_split_clause,[],[f430,f414,f190,f705]) ).

fof(f705,plain,
    ( spl5_78
  <=> ! [X0] :
        ( ~ aScalar0(X0)
        | sdtpldt0(X0,sz0z00) = sdtpldt0(sz0z00,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_78])]) ).

fof(f430,plain,
    ( ! [X0] :
        ( ~ aScalar0(X0)
        | sdtpldt0(X0,sz0z00) = sdtpldt0(sz0z00,X0) )
    | ~ spl5_4
    | ~ spl5_48 ),
    inference(resolution,[],[f415,f192]) ).

fof(f703,plain,
    ( spl5_77
    | ~ spl5_17
    | ~ spl5_34 ),
    inference(avatar_split_clause,[],[f345,f340,f249,f701]) ).

fof(f701,plain,
    ( spl5_77
  <=> ! [X0] :
        ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0)))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_77])]) ).

fof(f340,plain,
    ( spl5_34
  <=> ! [X0,X1] :
        ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).

fof(f345,plain,
    ( ! [X0] :
        ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0)))
        | ~ sP1(X0) )
    | ~ spl5_17
    | ~ spl5_34 ),
    inference(resolution,[],[f341,f250]) ).

fof(f341,plain,
    ( ! [X0,X1] :
        ( ~ sP0(X0,X1)
        | aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1)) )
    | ~ spl5_34 ),
    inference(avatar_component_clause,[],[f340]) ).

fof(f672,plain,
    ( spl5_76
    | ~ spl5_6
    | ~ spl5_32 ),
    inference(avatar_split_clause,[],[f334,f316,f200,f670]) ).

fof(f670,plain,
    ( spl5_76
  <=> ! [X0,X1] :
        ( ~ aScalar0(X0)
        | ~ aScalar0(X1)
        | sP2(sdtasdt0(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_76])]) ).

fof(f200,plain,
    ( spl5_6
  <=> ! [X0] :
        ( sP2(X0)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

fof(f316,plain,
    ( spl5_32
  <=> ! [X0,X1] :
        ( aScalar0(sdtasdt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).

fof(f334,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X0)
        | ~ aScalar0(X1)
        | sP2(sdtasdt0(X1,X0)) )
    | ~ spl5_6
    | ~ spl5_32 ),
    inference(resolution,[],[f317,f201]) ).

fof(f201,plain,
    ( ! [X0] :
        ( ~ aScalar0(X0)
        | sP2(X0) )
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f200]) ).

fof(f317,plain,
    ( ! [X0,X1] :
        ( aScalar0(sdtasdt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_32 ),
    inference(avatar_component_clause,[],[f316]) ).

fof(f668,plain,
    ( spl5_75
    | ~ spl5_6
    | ~ spl5_31 ),
    inference(avatar_split_clause,[],[f333,f312,f200,f666]) ).

fof(f666,plain,
    ( spl5_75
  <=> ! [X0,X1] :
        ( ~ aScalar0(X0)
        | ~ aScalar0(X1)
        | sP2(sdtpldt0(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_75])]) ).

fof(f312,plain,
    ( spl5_31
  <=> ! [X0,X1] :
        ( aScalar0(sdtpldt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).

fof(f333,plain,
    ( ! [X0,X1] :
        ( ~ aScalar0(X0)
        | ~ aScalar0(X1)
        | sP2(sdtpldt0(X1,X0)) )
    | ~ spl5_6
    | ~ spl5_31 ),
    inference(resolution,[],[f313,f201]) ).

fof(f313,plain,
    ( ! [X0,X1] :
        ( aScalar0(sdtpldt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_31 ),
    inference(avatar_component_clause,[],[f312]) ).

fof(f664,plain,
    ( spl5_74
    | ~ spl5_6
    | ~ spl5_30 ),
    inference(avatar_split_clause,[],[f332,f308,f200,f662]) ).

fof(f662,plain,
    ( spl5_74
  <=> ! [X0,X1] :
        ( ~ aNaturalNumber0(X0)
        | ~ aVector0(X1)
        | sP2(sdtlbdtrb0(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_74])]) ).

fof(f308,plain,
    ( spl5_30
  <=> ! [X0,X1] :
        ( aScalar0(sdtlbdtrb0(X0,X1))
        | ~ aNaturalNumber0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).

fof(f332,plain,
    ( ! [X0,X1] :
        ( ~ aNaturalNumber0(X0)
        | ~ aVector0(X1)
        | sP2(sdtlbdtrb0(X1,X0)) )
    | ~ spl5_6
    | ~ spl5_30 ),
    inference(resolution,[],[f309,f201]) ).

fof(f309,plain,
    ( ! [X0,X1] :
        ( aScalar0(sdtlbdtrb0(X0,X1))
        | ~ aNaturalNumber0(X1)
        | ~ aVector0(X0) )
    | ~ spl5_30 ),
    inference(avatar_component_clause,[],[f308]) ).

fof(f649,plain,
    ( spl5_73
    | ~ spl5_41 ),
    inference(avatar_split_clause,[],[f447,f386,f647]) ).

fof(f647,plain,
    ( spl5_73
  <=> ! [X0] :
        ( aScalar0(sdtasasdt0(X0,X0))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_73])]) ).

