TSTP Solution File: NUM960_5 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM960_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 08:43:59 EDT 2024

% Result   : Theorem 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  243
% Syntax   : Number of formulae    :  662 ( 214 unt;  36 typ;   0 def)
%            Number of atoms       : 1411 ( 233 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives : 1267 ( 482   ~; 453   |;  97   &)
%                                         ( 209 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   21 (  13   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :  145 ( 143 usr; 129 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   9 con; 0-3 aty)
%            Number of variables   :  619 ( 594   !;   7   ?; 619   :)
%                                         (  18  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    bool: $tType ).

tff(type_def_6,type,
    int: $tType ).

tff(type_def_7,type,
    nat: $tType ).

tff(func_def_0,type,
    minus_minus: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_1,type,
    one_one: 
      !>[X0: $tType] : X0 ).

tff(func_def_2,type,
    plus_plus: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_3,type,
    times_times: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_4,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_5,type,
    bit0: int > int ).

tff(func_def_6,type,
    bit1: int > int ).

tff(func_def_7,type,
    pls: int ).

tff(func_def_8,type,
    number_number_of: 
      !>[X0: $tType] : ( int > X0 ) ).

tff(func_def_9,type,
    power_power: 
      !>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).

tff(func_def_10,type,
    fFalse: bool ).

tff(func_def_11,type,
    fTrue: bool ).

tff(func_def_12,type,
    m: int ).

tff(func_def_13,type,
    s1: int ).

tff(func_def_14,type,
    s: int ).

tff(func_def_15,type,
    t: int ).

tff(func_def_16,type,
    sK0: int ).

tff(func_def_17,type,
    sK1: int ).

tff(pred_def_1,type,
    number: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    ring: 
      !>[X0: $tType] : $o ).

tff(pred_def_3,type,
    semiring: 
      !>[X0: $tType] : $o ).

tff(pred_def_4,type,
    number_ring: 
      !>[X0: $tType] : $o ).

tff(pred_def_5,type,
    ring_char_0: 
      !>[X0: $tType] : $o ).

tff(pred_def_6,type,
    linorder: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    number_semiring: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    linordered_idom: 
      !>[X0: $tType] : $o ).

tff(pred_def_9,type,
    linord219039673up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_10,type,
    zcong: ( int * int * int ) > $o ).

tff(pred_def_11,type,
    zprime: int > $o ).

tff(pred_def_12,type,
    ord_less: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_13,type,
    ord_less_eq: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_14,type,
    twoSqu1567020053sum2sq: int > $o ).

tff(pred_def_15,type,
    pp: bool > $o ).

tff(f1454,plain,
    $false,
    inference(avatar_sat_refutation,[],[f533,f538,f543,f548,f553,f558,f563,f568,f573,f578,f583,f588,f593,f598,f603,f608,f613,f618,f623,f627,f631,f636,f641,f646,f651,f657,f661,f665,f670,f674,f679,f683,f687,f691,f695,f699,f709,f718,f722,f726,f730,f734,f738,f742,f746,f750,f754,f758,f762,f766,f770,f774,f778,f782,f786,f790,f794,f805,f827,f831,f835,f839,f843,f847,f851,f855,f860,f864,f868,f872,f876,f880,f884,f888,f892,f896,f943,f964,f968,f972,f976,f980,f984,f1063,f1067,f1072,f1076,f1080,f1084,f1088,f1092,f1096,f1100,f1104,f1108,f1112,f1163,f1172,f1179,f1184,f1188,f1197,f1204,f1210,f1215,f1242,f1247,f1256,f1260,f1264,f1268,f1272,f1276,f1280,f1284,f1288,f1292,f1296,f1301,f1305,f1309,f1313,f1317,f1321,f1436,f1443,f1450,f1453]) ).

tff(f1453,plain,
    ( spl2_97
    | ~ spl2_27
    | ~ spl2_67
    | ~ spl2_128 ),
    inference(avatar_split_clause,[],[f1452,f1447,f857,f659,f1160]) ).

tff(f1160,plain,
    ( spl2_97
  <=> ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_97])]) ).

tff(f659,plain,
    ( spl2_27
  <=> ! [X0: int] : ( number_number_of(int,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).

tff(f857,plain,
    ( spl2_67
  <=> ( bit1(pls) = one_one(int) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_67])]) ).

tff(f1447,plain,
    ( spl2_128
  <=> ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_128])]) ).

tff(f1452,plain,
    ( ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)))
    | ~ spl2_27
    | ~ spl2_67
    | ~ spl2_128 ),
    inference(forward_demodulation,[],[f1451,f859]) ).

tff(f859,plain,
    ( ( bit1(pls) = one_one(int) )
    | ~ spl2_67 ),
    inference(avatar_component_clause,[],[f857]) ).

tff(f1451,plain,
    ( ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)))
    | ~ spl2_27
    | ~ spl2_128 ),
    inference(forward_demodulation,[],[f1449,f660]) ).

tff(f660,plain,
    ( ! [X0: int] : ( number_number_of(int,X0) = X0 )
    | ~ spl2_27 ),
    inference(avatar_component_clause,[],[f659]) ).

tff(f1449,plain,
    ( ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    | ~ spl2_128 ),
    inference(avatar_component_clause,[],[f1447]) ).

tff(f1450,plain,
    spl2_128,
    inference(avatar_split_clause,[],[f334,f1447]) ).

tff(f334,plain,
    ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ( zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    & ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    & ord_less_eq(int,zero_zero(int),s) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_s0p) ).

tff(f1443,plain,
    ( ~ spl2_127
    | ~ spl2_27
    | ~ spl2_67
    | spl2_126 ),
    inference(avatar_split_clause,[],[f1438,f1433,f857,f659,f1440]) ).

tff(f1440,plain,
    ( spl2_127
  <=> ord_less(int,t,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_127])]) ).

tff(f1433,plain,
    ( spl2_126
  <=> ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_126])]) ).

tff(f1438,plain,
    ( ~ ord_less(int,t,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)))
    | ~ spl2_27
    | ~ spl2_67
    | spl2_126 ),
    inference(forward_demodulation,[],[f1437,f859]) ).

tff(f1437,plain,
    ( ~ ord_less(int,t,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)))
    | ~ spl2_27
    | spl2_126 ),
    inference(forward_demodulation,[],[f1435,f660]) ).

tff(f1435,plain,
    ( ~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    | spl2_126 ),
    inference(avatar_component_clause,[],[f1433]) ).

tff(f1436,plain,
    ~ spl2_126,
    inference(avatar_split_clause,[],[f328,f1433]) ).

tff(f328,plain,
    ~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096_126_At_A_060_A4_A_K_Am_A_L_A1_096) ).

tff(f1321,plain,
    spl2_125,
    inference(avatar_split_clause,[],[f515,f1319]) ).

tff(f1319,plain,
    ( spl2_125
  <=> ! [X0: int,X1: int] :
        ( ~ ord_less(int,pls,X1)
        | ( one_one(int) = X1 )
        | ( one_one(int) != times_times(int,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_125])]) ).

tff(f515,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less(int,pls,X1)
      | ( one_one(int) = X1 )
      | ( one_one(int) != times_times(int,X1,X0) ) ),
    inference(forward_demodulation,[],[f429,f324]) ).

