TSTP Solution File: RNG072+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : RNG072+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 14:51:21 EDT 2024

% Result   : Theorem 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  189
% Syntax   : Number of formulae    :  567 ( 152 unt;   0 def)
%            Number of atoms       : 1588 ( 312 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 1730 ( 709   ~; 703   |; 139   &)
%                                         ( 131 <=>;  48  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  136 ( 134 usr; 127 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  18 con; 0-2 aty)
%            Number of variables   :  442 ( 434   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1322,plain,
    $false,
    inference(avatar_sat_refutation,[],[f244,f249,f254,f259,f264,f269,f274,f279,f284,f289,f294,f299,f304,f309,f314,f319,f324,f329,f334,f339,f344,f349,f353,f371,f376,f381,f386,f391,f396,f401,f406,f411,f416,f421,f426,f431,f436,f441,f447,f451,f455,f460,f464,f468,f472,f479,f484,f489,f493,f497,f505,f510,f518,f523,f528,f533,f537,f541,f545,f549,f554,f558,f562,f566,f575,f579,f583,f587,f591,f595,f599,f603,f613,f631,f635,f642,f646,f651,f665,f669,f676,f680,f684,f688,f693,f697,f704,f719,f720,f721,f722,f723,f724,f725,f726,f727,f728,f729,f730,f731,f767,f794,f886,f891,f896,f902,f906,f910,f914,f954,f958,f962,f1001,f1005,f1050,f1054,f1070,f1078,f1083,f1116,f1124,f1145,f1221,f1236,f1245,f1253,f1263,f1272,f1277,f1278,f1296,f1303,f1310,f1316,f1320,f1321]) ).

fof(f1321,plain,
    ( ~ spl5_15
    | ~ spl5_14
    | ~ spl5_72
    | spl5_114 ),
    inference(avatar_split_clause,[],[f1246,f1238,f597,f306,f311]) ).

fof(f311,plain,
    ( spl5_15
  <=> aScalar0(xR) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).

fof(f306,plain,
    ( spl5_14
  <=> aScalar0(xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).

fof(f597,plain,
    ( spl5_72
  <=> ! [X0,X1] :
        ( aScalar0(sdtpldt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_72])]) ).

fof(f1238,plain,
    ( spl5_114
  <=> aScalar0(sdtpldt0(xR,xS)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_114])]) ).

fof(f1246,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(xR)
    | ~ spl5_72
    | spl5_114 ),
    inference(resolution,[],[f1240,f598]) ).

fof(f598,plain,
    ( ! [X0,X1] :
        ( aScalar0(sdtpldt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) )
    | ~ spl5_72 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f1240,plain,
    ( ~ aScalar0(sdtpldt0(xR,xS))
    | spl5_114 ),
    inference(avatar_component_clause,[],[f1238]) ).

fof(f1320,plain,
    ( spl5_126
    | ~ spl5_43
    | ~ spl5_53 ),
    inference(avatar_split_clause,[],[f511,f508,f462,f1318]) ).

fof(f1318,plain,
    ( spl5_126
  <=> ! [X0] :
        ( ~ sP1(X0)
        | aVector0(sziznziztdt0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_126])]) ).

fof(f462,plain,
    ( spl5_43
  <=> ! [X0,X1] :
        ( aVector0(X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).

fof(f508,plain,
    ( spl5_53
  <=> ! [X0] :
        ( sP0(X0,sziznziztdt0(X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_53])]) ).

fof(f511,plain,
    ( ! [X0] :
        ( ~ sP1(X0)
        | aVector0(sziznziztdt0(X0)) )
    | ~ spl5_43
    | ~ spl5_53 ),
    inference(resolution,[],[f509,f463]) ).

fof(f463,plain,
    ( ! [X0,X1] :
        ( ~ sP0(X0,X1)
        | aVector0(X1) )
    | ~ spl5_43 ),
    inference(avatar_component_clause,[],[f462]) ).

fof(f509,plain,
    ( ! [X0] :
        ( sP0(X0,sziznziztdt0(X0))
        | ~ sP1(X0) )
    | ~ spl5_53 ),
    inference(avatar_component_clause,[],[f508]) ).

fof(f1316,plain,
    ( spl5_125
    | ~ spl5_23
    | ~ spl5_44 ),
    inference(avatar_split_clause,[],[f474,f466,f351,f1314]) ).

fof(f1314,plain,
    ( spl5_125
  <=> ! [X0] :
        ( ~ aScalar0(X0)
        | sP2(smndt0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_125])]) ).

fof(f351,plain,
    ( spl5_23
  <=> ! [X0] :
        ( sP2(X0)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).

fof(f466,plain,
    ( spl5_44
  <=> ! [X0] :
        ( aScalar0(smndt0(X0))
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).

fof(f474,plain,
    ( ! [X0] :
        ( ~ aScalar0(X0)
        | sP2(smndt0(X0)) )
    | ~ spl5_23
    | ~ spl5_44 ),
    inference(resolution,[],[f467,f352]) ).

fof(f352,plain,
    ( ! [X0] :
        ( ~ aScalar0(X0)
        | sP2(X0) )
    | ~ spl5_23 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f467,plain,
    ( ! [X0] :
        ( aScalar0(smndt0(X0))
        | ~ aScalar0(X0) )
    | ~ spl5_44 ),
    inference(avatar_component_clause,[],[f466]) ).

fof(f1310,plain,
    ( ~ spl5_12
    | spl5_124
    | ~ spl5_27
    | ~ spl5_59 ),
    inference(avatar_split_clause,[],[f570,f539,f383,f1307,f296]) ).

fof(f296,plain,
    ( spl5_12
  <=> aScalar0(xB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).

fof(f1307,plain,
    ( spl5_124
  <=> sdtlseqdt0(sz0z00,xG) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_124])]) ).

fof(f383,plain,
    ( spl5_27
  <=> xG = sdtasdt0(xB,xB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).

fof(f539,plain,
    ( spl5_59
  <=> ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_59])]) ).

fof(f570,plain,
    ( sdtlseqdt0(sz0z00,xG)
    | ~ aScalar0(xB)
    | ~ spl5_27
    | ~ spl5_59 ),
    inference(superposition,[],[f540,f385]) ).

fof(f385,plain,
    ( xG = sdtasdt0(xB,xB)
    | ~ spl5_27 ),
    inference(avatar_component_clause,[],[f383]) ).

fof(f540,plain,
    ( ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
        | ~ aScalar0(X0) )
    | ~ spl5_59 ),
    inference(avatar_component_clause,[],[f539]) ).

fof(f1303,plain,
    ( ~ spl5_13
    | spl5_123
    | ~ spl5_26
    | ~ spl5_59 ),
    inference(avatar_split_clause,[],[f569,f539,f378,f1300,f301]) ).

fof(f301,plain,
    ( spl5_13
  <=> aScalar0(xA) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).

fof(f1300,plain,
    ( spl5_123
  <=> sdtlseqdt0(sz0z00,xF) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_123])]) ).

fof(f378,plain,
    ( spl5_26
  <=> xF = sdtasdt0(xA,xA) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).

fof(f569,plain,
    ( sdtlseqdt0(sz0z00,xF)
    | ~ aScalar0(xA)
    | ~ spl5_26
    | ~ spl5_59 ),
    inference(superposition,[],[f540,f380]) ).