fof(f386,plain,
    ( spl5_41
  <=> ! [X0,X1] :
        ( aScalar0(sdtasasdt0(X0,X1))
        | aDimensionOf0(X0) != aDimensionOf0(X1)
        | ~ aVector0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).

fof(f447,plain,
    ( ! [X0] :
        ( aScalar0(sdtasasdt0(X0,X0))
        | ~ aVector0(X0) )
    | ~ spl5_41 ),
    inference(duplicate_literal_removal,[],[f446]) ).

fof(f446,plain,
    ( ! [X0] :
        ( aScalar0(sdtasasdt0(X0,X0))
        | ~ aVector0(X0)
        | ~ aVector0(X0) )
    | ~ spl5_41 ),
    inference(equality_resolution,[],[f387]) ).

fof(f387,plain,
    ( ! [X0,X1] :
        ( aDimensionOf0(X0) != aDimensionOf0(X1)
        | aScalar0(sdtasasdt0(X0,X1))
        | ~ aVector0(X1)
        | ~ aVector0(X0) )
    | ~ spl5_41 ),
    inference(avatar_component_clause,[],[f386]) ).

fof(f639,plain,
    ( ~ spl5_4
    | spl5_72
    | ~ spl5_38
    | ~ spl5_54 ),
    inference(avatar_split_clause,[],[f496,f490,f369,f637,f190]) ).

fof(f637,plain,
    ( spl5_72
  <=> ! [X0,X1] :
        ( sdtlseqdt0(X0,sdtasasdt0(X1,X1))
        | ~ aVector0(X1)
        | ~ iLess0(aDimensionOf0(X1),sz00)
        | ~ aScalar0(X0)
        | ~ aScalar0(sdtasasdt0(X1,X1))
        | ~ sdtlseqdt0(X0,sz0z00) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_72])]) ).

fof(f369,plain,
    ( spl5_38
  <=> ! [X0] :
        ( ~ iLess0(aDimensionOf0(X0),sz00)
        | sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).

fof(f496,plain,
    ( ! [X0,X1] :
        ( sdtlseqdt0(X0,sdtasasdt0(X1,X1))
        | ~ sdtlseqdt0(X0,sz0z00)
        | ~ aScalar0(sdtasasdt0(X1,X1))
        | ~ aScalar0(sz0z00)
        | ~ aScalar0(X0)
        | ~ iLess0(aDimensionOf0(X1),sz00)
        | ~ aVector0(X1) )
    | ~ spl5_38
    | ~ spl5_54 ),
    inference(resolution,[],[f491,f370]) ).

fof(f370,plain,
    ( ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        | ~ iLess0(aDimensionOf0(X0),sz00)
        | ~ aVector0(X0) )
    | ~ spl5_38 ),
    inference(avatar_component_clause,[],[f369]) ).

fof(f631,plain,
    ( spl5_71
    | ~ spl5_2
    | ~ spl5_5
    | ~ spl5_68 ),
    inference(avatar_split_clause,[],[f609,f605,f195,f180,f628]) ).

fof(f180,plain,
    ( spl5_2
  <=> aVector0(xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f195,plain,
    ( spl5_5
  <=> sz00 = aDimensionOf0(xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f605,plain,
    ( spl5_68
  <=> ! [X0] :
        ( sz0z00 = sdtasasdt0(X0,xs)
        | ~ aVector0(X0)
        | sz00 != aDimensionOf0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_68])]) ).

fof(f609,plain,
    ( ~ aVector0(xs)
    | sz0z00 = sdtasasdt0(xs,xs)
    | ~ spl5_5
    | ~ spl5_68 ),
    inference(trivial_inequality_removal,[],[f608]) ).

fof(f608,plain,
    ( sz00 != sz00
    | ~ aVector0(xs)
    | sz0z00 = sdtasasdt0(xs,xs)
    | ~ spl5_5
    | ~ spl5_68 ),
    inference(superposition,[],[f606,f197]) ).

fof(f197,plain,
    ( sz00 = aDimensionOf0(xs)
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f195]) ).

fof(f606,plain,
    ( ! [X0] :
        ( sz00 != aDimensionOf0(X0)
        | ~ aVector0(X0)
        | sz0z00 = sdtasasdt0(X0,xs) )
    | ~ spl5_68 ),
    inference(avatar_component_clause,[],[f605]) ).

fof(f626,plain,
    ( ~ spl5_4
    | spl5_70
    | ~ spl5_38
    | ~ spl5_46 ),
    inference(avatar_split_clause,[],[f469,f407,f369,f624,f190]) ).

fof(f624,plain,
    ( spl5_70
  <=> ! [X0] :
        ( sz0z00 = sdtasasdt0(X0,X0)
        | ~ aVector0(X0)
        | ~ iLess0(aDimensionOf0(X0),sz00)
        | ~ aScalar0(sdtasasdt0(X0,X0))
        | ~ sdtlseqdt0(sdtasasdt0(X0,X0),sz0z00) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_70])]) ).

fof(f407,plain,
    ( spl5_46
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ sdtlseqdt0(X1,X0)
        | ~ sdtlseqdt0(X0,X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_46])]) ).