tff(f324,plain,
    zero_zero(int) = pls,
    inference(cnf_transformation,[],[f84]) ).

tff(f84,axiom,
    zero_zero(int) = pls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Pls__def) ).

tff(f429,plain,
    ! [X0: int,X1: int] :
      ( ( one_one(int) = X1 )
      | ( one_one(int) != times_times(int,X1,X0) )
      | ~ ord_less(int,zero_zero(int),X1) ),
    inference(cnf_transformation,[],[f281]) ).

tff(f281,plain,
    ! [X0: int,X1: int] :
      ( ( ( ( one_one(int) = times_times(int,X1,X0) )
          | ( one_one(int) != X0 )
          | ( one_one(int) != X1 ) )
        & ( ( ( one_one(int) = X0 )
            & ( one_one(int) = X1 ) )
          | ( one_one(int) != times_times(int,X1,X0) ) ) )
      | ~ ord_less(int,zero_zero(int),X1) ),
    inference(flattening,[],[f280]) ).

tff(f280,plain,
    ! [X0: int,X1: int] :
      ( ( ( ( one_one(int) = times_times(int,X1,X0) )
          | ( one_one(int) != X0 )
          | ( one_one(int) != X1 ) )
        & ( ( ( one_one(int) = X0 )
            & ( one_one(int) = X1 ) )
          | ( one_one(int) != times_times(int,X1,X0) ) ) )
      | ~ ord_less(int,zero_zero(int),X1) ),
    inference(nnf_transformation,[],[f244]) ).

tff(f244,plain,
    ! [X0: int,X1: int] :
      ( ( ( one_one(int) = times_times(int,X1,X0) )
      <=> ( ( one_one(int) = X0 )
          & ( one_one(int) = X1 ) ) )
      | ~ ord_less(int,zero_zero(int),X1) ),
    inference(ennf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,zero_zero(int),X1)
     => ( ( one_one(int) = times_times(int,X1,X0) )
      <=> ( ( one_one(int) = X0 )
          & ( one_one(int) = X1 ) ) ) ),
    inference(rectify,[],[f87]) ).

tff(f87,axiom,
    ! [X24: int,X25: int] :
      ( ord_less(int,zero_zero(int),X25)
     => ( ( one_one(int) = times_times(int,X25,X24) )
      <=> ( ( one_one(int) = X24 )
          & ( one_one(int) = X25 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_pos__zmult__eq__1__iff) ).

tff(f1317,plain,
    spl2_124,
    inference(avatar_split_clause,[],[f514,f1315]) ).

tff(f1315,plain,
    ( spl2_124
  <=> ! [X0: int,X1: int] :
        ( ~ ord_less(int,pls,X1)
        | ( one_one(int) = X0 )
        | ( one_one(int) != times_times(int,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_124])]) ).

tff(f514,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less(int,pls,X1)
      | ( one_one(int) = X0 )
      | ( one_one(int) != times_times(int,X1,X0) ) ),
    inference(forward_demodulation,[],[f430,f324]) ).

tff(f430,plain,
    ! [X0: int,X1: int] :
      ( ( one_one(int) = X0 )
      | ( one_one(int) != times_times(int,X1,X0) )
      | ~ ord_less(int,zero_zero(int),X1) ),
    inference(cnf_transformation,[],[f281]) ).

tff(f1313,plain,
    spl2_123,
    inference(avatar_split_clause,[],[f511,f1311]) ).

tff(f1311,plain,
    ( spl2_123
  <=> ! [X0: int] :
        ( ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
        | ord_less(int,X0,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_123])]) ).

tff(f511,plain,
    ! [X0: int] :
      ( ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
      | ord_less(int,X0,pls) ),
    inference(forward_demodulation,[],[f510,f324]) ).

tff(f510,plain,
    ! [X0: int] :
      ( ord_less(int,X0,pls)
      | ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int)) ),
    inference(forward_demodulation,[],[f417,f324]) ).

tff(f417,plain,
    ! [X0: int] :
      ( ord_less(int,X0,zero_zero(int))
      | ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int)) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f279,plain,
    ! [X0: int] :
      ( ( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int))
        | ~ ord_less(int,X0,zero_zero(int)) )
      & ( ord_less(int,X0,zero_zero(int))
        | ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int)) ) ),
    inference(nnf_transformation,[],[f161]) ).

tff(f161,plain,
    ! [X0: int] :
      ( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int))
    <=> ord_less(int,X0,zero_zero(int)) ),
    inference(rectify,[],[f88]) ).

tff(f88,axiom,
    ! [X15: int] :
      ( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X15),X15),zero_zero(int))
    <=> ord_less(int,X15,zero_zero(int)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_odd__less__0__iff) ).

tff(f1309,plain,
    spl2_122,
    inference(avatar_split_clause,[],[f509,f1307]) ).

tff(f1307,plain,
    ( spl2_122
  <=> ! [X0: int] :
        ( ~ ord_less(int,X0,pls)
        | ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_122])]) ).

tff(f509,plain,
    ! [X0: int] :
      ( ~ ord_less(int,X0,pls)
      | ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) ),
    inference(forward_demodulation,[],[f508,f324]) ).

tff(f508,plain,
    ! [X0: int] :
      ( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
      | ~ ord_less(int,X0,zero_zero(int)) ),
    inference(forward_demodulation,[],[f418,f324]) ).

tff(f418,plain,
    ! [X0: int] :
      ( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int))
      | ~ ord_less(int,X0,zero_zero(int)) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f1305,plain,
    spl2_121,
    inference(avatar_split_clause,[],[f467,f1303]) ).

tff(f1303,plain,
    ( spl2_121
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_121])]) ).

tff(f467,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ord_less(int,X1,X0)
      | ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f301,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
        | ( ( X0 != X1 )
          & ~ ord_less(int,X1,X0) ) )
      & ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
    inference(flattening,[],[f300]) ).

tff(f300,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
        | ( ( X0 != X1 )
          & ~ ord_less(int,X1,X0) ) )
      & ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
    inference(nnf_transformation,[],[f190]) ).

tff(f190,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
    <=> ( ( X0 = X1 )
        | ord_less(int,X1,X0) ) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X15: int,X16: int] :
      ( ord_less(int,X16,plus_plus(int,X15,one_one(int)))
    <=> ( ( X15 = X16 )
        | ord_less(int,X16,X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_zless__add1__eq) ).

tff(f1301,plain,
    ( ~ spl2_120
    | ~ spl2_94
    | spl2_97 ),
    inference(avatar_split_clause,[],[f1199,f1160,f1102,f1298]) ).

tff(f1298,plain,
    ( spl2_120
  <=> ord_less_eq(int,s,times_times(int,bit0(bit0(one_one(int))),m)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_120])]) ).

tff(f1102,plain,
    ( spl2_94
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_94])]) ).

tff(f1199,plain,
    ( ~ ord_less_eq(int,s,times_times(int,bit0(bit0(one_one(int))),m))
    | ~ spl2_94
    | spl2_97 ),
    inference(resolution,[],[f1162,f1103]) ).