fof(f380,plain,
    ( xF = sdtasdt0(xA,xA)
    | ~ spl5_26 ),
    inference(avatar_component_clause,[],[f378]) ).

fof(f1296,plain,
    ( ~ spl5_2
    | spl5_122
    | ~ spl5_31
    | ~ spl5_58 ),
    inference(avatar_split_clause,[],[f568,f535,f403,f1293,f246]) ).

fof(f246,plain,
    ( spl5_2
  <=> aVector0(xp) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f1293,plain,
    ( spl5_122
  <=> sdtlseqdt0(sz0z00,xC) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_122])]) ).

fof(f403,plain,
    ( spl5_31
  <=> xC = sdtasasdt0(xp,xp) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).

fof(f535,plain,
    ( spl5_58
  <=> ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_58])]) ).

fof(f568,plain,
    ( sdtlseqdt0(sz0z00,xC)
    | ~ aVector0(xp)
    | ~ spl5_31
    | ~ spl5_58 ),
    inference(superposition,[],[f536,f405]) ).

fof(f405,plain,
    ( xC = sdtasasdt0(xp,xp)
    | ~ spl5_31 ),
    inference(avatar_component_clause,[],[f403]) ).

fof(f536,plain,
    ( ! [X0] :
        ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
        | ~ aVector0(X0) )
    | ~ spl5_58 ),
    inference(avatar_component_clause,[],[f535]) ).

fof(f1278,plain,
    ( ~ spl5_16
    | ~ spl5_72
    | spl5_115 ),
    inference(avatar_split_clause,[],[f1248,f1242,f597,f316]) ).

fof(f316,plain,
    ( spl5_16
  <=> aScalar0(xP) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).

fof(f1242,plain,
    ( spl5_115
  <=> aScalar0(sdtpldt0(xP,xP)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_115])]) ).

fof(f1248,plain,
    ( ~ aScalar0(xP)
    | ~ spl5_72
    | spl5_115 ),
    inference(duplicate_literal_removal,[],[f1247]) ).

fof(f1247,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(xP)
    | ~ spl5_72
    | spl5_115 ),
    inference(resolution,[],[f1244,f598]) ).

fof(f1244,plain,
    ( ~ aScalar0(sdtpldt0(xP,xP))
    | spl5_115 ),
    inference(avatar_component_clause,[],[f1242]) ).

fof(f1277,plain,
    ( ~ spl5_1
    | spl5_121
    | ~ spl5_30
    | ~ spl5_58 ),
    inference(avatar_split_clause,[],[f567,f535,f398,f1274,f241]) ).

fof(f241,plain,
    ( spl5_1
  <=> aVector0(xq) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f1274,plain,
    ( spl5_121
  <=> sdtlseqdt0(sz0z00,xD) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_121])]) ).

fof(f398,plain,
    ( spl5_30
  <=> xD = sdtasasdt0(xq,xq) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).

fof(f567,plain,
    ( sdtlseqdt0(sz0z00,xD)
    | ~ aVector0(xq)
    | ~ spl5_30
    | ~ spl5_58 ),
    inference(superposition,[],[f536,f400]) ).

fof(f400,plain,
    ( xD = sdtasasdt0(xq,xq)
    | ~ spl5_30 ),
    inference(avatar_component_clause,[],[f398]) ).

fof(f1272,plain,
    ( ~ spl5_119
    | spl5_120
    | ~ spl5_22
    | ~ spl5_53 ),
    inference(avatar_split_clause,[],[f513,f508,f346,f1269,f1265]) ).

fof(f1265,plain,
    ( spl5_119
  <=> sP1(xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_119])]) ).

fof(f1269,plain,
    ( spl5_120
  <=> sP0(xs,xp) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_120])]) ).

fof(f346,plain,
    ( spl5_22
  <=> xp = sziznziztdt0(xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).

fof(f513,plain,
    ( sP0(xs,xp)
    | ~ sP1(xs)
    | ~ spl5_22
    | ~ spl5_53 ),
    inference(superposition,[],[f509,f348]) ).

fof(f348,plain,
    ( xp = sziznziztdt0(xs)
    | ~ spl5_22 ),
    inference(avatar_component_clause,[],[f346]) ).

fof(f1263,plain,
    ( ~ spl5_117
    | spl5_118
    | ~ spl5_21
    | ~ spl5_53 ),
    inference(avatar_split_clause,[],[f512,f508,f341,f1260,f1256]) ).

fof(f1256,plain,
    ( spl5_117
  <=> sP1(xt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_117])]) ).

fof(f1260,plain,
    ( spl5_118
  <=> sP0(xt,xq) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_118])]) ).

fof(f341,plain,
    ( spl5_21
  <=> xq = sziznziztdt0(xt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).

fof(f512,plain,
    ( sP0(xt,xq)
    | ~ sP1(xt)
    | ~ spl5_21
    | ~ spl5_53 ),
    inference(superposition,[],[f509,f343]) ).

fof(f343,plain,
    ( xq = sziznziztdt0(xt)
    | ~ spl5_21 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f1253,plain,
    ( ~ spl5_3
    | spl5_116
    | ~ spl5_24
    | ~ spl5_41 ),
    inference(avatar_split_clause,[],[f473,f453,f368,f1250,f251]) ).

fof(f251,plain,
    ( spl5_3
  <=> aVector0(xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f1250,plain,
    ( spl5_116
  <=> aNaturalNumber0(aDimensionOf0(xt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_116])]) ).

fof(f368,plain,
    ( spl5_24
  <=> aDimensionOf0(xs) = aDimensionOf0(xt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).

fof(f453,plain,
    ( spl5_41
  <=> ! [X0] :
        ( aNaturalNumber0(aDimensionOf0(X0))
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).

fof(f473,plain,
    ( aNaturalNumber0(aDimensionOf0(xt))
    | ~ aVector0(xs)
    | ~ spl5_24
    | ~ spl5_41 ),
    inference(superposition,[],[f454,f370]) ).

fof(f370,plain,
    ( aDimensionOf0(xs) = aDimensionOf0(xt)
    | ~ spl5_24 ),
    inference(avatar_component_clause,[],[f368]) ).

fof(f454,plain,
    ( ! [X0] :
        ( aNaturalNumber0(aDimensionOf0(X0))
        | ~ aVector0(X0) )
    | ~ spl5_41 ),
    inference(avatar_component_clause,[],[f453]) ).

fof(f1245,plain,
    ( ~ spl5_114
    | ~ spl5_115
    | ~ spl5_37
    | ~ spl5_56
    | spl5_19
    | ~ spl5_108 ),
    inference(avatar_split_clause,[],[f1112,f1081,f331,f525,f433,f1242,f1238]) ).

fof(f433,plain,
    ( spl5_37
  <=> sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).

fof(f525,plain,
    ( spl5_56
  <=> sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_56])]) ).

fof(f331,plain,
    ( spl5_19
  <=> sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).

fof(f1081,plain,
    ( spl5_108
  <=> ! [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_108])]) ).

fof(f1112,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP))
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
    | ~ aScalar0(sdtpldt0(xP,xP))
    | ~ aScalar0(sdtpldt0(xR,xS))
    | spl5_19
    | ~ spl5_108 ),
    inference(duplicate_literal_removal,[],[f1091]) ).