fof(f469,plain,
    ( ! [X0] :
        ( sz0z00 = sdtasasdt0(X0,X0)
        | ~ sdtlseqdt0(sdtasasdt0(X0,X0),sz0z00)
        | ~ aScalar0(sz0z00)
        | ~ aScalar0(sdtasasdt0(X0,X0))
        | ~ iLess0(aDimensionOf0(X0),sz00)
        | ~ aVector0(X0) )
    | ~ spl5_38
    | ~ spl5_46 ),
    inference(resolution,[],[f408,f370]) ).

fof(f408,plain,
    ( ! [X0,X1] :
        ( ~ sdtlseqdt0(X1,X0)
        | X0 = X1
        | ~ sdtlseqdt0(X0,X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_46 ),
    inference(avatar_component_clause,[],[f407]) ).

fof(f613,plain,
    ( ~ spl5_2
    | spl5_69
    | ~ spl5_5
    | ~ spl5_51 ),
    inference(avatar_split_clause,[],[f493,f478,f195,f611,f180]) ).

fof(f611,plain,
    ( spl5_69
  <=> ! [X0] :
        ( aDimensionOf0(X0) != szszuzczcdt0(sz00)
        | sP0(X0,xs)
        | aNaturalNumber0(sK3(X0,xs)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_69])]) ).

fof(f478,plain,
    ( spl5_51
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | aNaturalNumber0(sK3(X0,X1))
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_51])]) ).

fof(f493,plain,
    ( ! [X0] :
        ( aDimensionOf0(X0) != szszuzczcdt0(sz00)
        | aNaturalNumber0(sK3(X0,xs))
        | sP0(X0,xs)
        | ~ aVector0(xs) )
    | ~ spl5_5
    | ~ spl5_51 ),
    inference(superposition,[],[f479,f197]) ).

fof(f479,plain,
    ( ! [X0,X1] :
        ( aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | aNaturalNumber0(sK3(X0,X1))
        | sP0(X0,X1)
        | ~ aVector0(X1) )
    | ~ spl5_51 ),
    inference(avatar_component_clause,[],[f478]) ).

fof(f607,plain,
    ( ~ spl5_2
    | spl5_68
    | ~ spl5_5
    | ~ spl5_57 ),
    inference(avatar_split_clause,[],[f531,f517,f195,f605,f180]) ).

fof(f517,plain,
    ( spl5_57
  <=> ! [X0,X1] :
        ( sz0z00 = sdtasasdt0(X0,X1)
        | sz00 != aDimensionOf0(X1)
        | sz00 != aDimensionOf0(X0)
        | ~ aVector0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_57])]) ).

fof(f531,plain,
    ( ! [X0] :
        ( sz0z00 = sdtasasdt0(X0,xs)
        | sz00 != aDimensionOf0(X0)
        | ~ aVector0(xs)
        | ~ aVector0(X0) )
    | ~ spl5_5
    | ~ spl5_57 ),
    inference(trivial_inequality_removal,[],[f530]) ).

fof(f530,plain,
    ( ! [X0] :
        ( sz00 != sz00
        | sz0z00 = sdtasasdt0(X0,xs)
        | sz00 != aDimensionOf0(X0)
        | ~ aVector0(xs)
        | ~ aVector0(X0) )
    | ~ spl5_5
    | ~ spl5_57 ),
    inference(superposition,[],[f518,f197]) ).

fof(f518,plain,
    ( ! [X0,X1] :
        ( sz00 != aDimensionOf0(X1)
        | sz0z00 = sdtasasdt0(X0,X1)
        | sz00 != aDimensionOf0(X0)
        | ~ aVector0(X1)
        | ~ aVector0(X0) )
    | ~ spl5_57 ),
    inference(avatar_component_clause,[],[f517]) ).

fof(f599,plain,
    spl5_67,
    inference(avatar_split_clause,[],[f148,f597]) ).

fof(f597,plain,
    ( spl5_67
  <=> ! [X0,X1] :
        ( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
        | sz00 = aDimensionOf0(X1)
        | aDimensionOf0(X0) != aDimensionOf0(X1)
        | ~ aVector0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_67])]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( ( sz00 != aDimensionOf0(X1)
          & aDimensionOf0(X0) = aDimensionOf0(X1) )
       => sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPN) ).

fof(f590,plain,
    spl5_66,
    inference(avatar_split_clause,[],[f169,f588]) ).

fof(f588,plain,
    ( spl5_66
  <=> ! [X0,X3,X2,X1] :
        ( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
        | ~ aScalar0(X3)
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_66])]) ).

fof(f169,plain,
    ! [X2,X3,X0,X1] :
      ( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X2,X3] :
      ( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1,X2,X3] :
      ( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1,X2,X3] :
      ( ( aScalar0(X3)
        & aScalar0(X2)
        & aScalar0(X1)
        & aScalar0(X0) )
     => sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr2) ).

fof(f582,plain,
    spl5_65,
    inference(avatar_split_clause,[],[f171,f580]) ).

fof(f580,plain,
    ( spl5_65
  <=> ! [X0,X3,X2,X1] :
        ( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
        | ~ sdtlseqdt0(X2,X3)
        | ~ sdtlseqdt0(sz0z00,X2)
        | ~ sdtlseqdt0(X0,X1)
        | ~ aScalar0(X3)
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_65])]) ).