tff(f1103,plain,
    ( ! [X0: int,X1: int] :
        ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
        | ~ ord_less_eq(int,X1,X0) )
    | ~ spl2_94 ),
    inference(avatar_component_clause,[],[f1102]) ).

tff(f1162,plain,
    ( ~ ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)))
    | spl2_97 ),
    inference(avatar_component_clause,[],[f1160]) ).

tff(f1296,plain,
    spl2_119,
    inference(avatar_split_clause,[],[f378,f1294]) ).

tff(f1294,plain,
    ( spl2_119
  <=> ! [X0: $tType,X1: int] :
        ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
        | ~ ord_less(int,X1,pls)
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_119])]) ).

tff(f378,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
      | ~ ord_less(int,X1,pls)
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f261,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
            | ~ ord_less(int,X1,pls) )
          & ( ord_less(int,X1,pls)
            | ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0)) ) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(nnf_transformation,[],[f227]) ).

tff(f227,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
        <=> ord_less(int,X1,pls) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(flattening,[],[f226]) ).

tff(f226,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
        <=> ord_less(int,X1,pls) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X1: int] :
          ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
        <=> ord_less(int,X1,pls) ) ),
    inference(rectify,[],[f65]) ).

tff(f65,axiom,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X4: int] :
          ( ord_less(X0,number_number_of(X0,X4),zero_zero(X0))
        <=> ord_less(int,X4,pls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__special_I3_J) ).

tff(f1292,plain,
    spl2_118,
    inference(avatar_split_clause,[],[f377,f1290]) ).

tff(f1290,plain,
    ( spl2_118
  <=> ! [X0: $tType,X1: int] :
        ( ord_less(int,X1,pls)
        | ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_118])]) ).

tff(f377,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less(int,X1,pls)
      | ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f1288,plain,
    spl2_117,
    inference(avatar_split_clause,[],[f374,f1286]) ).

tff(f1286,plain,
    ( spl2_117
  <=> ! [X0: $tType,X1: int] :
        ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
        | ~ ord_less(int,pls,X1)
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_117])]) ).

tff(f374,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
      | ~ ord_less(int,pls,X1)
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f259]) ).

tff(f259,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
            | ~ ord_less(int,pls,X1) )
          & ( ord_less(int,pls,X1)
            | ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(nnf_transformation,[],[f223]) ).

tff(f223,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
        <=> ord_less(int,pls,X1) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(flattening,[],[f222]) ).

tff(f222,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
        <=> ord_less(int,pls,X1) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f137]) ).

tff(f137,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X1: int] :
          ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
        <=> ord_less(int,pls,X1) ) ),
    inference(rectify,[],[f66]) ).

tff(f66,axiom,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X3: int] :
          ( ord_less(X0,zero_zero(X0),number_number_of(X0,X3))
        <=> ord_less(int,pls,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__special_I1_J) ).

tff(f1284,plain,
    spl2_116,
    inference(avatar_split_clause,[],[f373,f1282]) ).

tff(f1282,plain,
    ( spl2_116
  <=> ! [X0: $tType,X1: int] :
        ( ord_less(int,pls,X1)
        | ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_116])]) ).

tff(f373,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less(int,pls,X1)
      | ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f259]) ).

tff(f1280,plain,
    spl2_115,
    inference(avatar_split_clause,[],[f370,f1278]) ).

tff(f1278,plain,
    ( spl2_115
  <=> ! [X0: $tType,X1: int] :
        ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
        | ~ ord_less_eq(int,X1,pls)
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_115])]) ).

tff(f370,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
      | ~ ord_less_eq(int,X1,pls)
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f257]) ).

tff(f257,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
            | ~ ord_less_eq(int,X1,pls) )
          & ( ord_less_eq(int,X1,pls)
            | ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0)) ) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(nnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
        <=> ord_less_eq(int,X1,pls) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(flattening,[],[f218]) ).

tff(f218,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
        <=> ord_less_eq(int,X1,pls) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f135]) ).

tff(f135,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X1: int] :
          ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
        <=> ord_less_eq(int,X1,pls) ) ),
    inference(rectify,[],[f67]) ).

tff(f67,axiom,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X4: int] :
          ( ord_less_eq(X0,number_number_of(X0,X4),zero_zero(X0))
        <=> ord_less_eq(int,X4,pls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__special_I3_J) ).

tff(f1276,plain,
    spl2_114,
    inference(avatar_split_clause,[],[f369,f1274]) ).

tff(f1274,plain,
    ( spl2_114
  <=> ! [X0: $tType,X1: int] :
        ( ord_less_eq(int,X1,pls)
        | ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_114])]) ).

tff(f369,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less_eq(int,X1,pls)
      | ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f257]) ).

tff(f1272,plain,
    spl2_113,
    inference(avatar_split_clause,[],[f366,f1270]) ).

tff(f1270,plain,
    ( spl2_113
  <=> ! [X0: $tType,X1: int] :
        ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
        | ~ ord_less_eq(int,pls,X1)
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_113])]) ).

tff(f366,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
      | ~ ord_less_eq(int,pls,X1)
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f255]) ).

tff(f255,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
            | ~ ord_less_eq(int,pls,X1) )
          & ( ord_less_eq(int,pls,X1)
            | ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1)) ) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(nnf_transformation,[],[f215]) ).

tff(f215,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
        <=> ord_less_eq(int,pls,X1) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(flattening,[],[f214]) ).

tff(f214,plain,
    ! [X0: $tType] :
      ( ! [X1: int] :
          ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
        <=> ord_less_eq(int,pls,X1) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f133]) ).

tff(f133,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X1: int] :
          ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
        <=> ord_less_eq(int,pls,X1) ) ),
    inference(rectify,[],[f68]) ).

tff(f68,axiom,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X3: int] :
          ( ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X3))
        <=> ord_less_eq(int,pls,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__special_I1_J) ).

tff(f1268,plain,
    spl2_112,
    inference(avatar_split_clause,[],[f365,f1266]) ).

tff(f1266,plain,
    ( spl2_112
  <=> ! [X0: $tType,X1: int] :
        ( ord_less_eq(int,pls,X1)
        | ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_112])]) ).

tff(f365,plain,
    ! [X0: $tType,X1: int] :
      ( ord_less_eq(int,pls,X1)
      | ~ ord_less_eq(X0,zero_zero(X0),number_number_of(X0,X1))
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f255]) ).

tff(f1264,plain,
    spl2_111,
    inference(avatar_split_clause,[],[f348,f1262]) ).

tff(f1262,plain,
    ( spl2_111
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        | ~ ord_less(X0,X1,zero_zero(X0))
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_111])]) ).

tff(f348,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
      | ~ ord_less(X0,X1,zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f252,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
            | ~ ord_less(X0,X1,zero_zero(X0)) )
          & ( ord_less(X0,X1,zero_zero(X0))
            | ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0)) ) )
      | ~ linordered_idom(X0) ),
    inference(nnf_transformation,[],[f198]) ).

tff(f198,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        <=> ord_less(X0,X1,zero_zero(X0)) )
      | ~ linordered_idom(X0) ),
    inference(ennf_transformation,[],[f126]) ).

tff(f126,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0] :
          ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        <=> ord_less(X0,X1,zero_zero(X0)) ) ),
    inference(rectify,[],[f75]) ).