fof(f1091,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP))
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
    | ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP))
    | ~ aScalar0(sdtpldt0(xP,xP))
    | ~ aScalar0(sdtpldt0(xR,xS))
    | ~ aScalar0(sdtpldt0(xP,xP))
    | ~ aScalar0(sdtpldt0(xR,xS))
    | spl5_19
    | ~ spl5_108 ),
    inference(resolution,[],[f1082,f333]) ).

fof(f333,plain,
    ( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
    | spl5_19 ),
    inference(avatar_component_clause,[],[f331]) ).

fof(f1082,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) )
    | ~ spl5_108 ),
    inference(avatar_component_clause,[],[f1081]) ).

fof(f1236,plain,
    ( ~ spl5_113
    | spl5_20
    | ~ spl5_24 ),
    inference(avatar_split_clause,[],[f442,f368,f336,f1233]) ).

fof(f1233,plain,
    ( spl5_113
  <=> sz00 = aDimensionOf0(xt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_113])]) ).

fof(f336,plain,
    ( spl5_20
  <=> sz00 = aDimensionOf0(xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).

fof(f442,plain,
    ( sz00 != aDimensionOf0(xt)
    | spl5_20
    | ~ spl5_24 ),
    inference(superposition,[],[f338,f370]) ).

fof(f338,plain,
    ( sz00 != aDimensionOf0(xs)
    | spl5_20 ),
    inference(avatar_component_clause,[],[f336]) ).

fof(f1221,plain,
    ( spl5_112
    | ~ spl5_18
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f354,f351,f326,f1218]) ).

fof(f1218,plain,
    ( spl5_112
  <=> sP2(sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_112])]) ).

fof(f326,plain,
    ( spl5_18
  <=> aScalar0(sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).

fof(f354,plain,
    ( sP2(sz0z00)
    | ~ spl5_18
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f328]) ).

fof(f328,plain,
    ( aScalar0(sz0z00)
    | ~ spl5_18 ),
    inference(avatar_component_clause,[],[f326]) ).

fof(f1145,plain,
    spl5_111,
    inference(avatar_split_clause,[],[f214,f1143]) ).

fof(f1143,plain,
    ( spl5_111
  <=> ! [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_111])]) ).

fof(f214,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,[],[f94]) ).

fof(f94,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,[],[f93]) ).

fof(f93,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/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).

fof(f1124,plain,
    spl5_110,
    inference(avatar_split_clause,[],[f233,f1122]) ).

fof(f1122,plain,
    ( spl5_110
  <=> ! [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_110])]) ).

fof(f233,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,[],[f120]) ).

fof(f120,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,[],[f119]) ).

fof(f119,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/sandbox2/benchmark/theBenchmark.p',mDistr2) ).

fof(f1116,plain,
    spl5_109,
    inference(avatar_split_clause,[],[f238,f1114]) ).

fof(f1114,plain,
    ( spl5_109
  <=> ! [X0,X1] :
        ( ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xt))
        | sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
        | aDimensionOf0(X0) != aDimensionOf0(X1)
        | ~ aVector0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_109])]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xt))
      | sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(forward_demodulation,[],[f180,f141]) ).

fof(f141,plain,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).

fof(f180,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
      | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
      | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
      | ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( ( aVector0(X1)
        & aVector0(X0) )
     => ( aDimensionOf0(X0) = aDimensionOf0(X1)
       => ( iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
         => sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1652) ).

fof(f1083,plain,
    spl5_108,
    inference(avatar_split_clause,[],[f235,f1081]) ).

fof(f235,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,[],[f124]) ).

fof(f124,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,[],[f123]) ).

fof(f123,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/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).

fof(f1078,plain,
    spl5_107,
    inference(avatar_split_clause,[],[f194,f1076]) ).

fof(f1076,plain,
    ( spl5_107
  <=> ! [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_107])]) ).

fof(f194,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,[],[f135]) ).

fof(f135,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])],[f133,f134]) ).

fof(f134,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(f133,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,[],[f132]) ).

fof(f132,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,[],[f131]) ).

fof(f131,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,[],[f125]) ).

fof(f125,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(f1070,plain,
    spl5_106,
    inference(avatar_split_clause,[],[f234,f1068]) ).

fof(f1068,plain,
    ( spl5_106
  <=> ! [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_106])]) ).

fof(f234,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,[],[f122]) ).

fof(f122,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,[],[f121]) ).

fof(f121,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/sandbox2/benchmark/theBenchmark.p',mLEMon) ).

fof(f1054,plain,
    spl5_105,
    inference(avatar_split_clause,[],[f223,f1052]) ).

fof(f1052,plain,
    ( spl5_105
  <=> ! [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_105])]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( X0 = X1
      | sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( X0 = X1
      | sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f109]) ).

fof(f109,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/sandbox2/benchmark/theBenchmark.p',mSqrt) ).

fof(f1050,plain,
    spl5_104,
    inference(avatar_split_clause,[],[f213,f1048]) ).

fof(f1048,plain,
    ( spl5_104
  <=> ! [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_104])]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
      | sz00 = aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f91]) ).

fof(f91,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/sandbox2/benchmark/theBenchmark.p',mEqInit) ).

fof(f1005,plain,
    spl5_103,
    inference(avatar_split_clause,[],[f231,f1003]) ).

fof(f1003,plain,
    ( spl5_103
  <=> ! [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_103])]) ).

fof(f231,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,[],[f116]) ).

fof(f116,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,[],[f115]) ).

fof(f115,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/sandbox2/benchmark/theBenchmark.p',mDistr) ).

fof(f1001,plain,
    spl5_102,
    inference(avatar_split_clause,[],[f230,f999]) ).

fof(f999,plain,
    ( spl5_102
  <=> ! [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_102])]) ).

fof(f230,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,[],[f116]) ).

fof(f962,plain,
    spl5_101,
    inference(avatar_split_clause,[],[f239,f960]) ).

fof(f960,plain,
    ( spl5_101
  <=> ! [X0,X1] :
        ( sz0z00 = sdtasasdt0(X0,X1)
        | sz00 != aDimensionOf0(X1)
        | sz00 != aDimensionOf0(X0)
        | ~ aVector0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_101])]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | sz00 != aDimensionOf0(X0)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(inner_rewriting,[],[f215]) ).

fof(f215,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( sz0z00 = sdtasasdt0(X0,X1)
      | sz00 != aDimensionOf0(X1)
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f95]) ).

fof(f95,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/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).

fof(f958,plain,
    spl5_100,
    inference(avatar_split_clause,[],[f228,f956]) ).

fof(f956,plain,
    ( spl5_100
  <=> ! [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_100])]) ).

fof(f228,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f114,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,[],[f113]) ).

fof(f113,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/sandbox2/benchmark/theBenchmark.p',mArith) ).

fof(f954,plain,
    spl5_99,
    inference(avatar_split_clause,[],[f226,f952]) ).

fof(f952,plain,
    ( spl5_99
  <=> ! [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_99])]) ).

fof(f226,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f914,plain,
    spl5_98,
    inference(avatar_split_clause,[],[f232,f912]) ).