fof(f171,plain,
    ! [X2,X3,X0,X1] :
      ( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
      | ~ sdtlseqdt0(X2,X3)
      | ~ sdtlseqdt0(sz0z00,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1,X2,X3] :
      ( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
      | ~ sdtlseqdt0(X2,X3)
      | ~ sdtlseqdt0(sz0z00,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1,X2,X3] :
      ( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
      | ~ sdtlseqdt0(X2,X3)
      | ~ sdtlseqdt0(sz0z00,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0,X1,X2,X3] :
      ( ( aScalar0(X3)
        & aScalar0(X2)
        & aScalar0(X1)
        & aScalar0(X0) )
     => ( ( sdtlseqdt0(X2,X3)
          & sdtlseqdt0(sz0z00,X2)
          & sdtlseqdt0(X0,X1) )
       => sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).

fof(f577,plain,
    spl5_64,
    inference(avatar_split_clause,[],[f127,f575]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
      | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
      | ~ aVector0(X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
          & aNaturalNumber0(sK3(X0,X1)) )
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) )
      & ( ( ! [X3] :
              ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
              | ~ aNaturalNumber0(X3) )
          & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
          & aVector0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f108,f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
          & aNaturalNumber0(X2) )
     => ( sdtlbdtrb0(X1,sK3(X0,X1)) != sdtlbdtrb0(X0,sK3(X0,X1))
        & aNaturalNumber0(sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
            & aNaturalNumber0(X2) )
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) )
      & ( ( ! [X3] :
              ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
              | ~ aNaturalNumber0(X3) )
          & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
          & aVector0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
            & aNaturalNumber0(X2) )
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) )
      & ( ( ! [X2] :
              ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
              | ~ aNaturalNumber0(X2) )
          & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
          & aVector0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
            & aNaturalNumber0(X2) )
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) )
      & ( ( ! [X2] :
              ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
              | ~ aNaturalNumber0(X2) )
          & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
          & aVector0(X1) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ( ! [X2] :
            ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
            | ~ aNaturalNumber0(X2) )
        & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
        & aVector0(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f571,plain,
    spl5_63,
    inference(avatar_split_clause,[],[f170,f569]) ).

fof(f569,plain,
    ( spl5_63
  <=> ! [X0,X3,X2,X1] :
        ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
        | ~ sdtlseqdt0(X2,X3)
        | ~ sdtlseqdt0(X0,X1)
        | ~ aScalar0(X3)
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_63])]) ).

fof(f170,plain,
    ! [X2,X3,X0,X1] :
      ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
      | ~ sdtlseqdt0(X2,X3)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1,X2,X3] :
      ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
      | ~ sdtlseqdt0(X2,X3)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X2,X3] :
      ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
      | ~ sdtlseqdt0(X2,X3)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X3)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1,X2,X3] :
      ( ( aScalar0(X3)
        & aScalar0(X2)
        & aScalar0(X1)
        & aScalar0(X0) )
     => ( ( sdtlseqdt0(X2,X3)
          & sdtlseqdt0(X0,X1) )
       => sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMon) ).

fof(f561,plain,
    spl5_62,
    inference(avatar_split_clause,[],[f159,f559]) ).

fof(f559,plain,
    ( spl5_62
  <=> ! [X0,X1] :
        ( X0 = X1
        | sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
        | ~ sdtlseqdt0(sz0z00,X1)
        | ~ sdtlseqdt0(sz0z00,X0)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_62])]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( X0 = X1
      | sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( X0 = X1
      | sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( X0 = X1
      | sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( ( sdtasdt0(X0,X0) = sdtasdt0(X1,X1)
          & sdtlseqdt0(sz0z00,X1)
          & sdtlseqdt0(sz0z00,X0) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).

fof(f557,plain,
    spl5_61,
    inference(avatar_split_clause,[],[f147,f555]) ).

fof(f555,plain,
    ( spl5_61
  <=> ! [X0,X1] :
        ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
        | sz00 = aDimensionOf0(X1)
        | aDimensionOf0(X0) != aDimensionOf0(X1)
        | ~ aVector0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_61])]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( ( sz00 != aDimensionOf0(X1)
          & aDimensionOf0(X0) = aDimensionOf0(X1) )
       => aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).

fof(f553,plain,
    ( ~ spl5_2
    | spl5_60
    | ~ spl5_5
    | ~ spl5_41 ),
    inference(avatar_split_clause,[],[f445,f386,f195,f551,f180]) ).

fof(f551,plain,
    ( spl5_60
  <=> ! [X0] :
        ( sz00 != aDimensionOf0(X0)
        | ~ aVector0(X0)
        | aScalar0(sdtasasdt0(X0,xs)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_60])]) ).

fof(f445,plain,
    ( ! [X0] :
        ( sz00 != aDimensionOf0(X0)
        | aScalar0(sdtasasdt0(X0,xs))
        | ~ aVector0(xs)
        | ~ aVector0(X0) )
    | ~ spl5_5
    | ~ spl5_41 ),
    inference(superposition,[],[f387,f197]) ).

fof(f539,plain,
    spl5_59,
    inference(avatar_split_clause,[],[f167,f537]) ).

fof(f537,plain,
    ( spl5_59
  <=> ! [X2,X0,X1] :
        ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_59])]) ).

fof(f167,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1,X2] :
      ( ( aScalar0(X2)
        & aScalar0(X1)
        & aScalar0(X0) )
     => ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).