tff(f75,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X9: X0] :
          ( ord_less(X0,plus_plus(X0,X9,X9),zero_zero(X0))
        <=> ord_less(X0,X9,zero_zero(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_even__less__0__iff) ).

tff(f1260,plain,
    spl2_110,
    inference(avatar_split_clause,[],[f347,f1258]) ).

tff(f1258,plain,
    ( spl2_110
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,X1,zero_zero(X0))
        | ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_110])]) ).

tff(f347,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,X1,zero_zero(X0))
      | ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f1256,plain,
    ( ~ spl2_109
    | ~ spl2_95
    | spl2_97 ),
    inference(avatar_split_clause,[],[f1198,f1160,f1106,f1253]) ).

tff(f1253,plain,
    ( spl2_109
  <=> ord_less(int,s,times_times(int,bit0(bit0(one_one(int))),m)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_109])]) ).

tff(f1106,plain,
    ( spl2_95
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_95])]) ).

tff(f1198,plain,
    ( ~ ord_less(int,s,times_times(int,bit0(bit0(one_one(int))),m))
    | ~ spl2_95
    | spl2_97 ),
    inference(resolution,[],[f1162,f1107]) ).

tff(f1107,plain,
    ( ! [X0: int,X1: int] :
        ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
        | ~ ord_less(int,X1,X0) )
    | ~ spl2_95 ),
    inference(avatar_component_clause,[],[f1106]) ).

tff(f1247,plain,
    ( spl2_108
    | ~ spl2_67
    | ~ spl2_105 ),
    inference(avatar_split_clause,[],[f1211,f1207,f857,f1244]) ).

tff(f1244,plain,
    ( spl2_108
  <=> ord_less(int,sK1,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_108])]) ).

tff(f1207,plain,
    ( spl2_105
  <=> ord_less(int,sK1,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_105])]) ).

tff(f1211,plain,
    ( ord_less(int,sK1,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)))
    | ~ spl2_67
    | ~ spl2_105 ),
    inference(forward_demodulation,[],[f1209,f859]) ).

tff(f1209,plain,
    ( ord_less(int,sK1,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)))
    | ~ spl2_105 ),
    inference(avatar_component_clause,[],[f1207]) ).

tff(f1242,plain,
    ( spl2_107
    | ~ spl2_67
    | ~ spl2_104 ),
    inference(avatar_split_clause,[],[f1205,f1201,f857,f1239]) ).

tff(f1239,plain,
    ( spl2_107
  <=> zcong(s1,sK1,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_107])]) ).

tff(f1201,plain,
    ( spl2_104
  <=> zcong(s1,sK1,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_104])]) ).

tff(f1205,plain,
    ( zcong(s1,sK1,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)))
    | ~ spl2_67
    | ~ spl2_104 ),
    inference(forward_demodulation,[],[f1203,f859]) ).

tff(f1203,plain,
    ( zcong(s1,sK1,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)))
    | ~ spl2_104 ),
    inference(avatar_component_clause,[],[f1201]) ).

tff(f1215,plain,
    ( spl2_106
    | ~ spl2_67
    | ~ spl2_99 ),
    inference(avatar_split_clause,[],[f1180,f1177,f857,f1213]) ).

tff(f1213,plain,
    ( spl2_106
  <=> ! [X0: $tType] :
        ( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(one_one(int))) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_106])]) ).

tff(f1177,plain,
    ( spl2_99
  <=> ! [X0: $tType] :
        ( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_99])]) ).

tff(f1180,plain,
    ( ! [X0: $tType] :
        ( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(one_one(int))) )
        | ~ number_ring(X0) )
    | ~ spl2_67
    | ~ spl2_99 ),
    inference(forward_demodulation,[],[f1178,f859]) ).

tff(f1178,plain,
    ( ! [X0: $tType] :
        ( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
        | ~ number_ring(X0) )
    | ~ spl2_99 ),
    inference(avatar_component_clause,[],[f1177]) ).

tff(f1210,plain,
    spl2_105,
    inference(avatar_split_clause,[],[f527,f1207]) ).

tff(f527,plain,
    ord_less(int,sK1,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))),
    inference(forward_demodulation,[],[f474,f341]) ).

tff(f341,plain,
    ! [X0: int] : ( number_number_of(int,X0) = X0 ),
    inference(cnf_transformation,[],[f121]) ).

tff(f121,plain,
    ! [X0: int] : ( number_number_of(int,X0) = X0 ),
    inference(rectify,[],[f91]) ).

tff(f91,axiom,
    ! [X6: int] : ( number_number_of(int,X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_number__of__is__id) ).

tff(f474,plain,
    ord_less(int,sK1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    inference(cnf_transformation,[],[f304]) ).

tff(f304,plain,
    ( ! [X1: int] :
        ( ( sK1 = X1 )
        | ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
        | ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
        | ~ ord_less_eq(int,zero_zero(int),X1) )
    & zcong(s1,sK1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    & ord_less(int,sK1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    & ord_less_eq(int,zero_zero(int),sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f248,f303]) ).

tff(f303,plain,
    ( ? [X0: int] :
        ( ! [X1: int] :
            ( ( X0 = X1 )
            | ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
            | ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
            | ~ ord_less_eq(int,zero_zero(int),X1) )
        & zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
        & ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
        & ord_less_eq(int,zero_zero(int),X0) )
   => ( ! [X1: int] :
          ( ( sK1 = X1 )
          | ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          | ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          | ~ ord_less_eq(int,zero_zero(int),X1) )
      & zcong(s1,sK1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less(int,sK1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less_eq(int,zero_zero(int),sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f248,plain,
    ? [X0: int] :
      ( ! [X1: int] :
          ( ( X0 = X1 )
          | ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          | ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          | ~ ord_less_eq(int,zero_zero(int),X1) )
      & zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less_eq(int,zero_zero(int),X0) ),
    inference(flattening,[],[f247]) ).

tff(f247,plain,
    ? [X0: int] :
      ( ! [X1: int] :
          ( ( X0 = X1 )
          | ~ zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          | ~ ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          | ~ ord_less_eq(int,zero_zero(int),X1) )
      & zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less_eq(int,zero_zero(int),X0) ),
    inference(ennf_transformation,[],[f193]) ).

tff(f193,plain,
    ? [X0: int] :
      ( ! [X1: int] :
          ( ( zcong(s1,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
            & ord_less(int,X1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
            & ord_less_eq(int,zero_zero(int),X1) )
         => ( X0 = X1 ) )
      & zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less_eq(int,zero_zero(int),X0) ),
    inference(rectify,[],[f72]) ).

tff(f72,axiom,
    ? [X18: int] :
      ( ! [X19: int] :
          ( ( zcong(s1,X19,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
            & ord_less(int,X19,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
            & ord_less_eq(int,zero_zero(int),X19) )
         => ( X18 = X19 ) )
      & zcong(s1,X18,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less(int,X18,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less_eq(int,zero_zero(int),X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1_A_061_As_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).

tff(f1204,plain,
    spl2_104,
    inference(avatar_split_clause,[],[f526,f1201]) ).

tff(f526,plain,
    zcong(s1,sK1,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))),
    inference(forward_demodulation,[],[f475,f341]) ).