fof(f912,plain,
    ( spl5_98
  <=> ! [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_98])]) ).

fof(f232,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0,X1,X2] :
      ( sdtlseqdt0(X0,X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f117]) ).

fof(f117,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/sandbox2/benchmark/theBenchmark.p',mLETrn) ).

fof(f910,plain,
    spl5_97,
    inference(avatar_split_clause,[],[f225,f908]) ).

fof(f908,plain,
    ( spl5_97
  <=> ! [X0,X1] :
        ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
        | ~ sdtlseqdt0(sz0z00,X1)
        | ~ sdtlseqdt0(sz0z00,X0)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_97])]) ).

fof(f225,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,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,[],[f111]) ).

fof(f111,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/sandbox2/benchmark/theBenchmark.p',mPosMon) ).

fof(f906,plain,
    spl5_96,
    inference(avatar_split_clause,[],[f224,f904]) ).

fof(f904,plain,
    ( spl5_96
  <=> ! [X0,X1] :
        ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
        | ~ sdtlseqdt0(sz0z00,X1)
        | ~ sdtlseqdt0(sz0z00,X0)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_96])]) ).

fof(f224,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
      | ~ sdtlseqdt0(sz0z00,X1)
      | ~ sdtlseqdt0(sz0z00,X0)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f902,plain,
    spl5_95,
    inference(avatar_split_clause,[],[f193,f900]) ).

fof(f900,plain,
    ( spl5_95
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | aNaturalNumber0(sK3(X0,X1))
        | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
        | ~ aVector0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_95])]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | aNaturalNumber0(sK3(X0,X1))
      | aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
      | ~ aVector0(X1) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f896,plain,
    spl5_94,
    inference(avatar_split_clause,[],[f147,f893]) ).

fof(f893,plain,
    ( spl5_94
  <=> sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_94])]) ).

fof(f147,plain,
    sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,axiom,
    sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2405) ).

fof(f891,plain,
    ( spl5_93
    | ~ spl5_8
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f366,f351,f276,f888]) ).

fof(f888,plain,
    ( spl5_93
  <=> sP2(xN) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_93])]) ).

fof(f276,plain,
    ( spl5_8
  <=> aScalar0(xN) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

fof(f366,plain,
    ( sP2(xN)
    | ~ spl5_8
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f278]) ).

fof(f278,plain,
    ( aScalar0(xN)
    | ~ spl5_8 ),
    inference(avatar_component_clause,[],[f276]) ).

fof(f886,plain,
    spl5_92,
    inference(avatar_split_clause,[],[f146,f883]) ).

fof(f883,plain,
    ( spl5_92
  <=> sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_92])]) ).

fof(f146,plain,
    sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,axiom,
    sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2104) ).

fof(f794,plain,
    ( spl5_88
    | spl5_91 ),
    inference(avatar_split_clause,[],[f229,f792,f699]) ).

fof(f699,plain,
    ( spl5_88
  <=> ! [X2] : ~ aScalar0(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_88])]) ).

fof(f792,plain,
    ( spl5_91
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_91])]) ).

fof(f229,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f767,plain,
    ( spl5_90
    | ~ spl5_14
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f365,f351,f306,f764]) ).

fof(f764,plain,
    ( spl5_90
  <=> sP2(xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_90])]) ).

fof(f365,plain,
    ( sP2(xS)
    | ~ spl5_14
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f308]) ).

fof(f308,plain,
    ( aScalar0(xS)
    | ~ spl5_14 ),
    inference(avatar_component_clause,[],[f306]) ).

fof(f731,plain,
    ( ~ spl5_18
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f705]) ).

fof(f705,plain,
    ( $false
    | ~ spl5_18
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f328]) ).

fof(f700,plain,
    ( ! [X2] : ~ aScalar0(X2)
    | ~ spl5_88 ),
    inference(avatar_component_clause,[],[f699]) ).

fof(f730,plain,
    ( ~ spl5_13
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f707]) ).

fof(f707,plain,
    ( $false
    | ~ spl5_13
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f303]) ).

fof(f303,plain,
    ( aScalar0(xA)
    | ~ spl5_13 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f729,plain,
    ( ~ spl5_12
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f708]) ).

fof(f708,plain,
    ( $false
    | ~ spl5_12
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f298]) ).

fof(f298,plain,
    ( aScalar0(xB)
    | ~ spl5_12 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f728,plain,
    ( ~ spl5_10
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f709]) ).

fof(f709,plain,
    ( $false
    | ~ spl5_10
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f288]) ).

fof(f288,plain,
    ( aScalar0(xC)
    | ~ spl5_10 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f286,plain,
    ( spl5_10
  <=> aScalar0(xC) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).

fof(f727,plain,
    ( ~ spl5_9
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f710]) ).

fof(f710,plain,
    ( $false
    | ~ spl5_9
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f283]) ).

fof(f283,plain,
    ( aScalar0(xD)
    | ~ spl5_9 ),
    inference(avatar_component_clause,[],[f281]) ).

fof(f281,plain,
    ( spl5_9
  <=> aScalar0(xD) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).

fof(f726,plain,
    ( ~ spl5_11
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f711]) ).

fof(f711,plain,
    ( $false
    | ~ spl5_11
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f293]) ).

fof(f293,plain,
    ( aScalar0(xE)
    | ~ spl5_11 ),
    inference(avatar_component_clause,[],[f291]) ).

fof(f291,plain,
    ( spl5_11
  <=> aScalar0(xE) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).

fof(f725,plain,
    ( ~ spl5_5
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f712]) ).

fof(f712,plain,
    ( $false
    | ~ spl5_5
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f263]) ).

fof(f263,plain,
    ( aScalar0(xF)
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f261,plain,
    ( spl5_5
  <=> aScalar0(xF) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f724,plain,
    ( ~ spl5_6
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f713]) ).

fof(f713,plain,
    ( $false
    | ~ spl5_6
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f268]) ).

fof(f268,plain,
    ( aScalar0(xG)
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f266,plain,
    ( spl5_6
  <=> aScalar0(xG) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

fof(f723,plain,
    ( ~ spl5_7
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f714]) ).

fof(f714,plain,
    ( $false
    | ~ spl5_7
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f273]) ).

fof(f273,plain,
    ( aScalar0(xH)
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f271,plain,
    ( spl5_7
  <=> aScalar0(xH) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f722,plain,
    ( ~ spl5_15
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f715]) ).

fof(f715,plain,
    ( $false
    | ~ spl5_15
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f313]) ).

fof(f313,plain,
    ( aScalar0(xR)
    | ~ spl5_15 ),
    inference(avatar_component_clause,[],[f311]) ).

fof(f721,plain,
    ( ~ spl5_16
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f716]) ).

fof(f716,plain,
    ( $false
    | ~ spl5_16
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f318]) ).

fof(f318,plain,
    ( aScalar0(xP)
    | ~ spl5_16 ),
    inference(avatar_component_clause,[],[f316]) ).

fof(f720,plain,
    ( ~ spl5_14
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f717]) ).

fof(f717,plain,
    ( $false
    | ~ spl5_14
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f308]) ).

fof(f719,plain,
    ( ~ spl5_8
    | ~ spl5_88 ),
    inference(avatar_contradiction_clause,[],[f718]) ).