fof(f535,plain,
    spl5_58,
    inference(avatar_split_clause,[],[f166,f533]) ).

fof(f533,plain,
    ( spl5_58
  <=> ! [X2,X0,X1] :
        ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_58])]) ).

fof(f166,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f519,plain,
    spl5_57,
    inference(avatar_split_clause,[],[f173,f517]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | sz00 != aDimensionOf0(X0)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(inner_rewriting,[],[f149]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( ( sz00 = aDimensionOf0(X1)
          & aDimensionOf0(X0) = aDimensionOf0(X1) )
       => sz0z00 = sdtasasdt0(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).

fof(f515,plain,
    spl5_56,
    inference(avatar_split_clause,[],[f164,f513]) ).

fof(f513,plain,
    ( spl5_56
  <=> ! [X2,X0,X1] :
        ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        | ~ aScalar0(X2)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_56])]) ).

fof(f164,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        & sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        & sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        & sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        & sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        & sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        & sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( ( aScalar0(X2)
        & aScalar0(X1)
        & aScalar0(X0) )
     => ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        & sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        & sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        & sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).

fof(f511,plain,
    spl5_55,
    inference(avatar_split_clause,[],[f162,f509]) ).

fof(f162,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f492,plain,
    spl5_54,
    inference(avatar_split_clause,[],[f168,f490]) ).

fof(f168,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1,X2] :
      ( ( aScalar0(X2)
        & aScalar0(X1)
        & aScalar0(X0) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X0,X1) )
       => sdtlseqdt0(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).

fof(f488,plain,
    spl5_53,
    inference(avatar_split_clause,[],[f161,f486]) ).

fof(f486,plain,
    ( spl5_53
  <=> ! [X0,X1] :
        ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
        | ~ sdtlseqdt0(sz0z00,X1)
        | ~ sdtlseqdt0(sz0z00,X0)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_53])]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
        & sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) )
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
        & sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) )
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( ( sdtlseqdt0(sz0z00,X1)
          & sdtlseqdt0(sz0z00,X0) )
       => ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
          & sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).

fof(f484,plain,
    spl5_52,
    inference(avatar_split_clause,[],[f160,f482]) ).

fof(f482,plain,
    ( spl5_52
  <=> ! [X0,X1] :
        ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
        | ~ sdtlseqdt0(sz0z00,X1)
        | ~ sdtlseqdt0(sz0z00,X0)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_52])]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f480,plain,
    spl5_51,
    inference(avatar_split_clause,[],[f126,f478]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | aNaturalNumber0(sK3(X0,X1))
      | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
      | ~ aVector0(X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f463,plain,
    ( ~ spl5_2
    | spl5_50
    | ~ spl5_5
    | ~ spl5_41 ),
    inference(avatar_split_clause,[],[f444,f386,f195,f461,f180]) ).

fof(f461,plain,
    ( spl5_50
  <=> ! [X0] :
        ( sz00 != aDimensionOf0(X0)
        | ~ aVector0(X0)
        | aScalar0(sdtasasdt0(xs,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_50])]) ).

fof(f444,plain,
    ( ! [X0] :
        ( sz00 != aDimensionOf0(X0)
        | aScalar0(sdtasasdt0(xs,X0))
        | ~ aVector0(X0)
        | ~ aVector0(xs) )
    | ~ spl5_5
    | ~ spl5_41 ),
    inference(superposition,[],[f387,f197]) ).

fof(f438,plain,
    ( spl5_47
    | spl5_49 ),
    inference(avatar_split_clause,[],[f165,f436,f411]) ).

fof(f411,plain,
    ( spl5_47
  <=> ! [X2] : ~ aScalar0(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_47])]) ).

fof(f165,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f419,plain,
    ( ~ spl5_4
    | ~ spl5_47 ),
    inference(avatar_contradiction_clause,[],[f417]) ).

fof(f417,plain,
    ( $false
    | ~ spl5_4
    | ~ spl5_47 ),
    inference(resolution,[],[f412,f192]) ).

fof(f412,plain,
    ( ! [X2] : ~ aScalar0(X2)
    | ~ spl5_47 ),
    inference(avatar_component_clause,[],[f411]) ).

fof(f416,plain,
    ( spl5_47
    | spl5_48 ),
    inference(avatar_split_clause,[],[f163,f414,f411]) ).

fof(f163,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f409,plain,
    spl5_46,
    inference(avatar_split_clause,[],[f158,f407]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & sdtlseqdt0(X0,X1) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).

fof(f405,plain,
    spl5_45,
    inference(avatar_split_clause,[],[f156,f403]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
        & sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) )
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
        & sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) )
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
        & sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).

fof(f401,plain,
    spl5_44,
    inference(avatar_split_clause,[],[f155,f399]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f397,plain,
    spl5_43,
    inference(avatar_split_clause,[],[f154,f395]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).

fof(f393,plain,
    ( ~ spl5_2
    | ~ spl5_42
    | spl5_1
    | ~ spl5_5
    | ~ spl5_38 ),
    inference(avatar_split_clause,[],[f373,f369,f195,f175,f390,f180]) ).

fof(f390,plain,
    ( spl5_42
  <=> iLess0(sz00,sz00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).