tff(f475,plain,
    zcong(s1,sK1,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
    inference(cnf_transformation,[],[f304]) ).

tff(f1197,plain,
    ( spl2_102
    | ~ spl2_103 ),
    inference(avatar_split_clause,[],[f513,f1194,f1190]) ).

tff(f1190,plain,
    ( spl2_102
  <=> ( one_one(int) = times_times(int,one_one(int),one_one(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_102])]) ).

tff(f1194,plain,
    ( spl2_103
  <=> ord_less(int,pls,one_one(int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_103])]) ).

tff(f513,plain,
    ( ~ ord_less(int,pls,one_one(int))
    | ( one_one(int) = times_times(int,one_one(int),one_one(int)) ) ),
    inference(forward_demodulation,[],[f484,f324]) ).

tff(f484,plain,
    ( ( one_one(int) = times_times(int,one_one(int),one_one(int)) )
    | ~ ord_less(int,zero_zero(int),one_one(int)) ),
    inference(equality_resolution,[],[f483]) ).

tff(f483,plain,
    ! [X1: int] :
      ( ( one_one(int) = times_times(int,X1,one_one(int)) )
      | ( one_one(int) != X1 )
      | ~ ord_less(int,zero_zero(int),X1) ),
    inference(equality_resolution,[],[f431]) ).

tff(f431,plain,
    ! [X0: int,X1: int] :
      ( ( one_one(int) = times_times(int,X1,X0) )
      | ( one_one(int) != X0 )
      | ( one_one(int) != X1 )
      | ~ ord_less(int,zero_zero(int),X1) ),
    inference(cnf_transformation,[],[f281]) ).

tff(f1188,plain,
    spl2_101,
    inference(avatar_split_clause,[],[f512,f1186]) ).

tff(f1186,plain,
    ( spl2_101
  <=> ! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,times_times(int,bit0(X1),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_101])]) ).

tff(f512,plain,
    ! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,times_times(int,bit0(X1),X0),X0) ),
    inference(forward_demodulation,[],[f428,f421]) ).

tff(f421,plain,
    ! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
    inference(cnf_transformation,[],[f164]) ).

tff(f164,plain,
    ! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
    inference(rectify,[],[f35]) ).

tff(f35,axiom,
    ! [X5: int,X6: int] : ( bit0(times_times(int,X6,X5)) = times_times(int,bit0(X6),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__Bit0) ).

tff(f428,plain,
    ! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
    inference(cnf_transformation,[],[f171]) ).

tff(f171,plain,
    ! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X5: int,X6: int] : ( times_times(int,bit1(X6),X5) = plus_plus(int,bit0(times_times(int,X6,X5)),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mult__Bit1) ).

tff(f1184,plain,
    spl2_100,
    inference(avatar_split_clause,[],[f363,f1182]) ).

tff(f1182,plain,
    ( spl2_100
  <=> ! [X0: $tType,X2: int,X1: int] :
        ( ( X1 = X2 )
        | ( number_number_of(X0,X1) != number_number_of(X0,X2) )
        | ~ ring_char_0(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_100])]) ).

tff(f363,plain,
    ! [X0: $tType,X2: int,X1: int] :
      ( ( X1 = X2 )
      | ( number_number_of(X0,X1) != number_number_of(X0,X2) )
      | ~ ring_char_0(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f254]) ).

tff(f254,plain,
    ! [X0: $tType] :
      ( ! [X1: int,X2: int] :
          ( ( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
            | ( X1 != X2 ) )
          & ( ( X1 = X2 )
            | ( number_number_of(X0,X1) != number_number_of(X0,X2) ) ) )
      | ~ ring_char_0(X0)
      | ~ number_ring(X0) ),
    inference(nnf_transformation,[],[f213]) ).

tff(f213,plain,
    ! [X0: $tType] :
      ( ! [X1: int,X2: int] :
          ( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
        <=> ( X1 = X2 ) )
      | ~ ring_char_0(X0)
      | ~ number_ring(X0) ),
    inference(flattening,[],[f212]) ).

tff(f212,plain,
    ! [X0: $tType] :
      ( ! [X1: int,X2: int] :
          ( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
        <=> ( X1 = X2 ) )
      | ~ ring_char_0(X0)
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: $tType] :
      ( ( ring_char_0(X0)
        & number_ring(X0) )
     => ! [X1: int,X2: int] :
          ( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
        <=> ( X1 = X2 ) ) ),
    inference(rectify,[],[f17]) ).

tff(f17,axiom,
    ! [X0: $tType] :
      ( ( ring_char_0(X0)
        & number_ring(X0) )
     => ! [X3: int,X4: int] :
          ( ( number_number_of(X0,X3) = number_number_of(X0,X4) )
        <=> ( X3 = X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_eq__number__of) ).

tff(f1179,plain,
    spl2_99,
    inference(avatar_split_clause,[],[f351,f1177]) ).

tff(f351,plain,
    ! [X0: $tType] :
      ( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f201]) ).

tff(f201,plain,
    ! [X0: $tType] :
      ( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).

tff(f1172,plain,
    spl2_98,
    inference(avatar_split_clause,[],[f345,f1170]) ).

tff(f1170,plain,
    ( spl2_98
  <=> ! [X0: $tType,X1: X0] :
        ( ( zero_zero(X0) = X1 )
        | ( zero_zero(X0) != plus_plus(X0,X1,X1) )
        | ~ linord219039673up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_98])]) ).

tff(f345,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) = X1 )
      | ( zero_zero(X0) != plus_plus(X0,X1,X1) )
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f251]) ).

tff(f251,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
            | ( zero_zero(X0) != X1 ) )
          & ( ( zero_zero(X0) = X1 )
            | ( zero_zero(X0) != plus_plus(X0,X1,X1) ) ) )
      | ~ linord219039673up_add(X0) ),
    inference(nnf_transformation,[],[f197]) ).

tff(f197,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
        <=> ( zero_zero(X0) = X1 ) )
      | ~ linord219039673up_add(X0) ),
    inference(ennf_transformation,[],[f125]) ).

tff(f125,plain,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X1: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
        <=> ( zero_zero(X0) = X1 ) ) ),
    inference(rectify,[],[f20]) ).

tff(f20,axiom,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X9: X0] :
          ( ( plus_plus(X0,X9,X9) = zero_zero(X0) )
        <=> ( zero_zero(X0) = X9 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_double__eq__0__iff) ).

tff(f1163,plain,
    ( ~ spl2_97
    | spl2_26
    | ~ spl2_67
    | ~ spl2_92 ),
    inference(avatar_split_clause,[],[f1154,f1094,f857,f654,f1160]) ).

tff(f654,plain,
    ( spl2_26
  <=> ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).

tff(f1094,plain,
    ( spl2_92
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_92])]) ).

tff(f1154,plain,
    ( ~ ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)))
    | spl2_26
    | ~ spl2_67
    | ~ spl2_92 ),
    inference(forward_demodulation,[],[f1152,f859]) ).

tff(f1152,plain,
    ( ~ ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)))
    | spl2_26
    | ~ spl2_92 ),
    inference(resolution,[],[f1095,f656]) ).

tff(f656,plain,
    ( ~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),one_one(int)))
    | spl2_26 ),
    inference(avatar_component_clause,[],[f654]) ).