fof(f718,plain,
    ( $false
    | ~ spl5_8
    | ~ spl5_88 ),
    inference(resolution,[],[f700,f278]) ).

fof(f704,plain,
    ( spl5_88
    | spl5_89 ),
    inference(avatar_split_clause,[],[f227,f702,f699]) ).

fof(f702,plain,
    ( spl5_89
  <=> ! [X0,X1] :
        ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        | ~ aScalar0(X0)
        | ~ aScalar0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_89])]) ).

fof(f227,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aScalar0(X2)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f697,plain,
    spl5_87,
    inference(avatar_split_clause,[],[f222,f695]) ).

fof(f695,plain,
    ( spl5_87
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ sdtlseqdt0(X1,X0)
        | ~ sdtlseqdt0(X0,X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_87])]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f107]) ).

fof(f107,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/sandbox2/benchmark/theBenchmark.p',mLEASm) ).

fof(f693,plain,
    ( spl5_86
    | ~ spl5_16
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f364,f351,f316,f690]) ).

fof(f690,plain,
    ( spl5_86
  <=> sP2(xP) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_86])]) ).

fof(f364,plain,
    ( sP2(xP)
    | ~ spl5_16
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f318]) ).

fof(f688,plain,
    spl5_85,
    inference(avatar_split_clause,[],[f220,f686]) ).

fof(f686,plain,
    ( spl5_85
  <=> ! [X0,X1] :
        ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_85])]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,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,[],[f103]) ).

fof(f103,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/sandbox2/benchmark/theBenchmark.p',mMNeg) ).

fof(f684,plain,
    spl5_84,
    inference(avatar_split_clause,[],[f219,f682]) ).

fof(f682,plain,
    ( spl5_84
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_84])]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f680,plain,
    spl5_83,
    inference(avatar_split_clause,[],[f218,f678]) ).

fof(f678,plain,
    ( spl5_83
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_83])]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f101]) ).

fof(f101,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/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).

fof(f676,plain,
    spl5_82,
    inference(avatar_split_clause,[],[f212,f674]) ).

fof(f674,plain,
    ( spl5_82
  <=> ! [X0,X1] :
        ( aScalar0(sdtasasdt0(X0,X1))
        | aDimensionOf0(X0) != aDimensionOf0(X1)
        | ~ aVector0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_82])]) ).

fof(f212,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasasdt0(X0,X1))
      | aDimensionOf0(X0) != aDimensionOf0(X1)
      | ~ aVector0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f89]) ).

fof(f89,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/sandbox2/benchmark/theBenchmark.p',mScPr) ).

fof(f669,plain,
    spl5_81,
    inference(avatar_split_clause,[],[f210,f667]) ).

fof(f667,plain,
    ( spl5_81
  <=> ! [X0,X1] :
        ( X0 = X1
        | szszuzczcdt0(X0) != szszuzczcdt0(X1)
        | ~ aNaturalNumber0(X1)
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_81])]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( X0 = X1
      | szszuzczcdt0(X0) != szszuzczcdt0(X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( X0 = X1
      | szszuzczcdt0(X0) != szszuzczcdt0(X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f85]) ).

fof(f85,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/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).

fof(f665,plain,
    spl5_80,
    inference(avatar_split_clause,[],[f192,f663]) ).

fof(f663,plain,
    ( spl5_80
  <=> ! [X0,X1,X3] :
        ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
        | ~ aNaturalNumber0(X3)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_80])]) ).

fof(f192,plain,
    ! [X3,X0,X1] :
      ( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
      | ~ aNaturalNumber0(X3)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f651,plain,
    ( spl5_79
    | ~ spl5_15
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f363,f351,f311,f648]) ).

fof(f648,plain,
    ( spl5_79
  <=> sP2(xR) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_79])]) ).

fof(f363,plain,
    ( sP2(xR)
    | ~ spl5_15
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f313]) ).

fof(f646,plain,
    spl5_78,
    inference(avatar_split_clause,[],[f221,f644]) ).

fof(f644,plain,
    ( spl5_78
  <=> ! [X0,X1] :
        ( sdtlseqdt0(X1,X0)
        | sdtlseqdt0(X0,X1)
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_78])]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f105]) ).

fof(f105,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/sandbox2/benchmark/theBenchmark.p',mLETot) ).

fof(f642,plain,
    spl5_77,
    inference(avatar_split_clause,[],[f209,f640]) ).

fof(f640,plain,
    ( spl5_77
  <=> ! [X0] :
        ( szszuzczcdt0(sK4(X0)) = X0
        | sz00 = X0
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_77])]) ).

fof(f209,plain,
    ! [X0] :
      ( szszuzczcdt0(sK4(X0)) = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f138,plain,
    ! [X0] :
      ( ( szszuzczcdt0(sK4(X0)) = X0
        & aNaturalNumber0(sK4(X0)) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f84,f137]) ).

fof(f137,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aNaturalNumber0(X1) )
     => ( szszuzczcdt0(sK4(X0)) = X0
        & aNaturalNumber0(sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aNaturalNumber0(X1) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f83]) ).

fof(f83,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/sandbox2/benchmark/theBenchmark.p',mNatExtr) ).

fof(f635,plain,
    spl5_76,
    inference(avatar_split_clause,[],[f191,f633]) ).

fof(f633,plain,
    ( spl5_76
  <=> ! [X0,X1] :
        ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_76])]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f631,plain,
    spl5_75,
    inference(avatar_split_clause,[],[f189,f629]) ).

fof(f629,plain,
    ( spl5_75
  <=> ! [X0,X1] :
        ( sziznziztdt0(X0) = X1
        | ~ sP0(X0,X1)
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_75])]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( sziznziztdt0(X0) = X1
      | ~ sP0(X0,X1)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sziznziztdt0(X0) = X1
            | ~ sP0(X0,X1) )
          & ( sP0(X0,X1)
            | sziznziztdt0(X0) != X1 ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> sP0(X0,X1) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f613,plain,
    ( spl5_74
    | ~ spl5_7
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f362,f351,f271,f610]) ).

fof(f610,plain,
    ( spl5_74
  <=> sP2(xH) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_74])]) ).

fof(f362,plain,
    ( sP2(xH)
    | ~ spl5_7
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f273]) ).

fof(f603,plain,
    spl5_73,
    inference(avatar_split_clause,[],[f217,f601]) ).

fof(f601,plain,
    ( spl5_73
  <=> ! [X0,X1] :
        ( aScalar0(sdtasdt0(X0,X1))
        | ~ aScalar0(X1)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_73])]) ).

fof(f217,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( aScalar0(sdtasdt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,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/sandbox2/benchmark/theBenchmark.p',mMulSc) ).

fof(f599,plain,
    spl5_72,
    inference(avatar_split_clause,[],[f216,f597]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f97]) ).

fof(f97,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/sandbox2/benchmark/theBenchmark.p',mSumSc) ).

fof(f595,plain,
    spl5_71,
    inference(avatar_split_clause,[],[f211,f593]) ).

fof(f593,plain,
    ( spl5_71
  <=> ! [X0,X1] :
        ( aScalar0(sdtlbdtrb0(X0,X1))
        | ~ aNaturalNumber0(X1)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_71])]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( aScalar0(sdtlbdtrb0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,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/sandbox2/benchmark/theBenchmark.p',mElmSc) ).