fof(f373,plain,
    ( ~ iLess0(sz00,sz00)
    | ~ aVector0(xs)
    | spl5_1
    | ~ spl5_5
    | ~ spl5_38 ),
    inference(forward_demodulation,[],[f372,f197]) ).

fof(f372,plain,
    ( ~ iLess0(aDimensionOf0(xs),sz00)
    | ~ aVector0(xs)
    | spl5_1
    | ~ spl5_38 ),
    inference(resolution,[],[f370,f177]) ).

fof(f388,plain,
    spl5_41,
    inference(avatar_split_clause,[],[f146,f386]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( aDimensionOf0(X0) = aDimensionOf0(X1)
       => aScalar0(sdtasasdt0(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).

fof(f381,plain,
    spl5_40,
    inference(avatar_split_clause,[],[f151,f379]) ).

fof(f379,plain,
    ( spl5_40
  <=> ! [X0,X1] :
        ( X0 = X1
        | szszuzczcdt0(X0) != szszuzczcdt0(X1)
        | ~ aNaturalNumber0(X1)
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( X0 = X1
      | szszuzczcdt0(X0) != szszuzczcdt0(X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( X0 = X1
      | szszuzczcdt0(X0) != szszuzczcdt0(X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( X0 = X1
      | szszuzczcdt0(X0) != szszuzczcdt0(X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).

fof(f377,plain,
    spl5_39,
    inference(avatar_split_clause,[],[f125,f375]) ).

fof(f125,plain,
    ! [X3,X0,X1] :
      ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
      | ~ aNaturalNumber0(X3)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f371,plain,
    ( spl5_38
    | ~ spl5_5
    | ~ spl5_37 ),
    inference(avatar_split_clause,[],[f367,f364,f195,f369]) ).

fof(f364,plain,
    ( spl5_37
  <=> ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).

fof(f367,plain,
    ( ! [X0] :
        ( ~ iLess0(aDimensionOf0(X0),sz00)
        | sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        | ~ aVector0(X0) )
    | ~ spl5_5
    | ~ spl5_37 ),
    inference(forward_demodulation,[],[f365,f197]) ).

fof(f365,plain,
    ( ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
        | ~ aVector0(X0) )
    | ~ spl5_37 ),
    inference(avatar_component_clause,[],[f364]) ).

fof(f366,plain,
    spl5_37,
    inference(avatar_split_clause,[],[f117,f364]) ).

fof(f117,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
      | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
      | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
      | ~ aVector0(X0) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
      | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( aVector0(X0)
     => ( iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
       => sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1516) ).

fof(f353,plain,
    spl5_36,
    inference(avatar_split_clause,[],[f157,f351]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( sdtlseqdt0(X1,X0)
        | sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).

fof(f349,plain,
    spl5_35,
    inference(avatar_split_clause,[],[f145,f347]) ).

fof(f145,plain,
    ! [X0] :
      ( szszuzczcdt0(sK4(X0)) = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ( szszuzczcdt0(sK4(X0)) = X0
        & aNaturalNumber0(sK4(X0)) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f59,f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aNaturalNumber0(X1) )
     => ( szszuzczcdt0(sK4(X0)) = X0
        & aNaturalNumber0(sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aNaturalNumber0(X1) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aNaturalNumber0(X1) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ( sz00 != X0
        & aNaturalNumber0(X0) )
     => ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aNaturalNumber0(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).

fof(f342,plain,
    spl5_34,
    inference(avatar_split_clause,[],[f124,f340]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f338,plain,
    spl5_33,
    inference(avatar_split_clause,[],[f122,f336]) ).

fof(f336,plain,
    ( spl5_33
  <=> ! [X0,X1] :
        ( sziznziztdt0(X0) = X1
        | ~ sP0(X0,X1)
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( sziznziztdt0(X0) = X1
      | ~ sP0(X0,X1)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sziznziztdt0(X0) = X1
            | ~ sP0(X0,X1) )
          & ( sP0(X0,X1)
            | sziznziztdt0(X0) != X1 ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> sP0(X0,X1) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f318,plain,
    spl5_32,
    inference(avatar_split_clause,[],[f153,f316]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => aScalar0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

fof(f314,plain,
    spl5_31,
    inference(avatar_split_clause,[],[f152,f312]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => aScalar0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).

fof(f310,plain,
    spl5_30,
    inference(avatar_split_clause,[],[f150,f308]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aVector0(X0) )
     => aScalar0(sdtlbdtrb0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).

fof(f306,plain,
    spl5_29,
    inference(avatar_split_clause,[],[f144,f304]) ).

fof(f304,plain,
    ( spl5_29
  <=> ! [X0] :
        ( aNaturalNumber0(sK4(X0))
        | sz00 = X0
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).

fof(f144,plain,
    ! [X0] :
      ( aNaturalNumber0(sK4(X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f302,plain,
    spl5_28,
    inference(avatar_split_clause,[],[f140,f300]) ).

fof(f300,plain,
    ( spl5_28
  <=> ! [X0] :
        ( sz0z00 = sdtpldt0(smndt0(X0),X0)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).

fof(f140,plain,
    ! [X0] :
      ( sz0z00 = sdtpldt0(smndt0(X0),X0)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 )
      | ~ sP2(X0) ),
    inference(nnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 )
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f298,plain,
    spl5_27,
    inference(avatar_split_clause,[],[f139,f296]) ).