tff(f1095,plain,
    ( ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
        | ~ ord_less(int,X1,X0) )
    | ~ spl2_92 ),
    inference(avatar_component_clause,[],[f1094]) ).

tff(f1112,plain,
    spl2_96,
    inference(avatar_split_clause,[],[f497,f1110]) ).

tff(f1110,plain,
    ( spl2_96
  <=> ! [X0: int] :
        ( ~ ord_less_eq(int,pls,X0)
        | ord_less(int,pls,plus_plus(int,one_one(int),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_96])]) ).

tff(f497,plain,
    ! [X0: int] :
      ( ~ ord_less_eq(int,pls,X0)
      | ord_less(int,pls,plus_plus(int,one_one(int),X0)) ),
    inference(forward_demodulation,[],[f496,f324]) ).

tff(f496,plain,
    ! [X0: int] :
      ( ord_less(int,pls,plus_plus(int,one_one(int),X0))
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(forward_demodulation,[],[f362,f324]) ).

tff(f362,plain,
    ! [X0: int] :
      ( ord_less(int,zero_zero(int),plus_plus(int,one_one(int),X0))
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f211]) ).

tff(f211,plain,
    ! [X0: int] :
      ( ord_less(int,zero_zero(int),plus_plus(int,one_one(int),X0))
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(ennf_transformation,[],[f131]) ).

tff(f131,plain,
    ! [X0: int] :
      ( ord_less_eq(int,zero_zero(int),X0)
     => ord_less(int,zero_zero(int),plus_plus(int,one_one(int),X0)) ),
    inference(rectify,[],[f97]) ).

tff(f97,axiom,
    ! [X14: int] :
      ( ord_less_eq(int,zero_zero(int),X14)
     => ord_less(int,zero_zero(int),plus_plus(int,one_one(int),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_le__imp__0__less) ).

tff(f1108,plain,
    spl2_95,
    inference(avatar_split_clause,[],[f468,f1106]) ).

tff(f468,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f1104,plain,
    spl2_94,
    inference(avatar_split_clause,[],[f466,f1102]) ).

tff(f466,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f299,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
        | ~ ord_less_eq(int,X1,X0) )
      & ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
    inference(nnf_transformation,[],[f189]) ).

tff(f189,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
    <=> ord_less_eq(int,X1,X0) ),
    inference(rectify,[],[f63]) ).

tff(f63,axiom,
    ! [X15: int,X16: int] :
      ( ord_less(int,X16,plus_plus(int,X15,one_one(int)))
    <=> ord_less_eq(int,X16,X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_zle__add1__eq__le) ).

tff(f1100,plain,
    spl2_93,
    inference(avatar_split_clause,[],[f465,f1098]) ).

tff(f1098,plain,
    ( spl2_93
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_93])]) ).

tff(f465,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f1096,plain,
    spl2_92,
    inference(avatar_split_clause,[],[f464,f1094]) ).

tff(f464,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f298]) ).

tff(f298,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
        | ~ ord_less(int,X1,X0) )
      & ( ord_less(int,X1,X0)
        | ~ ord_less_eq(int,X1,minus_minus(int,X0,one_one(int))) ) ),
    inference(nnf_transformation,[],[f188]) ).

tff(f188,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f64]) ).

tff(f64,axiom,
    ! [X15: int,X16: int] :
      ( ord_less_eq(int,X16,minus_minus(int,X15,one_one(int)))
    <=> ord_less(int,X16,X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_zle__diff1__eq) ).

tff(f1092,plain,
    spl2_91,
    inference(avatar_split_clause,[],[f463,f1090]) ).

tff(f1090,plain,
    ( spl2_91
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less_eq(int,X1,minus_minus(int,X0,one_one(int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_91])]) ).

tff(f463,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less_eq(int,X1,minus_minus(int,X0,one_one(int))) ),
    inference(cnf_transformation,[],[f298]) ).

tff(f1088,plain,
    spl2_90,
    inference(avatar_split_clause,[],[f427,f1086]) ).

tff(f1086,plain,
    ( spl2_90
  <=> ! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).

tff(f427,plain,
    ! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
    inference(cnf_transformation,[],[f170]) ).

tff(f170,plain,
    ! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
    inference(rectify,[],[f36]) ).

tff(f36,axiom,
    ! [X5: int,X6: int] : ( plus_plus(int,bit0(X6),bit0(X5)) = bit0(plus_plus(int,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_add__Bit0__Bit0) ).

tff(f1084,plain,
    spl2_89,
    inference(avatar_split_clause,[],[f426,f1082]) ).

tff(f1082,plain,
    ( spl2_89
  <=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).

tff(f426,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f169]) ).

tff(f169,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X5: int,X6: int] : ( plus_plus(int,bit1(X6),bit0(X5)) = bit1(plus_plus(int,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_add__Bit1__Bit0) ).

tff(f1080,plain,
    spl2_88,
    inference(avatar_split_clause,[],[f425,f1078]) ).

tff(f1078,plain,
    ( spl2_88
  <=> ! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit0(X0)) = bit1(minus_minus(int,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_88])]) ).

tff(f425,plain,
    ! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit0(X0)) = bit1(minus_minus(int,X1,X0)) ),
    inference(cnf_transformation,[],[f168]) ).

tff(f168,plain,
    ! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit0(X0)) = bit1(minus_minus(int,X1,X0)) ),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X5: int,X6: int] : ( minus_minus(int,bit1(X6),bit0(X5)) = bit1(minus_minus(int,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_diff__bin__simps_I9_J) ).

tff(f1076,plain,
    spl2_87,
    inference(avatar_split_clause,[],[f424,f1074]) ).

tff(f1074,plain,
    ( spl2_87
  <=> ! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit1(X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_87])]) ).

tff(f424,plain,
    ! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit1(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit1(X1),bit1(X0)) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ! [X5: int,X6: int] : ( minus_minus(int,bit1(X6),bit1(X5)) = bit0(minus_minus(int,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_diff__bin__simps_I10_J) ).

tff(f1072,plain,
    ( ~ spl2_86
    | spl2_26
    | ~ spl2_67 ),
    inference(avatar_split_clause,[],[f898,f857,f654,f1069]) ).

tff(f1069,plain,
    ( spl2_86
  <=> ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_86])]) ).

tff(f898,plain,
    ( ~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(one_one(int))),m),one_one(int)),one_one(int)))
    | spl2_26
    | ~ spl2_67 ),
    inference(superposition,[],[f656,f859]) ).

tff(f1067,plain,
    spl2_85,
    inference(avatar_split_clause,[],[f423,f1065]) ).

tff(f1065,plain,
    ( spl2_85
  <=> ! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit0(X1),bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_85])]) ).

tff(f423,plain,
    ! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit0(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f166]) ).

tff(f166,plain,
    ! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit0(X1),bit0(X0)) ),
    inference(rectify,[],[f37]) ).

tff(f37,axiom,
    ! [X5: int,X6: int] : ( bit0(minus_minus(int,X6,X5)) = minus_minus(int,bit0(X6),bit0(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_diff__bin__simps_I7_J) ).

tff(f1063,plain,
    spl2_84,
    inference(avatar_split_clause,[],[f422,f1061]) ).