fof(f591,plain,
    spl5_70,
    inference(avatar_split_clause,[],[f208,f589]) ).

fof(f589,plain,
    ( spl5_70
  <=> ! [X0] :
        ( aNaturalNumber0(sK4(X0))
        | sz00 = X0
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_70])]) ).

fof(f208,plain,
    ! [X0] :
      ( aNaturalNumber0(sK4(X0))
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f587,plain,
    spl5_69,
    inference(avatar_split_clause,[],[f204,f585]) ).

fof(f585,plain,
    ( spl5_69
  <=> ! [X0] :
        ( sz0z00 = sdtpldt0(smndt0(X0),X0)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_69])]) ).

fof(f204,plain,
    ! [X0] :
      ( sz0z00 = sdtpldt0(smndt0(X0),X0)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,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,[],[f128]) ).

fof(f128,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(f583,plain,
    spl5_68,
    inference(avatar_split_clause,[],[f203,f581]) ).

fof(f581,plain,
    ( spl5_68
  <=> ! [X0] :
        ( sz0z00 = sdtpldt0(X0,smndt0(X0))
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_68])]) ).

fof(f203,plain,
    ! [X0] :
      ( sz0z00 = sdtpldt0(X0,smndt0(X0))
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f579,plain,
    spl5_67,
    inference(avatar_split_clause,[],[f195,f577]) ).

fof(f577,plain,
    ( spl5_67
  <=> ! [X0] :
        ( sP1(X0)
        | sz00 = aDimensionOf0(X0)
        | ~ aVector0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_67])]) ).

fof(f195,plain,
    ! [X0] :
      ( sP1(X0)
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( sP1(X0)
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(definition_folding,[],[f78,f126,f125]) ).

fof(f78,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,[],[f77]) ).

fof(f77,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/sandbox2/benchmark/theBenchmark.p',mDefInit) ).

fof(f575,plain,
    ( spl5_66
    | ~ spl5_6
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f361,f351,f266,f572]) ).

fof(f572,plain,
    ( spl5_66
  <=> sP2(xG) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_66])]) ).

fof(f361,plain,
    ( sP2(xG)
    | ~ spl5_6
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f268]) ).

fof(f566,plain,
    spl5_65,
    inference(avatar_split_clause,[],[f205,f564]) ).

fof(f564,plain,
    ( spl5_65
  <=> ! [X0] :
        ( smndt0(smndt0(X0)) = X0
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_65])]) ).

fof(f205,plain,
    ! [X0] :
      ( smndt0(smndt0(X0)) = X0
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f562,plain,
    spl5_64,
    inference(avatar_split_clause,[],[f202,f560]) ).

fof(f560,plain,
    ( spl5_64
  <=> ! [X0] :
        ( sz0z00 = sdtasdt0(sz0z00,X0)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_64])]) ).

fof(f202,plain,
    ! [X0] :
      ( sz0z00 = sdtasdt0(sz0z00,X0)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f558,plain,
    spl5_63,
    inference(avatar_split_clause,[],[f201,f556]) ).

fof(f556,plain,
    ( spl5_63
  <=> ! [X0] :
        ( sz0z00 = sdtasdt0(X0,sz0z00)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_63])]) ).

fof(f201,plain,
    ! [X0] :
      ( sz0z00 = sdtasdt0(X0,sz0z00)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f554,plain,
    ( spl5_62
    | ~ spl5_5
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f360,f351,f261,f551]) ).

fof(f551,plain,
    ( spl5_62
  <=> sP2(xF) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_62])]) ).

fof(f360,plain,
    ( sP2(xF)
    | ~ spl5_5
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f263]) ).

fof(f549,plain,
    spl5_61,
    inference(avatar_split_clause,[],[f200,f547]) ).

fof(f547,plain,
    ( spl5_61
  <=> ! [X0] :
        ( sdtpldt0(sz0z00,X0) = X0
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_61])]) ).

fof(f200,plain,
    ! [X0] :
      ( sdtpldt0(sz0z00,X0) = X0
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f545,plain,
    spl5_60,
    inference(avatar_split_clause,[],[f199,f543]) ).

fof(f543,plain,
    ( spl5_60
  <=> ! [X0] :
        ( sdtpldt0(X0,sz0z00) = X0
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_60])]) ).

fof(f199,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz0z00) = X0
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f541,plain,
    spl5_59,
    inference(avatar_split_clause,[],[f198,f539]) ).

fof(f198,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,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/sandbox2/benchmark/theBenchmark.p',mSqPos) ).

fof(f537,plain,
    spl5_58,
    inference(avatar_split_clause,[],[f187,f535]) ).

fof(f187,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0] :
      ( aVector0(X0)
     => sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).

fof(f533,plain,
    spl5_57,
    inference(avatar_split_clause,[],[f145,f530]) ).

fof(f530,plain,
    ( spl5_57
  <=> sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_57])]) ).

fof(f145,plain,
    sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,axiom,
    sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).

fof(f528,plain,
    spl5_56,
    inference(avatar_split_clause,[],[f144,f525]) ).

fof(f144,plain,
    sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,axiom,
    sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2610) ).

fof(f523,plain,
    ~ spl5_55,
    inference(avatar_split_clause,[],[f143,f520]) ).

fof(f520,plain,
    ( spl5_55
  <=> sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_55])]) ).

fof(f143,plain,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2590) ).

fof(f518,plain,
    ( spl5_54
    | ~ spl5_11
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f359,f351,f291,f515]) ).

fof(f515,plain,
    ( spl5_54
  <=> sP2(xE) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_54])]) ).

fof(f359,plain,
    ( sP2(xE)
    | ~ spl5_11
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f293]) ).

fof(f510,plain,
    spl5_53,
    inference(avatar_split_clause,[],[f236,f508]) ).

fof(f236,plain,
    ! [X0] :
      ( sP0(X0,sziznziztdt0(X0))
      | ~ sP1(X0) ),
    inference(equality_resolution,[],[f188]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sziznziztdt0(X0) != X1
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f505,plain,
    ( spl5_51
    | spl5_52 ),
    inference(avatar_split_clause,[],[f206,f502,f499]) ).

fof(f499,plain,
    ( spl5_51
  <=> ! [X0] : ~ sP2(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_51])]) ).

fof(f502,plain,
    ( spl5_52
  <=> sz0z00 = smndt0(sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_52])]) ).

fof(f206,plain,
    ! [X0] :
      ( sz0z00 = smndt0(sz0z00)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f497,plain,
    spl5_50,
    inference(avatar_split_clause,[],[f185,f495]) ).

fof(f495,plain,
    ( spl5_50
  <=> ! [X0] :
        ( sz00 != szszuzczcdt0(X0)
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_50])]) ).

fof(f185,plain,
    ! [X0] :
      ( sz00 != szszuzczcdt0(X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,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/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).

fof(f493,plain,
    spl5_49,
    inference(avatar_split_clause,[],[f183,f491]) ).

fof(f491,plain,
    ( spl5_49
  <=> ! [X0] :
        ( iLess0(X0,szszuzczcdt0(X0))
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_49])]) ).

fof(f183,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,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/sandbox2/benchmark/theBenchmark.p',mIH) ).