fof(f296,plain,
    ( spl5_27
  <=> ! [X0] :
        ( sz0z00 = sdtpldt0(X0,smndt0(X0))
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).

fof(f139,plain,
    ! [X0] :
      ( sz0z00 = sdtpldt0(X0,smndt0(X0))
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f294,plain,
    spl5_26,
    inference(avatar_split_clause,[],[f128,f292]) ).

fof(f292,plain,
    ( spl5_26
  <=> ! [X0] :
        ( sP1(X0)
        | sz00 = aDimensionOf0(X0)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).

fof(f128,plain,
    ! [X0] :
      ( sP1(X0)
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( sP1(X0)
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(definition_folding,[],[f51,f101,f100]) ).

fof(f51,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                | ~ aNaturalNumber0(X2) )
            & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
            & aVector0(X1) ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                | ~ aNaturalNumber0(X2) )
            & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
            & aVector0(X1) ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0] :
      ( aVector0(X0)
     => ( sz00 != aDimensionOf0(X0)
       => ! [X1] :
            ( sziznziztdt0(X0) = X1
          <=> ( ! [X2] :
                  ( aNaturalNumber0(X2)
                 => sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
              & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
              & aVector0(X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInit) ).

fof(f290,plain,
    ( spl5_25
    | ~ spl5_9
    | ~ spl5_17 ),
    inference(avatar_split_clause,[],[f252,f249,f214,f288]) ).

fof(f288,plain,
    ( spl5_25
  <=> ! [X0] :
        ( ~ sP1(X0)
        | aVector0(sziznziztdt0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).

fof(f214,plain,
    ( spl5_9
  <=> ! [X0,X1] :
        ( aVector0(X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).

fof(f252,plain,
    ( ! [X0] :
        ( ~ sP1(X0)
        | aVector0(sziznziztdt0(X0)) )
    | ~ spl5_9
    | ~ spl5_17 ),
    inference(resolution,[],[f250,f215]) ).

fof(f215,plain,
    ( ! [X0,X1] :
        ( ~ sP0(X0,X1)
        | aVector0(X1) )
    | ~ spl5_9 ),
    inference(avatar_component_clause,[],[f214]) ).

fof(f280,plain,
    spl5_24,
    inference(avatar_split_clause,[],[f141,f278]) ).

fof(f278,plain,
    ( spl5_24
  <=> ! [X0] :
        ( smndt0(smndt0(X0)) = X0
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).

fof(f141,plain,
    ! [X0] :
      ( smndt0(smndt0(X0)) = X0
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f276,plain,
    spl5_23,
    inference(avatar_split_clause,[],[f138,f274]) ).

fof(f274,plain,
    ( spl5_23
  <=> ! [X0] :
        ( sz0z00 = sdtasdt0(sz0z00,X0)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).

fof(f138,plain,
    ! [X0] :
      ( sz0z00 = sdtasdt0(sz0z00,X0)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f272,plain,
    spl5_22,
    inference(avatar_split_clause,[],[f137,f270]) ).

fof(f270,plain,
    ( spl5_22
  <=> ! [X0] :
        ( sz0z00 = sdtasdt0(X0,sz0z00)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).

fof(f137,plain,
    ! [X0] :
      ( sz0z00 = sdtasdt0(X0,sz0z00)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f268,plain,
    spl5_21,
    inference(avatar_split_clause,[],[f136,f266]) ).

fof(f266,plain,
    ( spl5_21
  <=> ! [X0] :
        ( sdtpldt0(sz0z00,X0) = X0
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).

fof(f136,plain,
    ! [X0] :
      ( sdtpldt0(sz0z00,X0) = X0
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f264,plain,
    ( spl5_20
    | ~ spl5_6
    | ~ spl5_11 ),
    inference(avatar_split_clause,[],[f230,f222,f200,f262]) ).

fof(f262,plain,
    ( spl5_20
  <=> ! [X0] :
        ( ~ aScalar0(X0)
        | sP2(smndt0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).

fof(f230,plain,
    ( ! [X0] :
        ( ~ aScalar0(X0)
        | sP2(smndt0(X0)) )
    | ~ spl5_6
    | ~ spl5_11 ),
    inference(resolution,[],[f223,f201]) ).

fof(f260,plain,
    spl5_19,
    inference(avatar_split_clause,[],[f135,f258]) ).

fof(f258,plain,
    ( spl5_19
  <=> ! [X0] :
        ( sdtpldt0(X0,sz0z00) = X0
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).

fof(f135,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz0z00) = X0
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f256,plain,
    spl5_18,
    inference(avatar_split_clause,[],[f134,f254]) ).

fof(f254,plain,
    ( spl5_18
  <=> ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).

fof(f134,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).

fof(f251,plain,
    spl5_17,
    inference(avatar_split_clause,[],[f172,f249]) ).

fof(f172,plain,
    ! [X0] :
      ( sP0(X0,sziznziztdt0(X0))
      | ~ sP1(X0) ),
    inference(equality_resolution,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sziznziztdt0(X0) != X1
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f246,plain,
    ( spl5_15
    | spl5_16 ),
    inference(avatar_split_clause,[],[f142,f243,f240]) ).