tff(f1061,plain,
    ( spl2_84
  <=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_84])]) ).

tff(f422,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X5: int,X6: int] : ( bit1(plus_plus(int,X6,X5)) = plus_plus(int,bit0(X6),bit1(X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_add__Bit0__Bit1) ).

tff(f984,plain,
    spl2_83,
    inference(avatar_split_clause,[],[f517,f982]) ).

tff(f982,plain,
    ( spl2_83
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,minus_minus(int,X1,X0),pls)
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_83])]) ).

tff(f517,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,minus_minus(int,X1,X0),pls)
      | ~ ord_less(int,X1,X0) ),
    inference(forward_demodulation,[],[f432,f324]) ).

tff(f432,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f282]) ).

tff(f282,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,X0)
        | ~ ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) )
      & ( ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
        | ~ ord_less(int,X1,X0) ) ),
    inference(nnf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
    <=> ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) ),
    inference(rectify,[],[f80]) ).

tff(f80,axiom,
    ! [X7: int,X8: int] :
      ( ord_less(int,X8,X7)
    <=> ord_less(int,minus_minus(int,X8,X7),zero_zero(int)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_less__bin__lemma) ).

tff(f980,plain,
    spl2_82,
    inference(avatar_split_clause,[],[f516,f978]) ).

tff(f978,plain,
    ( spl2_82
  <=> ! [X0: int,X1: int] :
        ( ~ ord_less(int,minus_minus(int,X1,X0),pls)
        | ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_82])]) ).

tff(f516,plain,
    ! [X0: int,X1: int] :
      ( ~ ord_less(int,minus_minus(int,X1,X0),pls)
      | ord_less(int,X1,X0) ),
    inference(forward_demodulation,[],[f433,f324]) ).

tff(f433,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) ),
    inference(cnf_transformation,[],[f282]) ).

tff(f976,plain,
    spl2_81,
    inference(avatar_split_clause,[],[f477,f974]) ).

tff(f974,plain,
    ( spl2_81
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
        | ~ linord219039673up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).

tff(f477,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
      | ~ linord219039673up_add(X0) ),
    inference(equality_resolution,[],[f346]) ).

tff(f346,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
      | ( zero_zero(X0) != X1 )
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f251]) ).

tff(f972,plain,
    spl2_80,
    inference(avatar_split_clause,[],[f436,f970]) ).

tff(f970,plain,
    ( spl2_80
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_80])]) ).

tff(f436,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f284]) ).

tff(f284,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) )
      & ( ( ( X0 != X1 )
          & ord_less_eq(int,X1,X0) )
        | ~ ord_less(int,X1,X0) ) ),
    inference(flattening,[],[f283]) ).

tff(f283,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) )
      & ( ( ( X0 != X1 )
          & ord_less_eq(int,X1,X0) )
        | ~ ord_less(int,X1,X0) ) ),
    inference(nnf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
    <=> ( ( X0 != X1 )
        & ord_less_eq(int,X1,X0) ) ),
    inference(rectify,[],[f83]) ).

tff(f83,axiom,
    ! [X16: int,X15: int] :
      ( ord_less(int,X15,X16)
    <=> ( ( X15 != X16 )
        & ord_less_eq(int,X15,X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__int__def) ).

tff(f968,plain,
    spl2_79,
    inference(avatar_split_clause,[],[f421,f966]) ).

tff(f966,plain,
    ( spl2_79
  <=> ! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_79])]) ).

tff(f964,plain,
    spl2_78,
    inference(avatar_split_clause,[],[f344,f962]) ).

tff(f962,plain,
    ( spl2_78
  <=> ! [X0: int] : ( minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_78])]) ).

tff(f344,plain,
    ! [X0: int] : ( minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)) ),
    inference(cnf_transformation,[],[f124]) ).

tff(f124,plain,
    ! [X0: int] : ( minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X5: int] : ( minus_minus(int,pls,bit0(X5)) = bit0(minus_minus(int,pls,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_diff__bin__simps_I3_J) ).

tff(f943,plain,
    ( ~ spl2_77
    | ~ spl2_20
    | ~ spl2_67 ),
    inference(avatar_split_clause,[],[f899,f857,f625,f940]) ).

tff(f940,plain,
    ( spl2_77
  <=> ( pls = one_one(int) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_77])]) ).

tff(f625,plain,
    ( spl2_20
  <=> ! [X0: int] : ( pls != bit1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).

tff(f899,plain,
    ( ( pls != one_one(int) )
    | ~ spl2_20
    | ~ spl2_67 ),
    inference(superposition,[],[f626,f859]) ).

tff(f626,plain,
    ( ! [X0: int] : ( pls != bit1(X0) )
    | ~ spl2_20 ),
    inference(avatar_component_clause,[],[f625]) ).

tff(f896,plain,
    spl2_76,
    inference(avatar_split_clause,[],[f495,f894]) ).

tff(f894,plain,
    ( spl2_76
  <=> ! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_76])]) ).

tff(f495,plain,
    ! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
    inference(forward_demodulation,[],[f343,f324]) ).

tff(f343,plain,
    ! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
    inference(cnf_transformation,[],[f123]) ).

tff(f123,plain,
    ! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X14: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X14),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_odd__nonzero) ).

tff(f892,plain,
    spl2_75,
    inference(avatar_split_clause,[],[f460,f890]) ).

tff(f890,plain,
    ( spl2_75
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,bit0(X1),bit0(X0))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_75])]) ).

tff(f460,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit0(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f296,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,bit0(X1),bit0(X0))
        | ~ ord_less(int,X1,X0) )
      & ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit0(X1),bit0(X0)) ) ),
    inference(nnf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit0(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f82]) ).

tff(f82,axiom,
    ! [X22: int,X23: int] :
      ( ord_less(int,bit0(X23),bit0(X22))
    <=> ord_less(int,X23,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_less__int__code_I13_J) ).

tff(f888,plain,
    spl2_74,
    inference(avatar_split_clause,[],[f459,f886]) ).

tff(f886,plain,
    ( spl2_74
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit0(X1),bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_74])]) ).

tff(f459,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,bit0(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f884,plain,
    spl2_73,
    inference(avatar_split_clause,[],[f458,f882]) ).

tff(f882,plain,
    ( spl2_73
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,bit0(X1),bit1(X0))
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_73])]) ).

tff(f458,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit1(X0))
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f295,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,bit0(X1),bit1(X0))
        | ~ ord_less_eq(int,X1,X0) )
      & ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,bit0(X1),bit1(X0)) ) ),
    inference(nnf_transformation,[],[f185]) ).

tff(f185,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit1(X0))
    <=> ord_less_eq(int,X1,X0) ),
    inference(rectify,[],[f62]) ).

tff(f62,axiom,
    ! [X7: int,X8: int] :
      ( ord_less(int,bit0(X8),bit1(X7))
    <=> ord_less_eq(int,X8,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rel__simps_I15_J) ).

tff(f880,plain,
    spl2_72,
    inference(avatar_split_clause,[],[f457,f878]) ).

tff(f878,plain,
    ( spl2_72
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,bit0(X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_72])]) ).

tff(f457,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less(int,bit0(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f876,plain,
    spl2_71,
    inference(avatar_split_clause,[],[f454,f874]) ).