fof(f489,plain,
    ( spl5_48
    | ~ spl5_9
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f358,f351,f281,f486]) ).

fof(f486,plain,
    ( spl5_48
  <=> sP2(xD) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_48])]) ).

fof(f358,plain,
    ( sP2(xD)
    | ~ spl5_9
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f283]) ).

fof(f484,plain,
    spl5_47,
    inference(avatar_split_clause,[],[f237,f481]) ).

fof(f481,plain,
    ( spl5_47
  <=> xA = sdtlbdtrb0(xs,aDimensionOf0(xt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_47])]) ).

fof(f237,plain,
    xA = sdtlbdtrb0(xs,aDimensionOf0(xt)),
    inference(forward_demodulation,[],[f171,f141]) ).

fof(f171,plain,
    xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,axiom,
    ( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
    & aScalar0(xA) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).

fof(f479,plain,
    spl5_46,
    inference(avatar_split_clause,[],[f169,f476]) ).

fof(f476,plain,
    ( spl5_46
  <=> xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_46])]) ).

fof(f169,plain,
    xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,axiom,
    ( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
    & aScalar0(xB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).

fof(f472,plain,
    spl5_45,
    inference(avatar_split_clause,[],[f197,f470]) ).

fof(f470,plain,
    ( spl5_45
  <=> ! [X0] :
        ( sdtlseqdt0(X0,X0)
        | ~ aScalar0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_45])]) ).

fof(f197,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( sdtlseqdt0(X0,X0)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => sdtlseqdt0(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).

fof(f468,plain,
    spl5_44,
    inference(avatar_split_clause,[],[f196,f466]) ).

fof(f196,plain,
    ! [X0] :
      ( aScalar0(smndt0(X0))
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( aScalar0(smndt0(X0))
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( aScalar0(X0)
     => aScalar0(smndt0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).

fof(f464,plain,
    spl5_43,
    inference(avatar_split_clause,[],[f190,f462]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( aVector0(X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f460,plain,
    ( spl5_42
    | ~ spl5_10
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f357,f351,f286,f457]) ).

fof(f457,plain,
    ( spl5_42
  <=> sP2(xC) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).

fof(f357,plain,
    ( sP2(xC)
    | ~ spl5_10
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f288]) ).

fof(f455,plain,
    spl5_41,
    inference(avatar_split_clause,[],[f186,f453]) ).

fof(f186,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( aVector0(X0)
     => aNaturalNumber0(aDimensionOf0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).

fof(f451,plain,
    spl5_40,
    inference(avatar_split_clause,[],[f184,f449]) ).

fof(f449,plain,
    ( spl5_40
  <=> ! [X0] :
        ( aNaturalNumber0(szszuzczcdt0(X0))
        | ~ aNaturalNumber0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).

fof(f184,plain,
    ! [X0] :
      ( aNaturalNumber0(szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f447,plain,
    ( spl5_39
    | ~ spl5_12
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f356,f351,f296,f444]) ).

fof(f444,plain,
    ( spl5_39
  <=> sP2(xB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).

fof(f356,plain,
    ( sP2(xB)
    | ~ spl5_12
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f298]) ).

fof(f441,plain,
    spl5_38,
    inference(avatar_split_clause,[],[f179,f438]) ).

fof(f438,plain,
    ( spl5_38
  <=> sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).

fof(f179,plain,
    sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    ( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
    & sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2628) ).

fof(f436,plain,
    spl5_37,
    inference(avatar_split_clause,[],[f178,f433]) ).

fof(f178,plain,
    sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
    inference(cnf_transformation,[],[f62]) ).

fof(f431,plain,
    spl5_36,
    inference(avatar_split_clause,[],[f177,f428]) ).

fof(f428,plain,
    ( spl5_36
  <=> xP = sdtasdt0(xE,xH) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).

fof(f177,plain,
    xP = sdtasdt0(xE,xH),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,axiom,
    ( xP = sdtasdt0(xE,xH)
    & aScalar0(xP) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).

fof(f426,plain,
    spl5_35,
    inference(avatar_split_clause,[],[f175,f423]) ).

fof(f423,plain,
    ( spl5_35
  <=> xR = sdtasdt0(xC,xG) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).

fof(f175,plain,
    xR = sdtasdt0(xC,xG),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,axiom,
    ( xR = sdtasdt0(xC,xG)
    & aScalar0(xR) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).

fof(f421,plain,
    ( spl5_34
    | ~ spl5_13
    | ~ spl5_23 ),
    inference(avatar_split_clause,[],[f355,f351,f301,f418]) ).

fof(f418,plain,
    ( spl5_34
  <=> sP2(xA) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).

fof(f355,plain,
    ( sP2(xA)
    | ~ spl5_13
    | ~ spl5_23 ),
    inference(resolution,[],[f352,f303]) ).

fof(f416,plain,
    spl5_33,
    inference(avatar_split_clause,[],[f173,f413]) ).

fof(f413,plain,
    ( spl5_33
  <=> xS = sdtasdt0(xF,xD) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).

fof(f173,plain,
    xS = sdtasdt0(xF,xD),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,axiom,
    ( xS = sdtasdt0(xF,xD)
    & aScalar0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).

fof(f411,plain,
    spl5_32,
    inference(avatar_split_clause,[],[f167,f408]) ).

fof(f408,plain,
    ( spl5_32
  <=> xE = sdtasasdt0(xp,xq) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).

fof(f167,plain,
    xE = sdtasasdt0(xp,xq),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,axiom,
    ( xE = sdtasasdt0(xp,xq)
    & aScalar0(xE) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).

fof(f406,plain,
    spl5_31,
    inference(avatar_split_clause,[],[f165,f403]) ).

fof(f165,plain,
    xC = sdtasasdt0(xp,xp),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,axiom,
    ( xC = sdtasasdt0(xp,xp)
    & aScalar0(xC) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).

fof(f401,plain,
    spl5_30,
    inference(avatar_split_clause,[],[f163,f398]) ).

fof(f163,plain,
    xD = sdtasasdt0(xq,xq),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,axiom,
    ( xD = sdtasasdt0(xq,xq)
    & aScalar0(xD) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).

fof(f396,plain,
    spl5_29,
    inference(avatar_split_clause,[],[f161,f393]) ).

fof(f393,plain,
    ( spl5_29
  <=> xN = sdtasdt0(xR,xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).

fof(f161,plain,
    xN = sdtasdt0(xR,xS),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,axiom,
    ( xN = sdtasdt0(xR,xS)
    & aScalar0(xN) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).

fof(f391,plain,
    spl5_28,
    inference(avatar_split_clause,[],[f159,f388]) ).

fof(f388,plain,
    ( spl5_28
  <=> xH = sdtasdt0(xA,xB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).

fof(f159,plain,
    xH = sdtasdt0(xA,xB),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,axiom,
    ( xH = sdtasdt0(xA,xB)
    & aScalar0(xH) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).

fof(f386,plain,
    spl5_27,
    inference(avatar_split_clause,[],[f157,f383]) ).

fof(f157,plain,
    xG = sdtasdt0(xB,xB),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,axiom,
    ( xG = sdtasdt0(xB,xB)
    & aScalar0(xG) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).

fof(f381,plain,
    spl5_26,
    inference(avatar_split_clause,[],[f155,f378]) ).