fof(f240,plain,
    ( spl5_15
  <=> ! [X0] : ~ sP2(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).

fof(f142,plain,
    ! [X0] :
      ( sz0z00 = smndt0(sz0z00)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f238,plain,
    spl5_14,
    inference(avatar_split_clause,[],[f131,f236]) ).

fof(f236,plain,
    ( spl5_14
  <=> ! [X0] :
        ( sz00 != szszuzczcdt0(X0)
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).

fof(f131,plain,
    ! [X0] :
      ( sz00 != szszuzczcdt0(X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ( sz00 != szszuzczcdt0(X0)
        & aNaturalNumber0(szszuzczcdt0(X0)) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 != szszuzczcdt0(X0)
        & aNaturalNumber0(szszuzczcdt0(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).

fof(f234,plain,
    spl5_13,
    inference(avatar_split_clause,[],[f129,f232]) ).

fof(f232,plain,
    ( spl5_13
  <=> ! [X0] :
        ( iLess0(X0,szszuzczcdt0(X0))
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).

fof(f129,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => iLess0(X0,szszuzczcdt0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).

fof(f228,plain,
    spl5_12,
    inference(avatar_split_clause,[],[f133,f226]) ).

fof(f133,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => sdtlseqdt0(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).

fof(f224,plain,
    spl5_11,
    inference(avatar_split_clause,[],[f132,f222]) ).

fof(f132,plain,
    ! [X0] :
      ( aScalar0(smndt0(X0))
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( aScalar0(smndt0(X0))
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => aScalar0(smndt0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

fof(f220,plain,
    spl5_10,
    inference(avatar_split_clause,[],[f130,f218]) ).

fof(f130,plain,
    ! [X0] :
      ( aNaturalNumber0(szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f216,plain,
    spl5_9,
    inference(avatar_split_clause,[],[f123,f214]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( aVector0(X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f212,plain,
    spl5_8,
    inference(avatar_split_clause,[],[f120,f210]) ).

fof(f120,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( aVector0(X0)
     => aNaturalNumber0(aDimensionOf0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).

fof(f208,plain,
    ( spl5_7
    | ~ spl5_4
    | ~ spl5_6 ),
    inference(avatar_split_clause,[],[f203,f200,f190,f205]) ).

fof(f205,plain,
    ( spl5_7
  <=> sP2(sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f203,plain,
    ( sP2(sz0z00)
    | ~ spl5_4
    | ~ spl5_6 ),
    inference(resolution,[],[f201,f192]) ).

fof(f202,plain,
    spl5_6,
    inference(avatar_split_clause,[],[f143,f200]) ).

fof(f143,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ aScalar0(X0) ),
    inference(definition_folding,[],[f57,f103]) ).

fof(f57,plain,
    ! [X0] :
      ( ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 )
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

fof(f198,plain,
    ( spl5_5
    | spl5_1 ),
    inference(avatar_split_clause,[],[f114,f175,f195]) ).

fof(f114,plain,
    ( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
    | sz00 = aDimensionOf0(xs) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
    & ( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
      | sz00 = aDimensionOf0(xs) ) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,negated_conjecture,
    ~ ( ( sz00 != aDimensionOf0(xs)
       => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
     => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    inference(negated_conjecture,[],[f39]) ).

fof(f39,conjecture,
    ( ( sz00 != aDimensionOf0(xs)
     => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
   => sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f193,plain,
    spl5_4,
    inference(avatar_split_clause,[],[f119,f190]) ).

fof(f119,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

fof(f188,plain,
    spl5_3,
    inference(avatar_split_clause,[],[f118,f185]) ).

fof(f185,plain,
    ( spl5_3
  <=> aNaturalNumber0(sz00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f118,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).

fof(f183,plain,
    spl5_2,
    inference(avatar_split_clause,[],[f116,f180]) ).

fof(f116,plain,
    aVector0(xs),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    aVector0(xs),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).

fof(f178,plain,
    ~ spl5_1,
    inference(avatar_split_clause,[],[f115,f175]) ).

fof(f115,plain,
    ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
    inference(cnf_transformation,[],[f46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n019.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   : Sat May 18 12:31:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (16298)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (16301)WARNING: value z3 for option sas not known
% 0.20/0.37  % (16302)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (16299)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37  % (16300)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  % (16301)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)
% 0.20/0.38  % (16303)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)
% 0.20/0.38  % (16304)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)
% 0.20/0.38  % (16305)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)
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.39  TRYING [3]
% 0.20/0.39  TRYING [3]
% 0.20/0.40  % (16303)First to succeed.
% 0.20/0.40  % (16303)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16298"
% 0.20/0.40  TRYING [1]
% 0.20/0.40  % (16303)Refutation found. Thanks to Tanya!
% 0.20/0.40  % SZS status Theorem for theBenchmark
% 0.20/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41  % (16303)------------------------------
% 0.20/0.41  % (16303)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.41  % (16303)Termination reason: Refutation
% 0.20/0.41  
% 0.20/0.41  % (16303)Memory used [KB]: 1264
% 0.20/0.41  % (16303)Time elapsed: 0.029 s
% 0.20/0.41  % (16303)Instructions burned: 42 (million)
% 0.20/0.41  % (16298)Success in time 0.047 s
%------------------------------------------------------------------------------