fof(f155,plain,
    xF = sdtasdt0(xA,xA),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,axiom,
    ( xF = sdtasdt0(xA,xA)
    & aScalar0(xF) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

fof(f376,plain,
    spl5_25,
    inference(avatar_split_clause,[],[f142,f373]) ).

fof(f373,plain,
    ( spl5_25
  <=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).

fof(f142,plain,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,axiom,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2004) ).

fof(f371,plain,
    spl5_24,
    inference(avatar_split_clause,[],[f141,f368]) ).

fof(f353,plain,
    spl5_23,
    inference(avatar_split_clause,[],[f207,f351]) ).

fof(f207,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ aScalar0(X0) ),
    inference(definition_folding,[],[f82,f128]) ).

fof(f82,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/sandbox2/benchmark/theBenchmark.p',mScZero) ).

fof(f349,plain,
    spl5_22,
    inference(avatar_split_clause,[],[f151,f346]) ).

fof(f151,plain,
    xp = sziznziztdt0(xs),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    ( xp = sziznziztdt0(xs)
    & aVector0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).

fof(f344,plain,
    spl5_21,
    inference(avatar_split_clause,[],[f149,f341]) ).

fof(f149,plain,
    xq = sziznziztdt0(xt),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,axiom,
    ( xq = sziznziztdt0(xt)
    & aVector0(xq) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).

fof(f339,plain,
    ~ spl5_20,
    inference(avatar_split_clause,[],[f140,f336]) ).

fof(f140,plain,
    sz00 != aDimensionOf0(xs),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    sz00 != aDimensionOf0(xs),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).

fof(f334,plain,
    ~ spl5_19,
    inference(avatar_split_clause,[],[f139,f331]) ).

fof(f139,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    inference(flattening,[],[f64]) ).

fof(f64,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    inference(negated_conjecture,[],[f63]) ).

fof(f63,conjecture,
    sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f329,plain,
    spl5_18,
    inference(avatar_split_clause,[],[f182,f326]) ).

fof(f182,plain,
    aScalar0(sz0z00),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).

fof(f324,plain,
    spl5_17,
    inference(avatar_split_clause,[],[f181,f321]) ).

fof(f321,plain,
    ( spl5_17
  <=> aNaturalNumber0(sz00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).

fof(f181,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNat) ).

fof(f319,plain,
    spl5_16,
    inference(avatar_split_clause,[],[f176,f316]) ).

fof(f176,plain,
    aScalar0(xP),
    inference(cnf_transformation,[],[f53]) ).

fof(f314,plain,
    spl5_15,
    inference(avatar_split_clause,[],[f174,f311]) ).

fof(f174,plain,
    aScalar0(xR),
    inference(cnf_transformation,[],[f52]) ).

fof(f309,plain,
    spl5_14,
    inference(avatar_split_clause,[],[f172,f306]) ).

fof(f172,plain,
    aScalar0(xS),
    inference(cnf_transformation,[],[f54]) ).

fof(f304,plain,
    spl5_13,
    inference(avatar_split_clause,[],[f170,f301]) ).

fof(f170,plain,
    aScalar0(xA),
    inference(cnf_transformation,[],[f44]) ).

fof(f299,plain,
    spl5_12,
    inference(avatar_split_clause,[],[f168,f296]) ).

fof(f168,plain,
    aScalar0(xB),
    inference(cnf_transformation,[],[f45]) ).

fof(f294,plain,
    spl5_11,
    inference(avatar_split_clause,[],[f166,f291]) ).

fof(f166,plain,
    aScalar0(xE),
    inference(cnf_transformation,[],[f48]) ).

fof(f289,plain,
    spl5_10,
    inference(avatar_split_clause,[],[f164,f286]) ).

fof(f164,plain,
    aScalar0(xC),
    inference(cnf_transformation,[],[f46]) ).

fof(f284,plain,
    spl5_9,
    inference(avatar_split_clause,[],[f162,f281]) ).

fof(f162,plain,
    aScalar0(xD),
    inference(cnf_transformation,[],[f47]) ).

fof(f279,plain,
    spl5_8,
    inference(avatar_split_clause,[],[f160,f276]) ).

fof(f160,plain,
    aScalar0(xN),
    inference(cnf_transformation,[],[f55]) ).

fof(f274,plain,
    spl5_7,
    inference(avatar_split_clause,[],[f158,f271]) ).

fof(f158,plain,
    aScalar0(xH),
    inference(cnf_transformation,[],[f51]) ).

fof(f269,plain,
    spl5_6,
    inference(avatar_split_clause,[],[f156,f266]) ).

fof(f156,plain,
    aScalar0(xG),
    inference(cnf_transformation,[],[f50]) ).

fof(f264,plain,
    spl5_5,
    inference(avatar_split_clause,[],[f154,f261]) ).

fof(f154,plain,
    aScalar0(xF),
    inference(cnf_transformation,[],[f49]) ).

fof(f259,plain,
    spl5_4,
    inference(avatar_split_clause,[],[f153,f256]) ).

fof(f256,plain,
    ( spl5_4
  <=> aVector0(xt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f153,plain,
    aVector0(xt),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    ( aVector0(xt)
    & aVector0(xs) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).

fof(f254,plain,
    spl5_3,
    inference(avatar_split_clause,[],[f152,f251]) ).

fof(f152,plain,
    aVector0(xs),
    inference(cnf_transformation,[],[f38]) ).

fof(f249,plain,
    spl5_2,
    inference(avatar_split_clause,[],[f150,f246]) ).

fof(f150,plain,
    aVector0(xp),
    inference(cnf_transformation,[],[f42]) ).

fof(f244,plain,
    spl5_1,
    inference(avatar_split_clause,[],[f148,f241]) ).

fof(f148,plain,
    aVector0(xq),
    inference(cnf_transformation,[],[f43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : RNG072+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 02:16:03 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (7702)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (7703)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (7709)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)
% 0.21/0.39  % (7705)WARNING: value z3 for option sas not known
% 0.21/0.39  % (7705)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)
% 0.21/0.39  TRYING [1]
% 0.21/0.39  TRYING [2]
% 0.21/0.39  % (7706)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39  % (7704)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.39  % (7707)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)
% 0.21/0.39  % (7708)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)
% 0.21/0.40  TRYING [3]
% 0.21/0.40  TRYING [1]
% 0.21/0.40  TRYING [2]
% 0.21/0.41  TRYING [3]
% 0.21/0.42  % (7707)First to succeed.
% 0.21/0.43  % (7707)Refutation found. Thanks to Tanya!
% 0.21/0.43  % SZS status Theorem for theBenchmark
% 0.21/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43  % (7707)------------------------------
% 0.21/0.43  % (7707)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.43  % (7707)Termination reason: Refutation
% 0.21/0.43  
% 0.21/0.43  % (7707)Memory used [KB]: 1523
% 0.21/0.43  % (7707)Time elapsed: 0.039 s
% 0.21/0.43  % (7707)Instructions burned: 60 (million)
% 0.21/0.43  % (7707)------------------------------
% 0.21/0.43  % (7707)------------------------------
% 0.21/0.43  % (7702)Success in time 0.069 s
%------------------------------------------------------------------------------