tff(f874,plain,
    ( spl2_71
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,bit1(X1),bit0(X0))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_71])]) ).

tff(f454,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit0(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f293]) ).

tff(f293,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,bit1(X1),bit0(X0))
        | ~ ord_less(int,X1,X0) )
      & ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit1(X1),bit0(X0)) ) ),
    inference(nnf_transformation,[],[f183]) ).

tff(f183,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit0(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X22: int,X23: int] :
      ( ord_less(int,bit1(X23),bit0(X22))
    <=> ord_less(int,X23,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__int__code_I15_J) ).

tff(f872,plain,
    spl2_70,
    inference(avatar_split_clause,[],[f453,f870]) ).

tff(f870,plain,
    ( spl2_70
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit1(X1),bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_70])]) ).

tff(f453,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,bit1(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f293]) ).

tff(f868,plain,
    spl2_69,
    inference(avatar_split_clause,[],[f450,f866]) ).

tff(f866,plain,
    ( spl2_69
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,bit1(X1),bit1(X0))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_69])]) ).

tff(f450,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit1(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f291,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,bit1(X1),bit1(X0))
        | ~ ord_less(int,X1,X0) )
      & ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
    inference(nnf_transformation,[],[f181]) ).

tff(f181,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit1(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f81]) ).

tff(f81,axiom,
    ! [X22: int,X23: int] :
      ( ord_less(int,bit1(X23),bit1(X22))
    <=> ord_less(int,X23,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_less__int__code_I16_J) ).

tff(f864,plain,
    spl2_68,
    inference(avatar_split_clause,[],[f449,f862]) ).

tff(f862,plain,
    ( spl2_68
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_68])]) ).

tff(f449,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,bit1(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f860,plain,
    ( spl2_67
    | ~ spl2_27
    | ~ spl2_58 ),
    inference(avatar_split_clause,[],[f821,f802,f659,f857]) ).

tff(f802,plain,
    ( spl2_58
  <=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_58])]) ).

tff(f821,plain,
    ( ( bit1(pls) = one_one(int) )
    | ~ spl2_27
    | ~ spl2_58 ),
    inference(superposition,[],[f804,f660]) ).

tff(f804,plain,
    ( ( one_one(int) = number_number_of(int,bit1(pls)) )
    | ~ spl2_58 ),
    inference(avatar_component_clause,[],[f802]) ).

tff(f855,plain,
    spl2_66,
    inference(avatar_split_clause,[],[f448,f853]) ).

tff(f853,plain,
    ( spl2_66
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,bit0(X1),bit0(X0))
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_66])]) ).

tff(f448,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit0(X1),bit0(X0))
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f290]) ).

tff(f290,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less_eq(int,bit0(X1),bit0(X0))
        | ~ ord_less_eq(int,X1,X0) )
      & ( ord_less_eq(int,X1,X0)
        | ~ ord_less_eq(int,bit0(X1),bit0(X0)) ) ),
    inference(nnf_transformation,[],[f180]) ).

tff(f180,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit0(X1),bit0(X0))
    <=> ord_less_eq(int,X1,X0) ),
    inference(rectify,[],[f33]) ).

tff(f33,axiom,
    ! [X7: int,X8: int] :
      ( ord_less_eq(int,bit0(X8),bit0(X7))
    <=> ord_less_eq(int,X8,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I31_J) ).

tff(f851,plain,
    spl2_65,
    inference(avatar_split_clause,[],[f447,f849]) ).

tff(f849,plain,
    ( spl2_65
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less_eq(int,bit0(X1),bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_65])]) ).

tff(f447,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less_eq(int,bit0(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f290]) ).

tff(f847,plain,
    spl2_64,
    inference(avatar_split_clause,[],[f446,f845]) ).

tff(f845,plain,
    ( spl2_64
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,bit0(X1),bit1(X0))
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_64])]) ).

tff(f446,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit0(X1),bit1(X0))
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f289]) ).

tff(f289,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less_eq(int,bit0(X1),bit1(X0))
        | ~ ord_less_eq(int,X1,X0) )
      & ( ord_less_eq(int,X1,X0)
        | ~ ord_less_eq(int,bit0(X1),bit1(X0)) ) ),
    inference(nnf_transformation,[],[f179]) ).

tff(f179,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit0(X1),bit1(X0))
    <=> ord_less_eq(int,X1,X0) ),
    inference(rectify,[],[f54]) ).

tff(f54,axiom,
    ! [X7: int,X8: int] :
      ( ord_less_eq(int,bit0(X8),bit1(X7))
    <=> ord_less_eq(int,X8,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I32_J) ).

tff(f843,plain,
    spl2_63,
    inference(avatar_split_clause,[],[f445,f841]) ).

tff(f841,plain,
    ( spl2_63
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less_eq(int,bit0(X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_63])]) ).

tff(f445,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less_eq(int,bit0(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f289]) ).

tff(f839,plain,
    spl2_62,
    inference(avatar_split_clause,[],[f444,f837]) ).

tff(f837,plain,
    ( spl2_62
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,bit1(X1),bit0(X0))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_62])]) ).

tff(f444,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit1(X1),bit0(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f288]) ).

tff(f288,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less_eq(int,bit1(X1),bit0(X0))
        | ~ ord_less(int,X1,X0) )
      & ( ord_less(int,X1,X0)
        | ~ ord_less_eq(int,bit1(X1),bit0(X0)) ) ),
    inference(nnf_transformation,[],[f178]) ).

tff(f178,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit1(X1),bit0(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f61]) ).

tff(f61,axiom,
    ! [X7: int,X8: int] :
      ( ord_less_eq(int,bit1(X8),bit0(X7))
    <=> ord_less(int,X8,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rel__simps_I33_J) ).

tff(f835,plain,
    spl2_61,
    inference(avatar_split_clause,[],[f443,f833]) ).

tff(f833,plain,
    ( spl2_61
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less_eq(int,bit1(X1),bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_61])]) ).

tff(f443,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less_eq(int,bit1(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f288]) ).

tff(f831,plain,
    spl2_60,
    inference(avatar_split_clause,[],[f442,f829]) ).

tff(f829,plain,
    ( spl2_60
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,bit1(X1),bit1(X0))
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_60])]) ).

tff(f442,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit1(X1),bit1(X0))
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f287,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less_eq(int,bit1(X1),bit1(X0))
        | ~ ord_less_eq(int,X1,X0) )
      & ( ord_less_eq(int,X1,X0)
        | ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
    inference(nnf_transformation,[],[f177]) ).

tff(f177,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,bit1(X1),bit1(X0))
    <=> ord_less_eq(int,X1,X0) ),
    inference(rectify,[],[f31]) ).

tff(f31,axiom,
    ! [X7: int,X8: int] :
      ( ord_less_eq(int,bit1(X8),bit1(X7))
    <=> ord_less_eq(int,X8,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rel__simps_I34_J) ).

tff(f827,plain,
    spl2_59,
    inference(avatar_split_clause,[],[f441,f825]) ).

tff(f825,plain,
    ( spl2_59
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_59])]) ).

tff(f441,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less_eq(int,bit1(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f805,plain,
    ( spl2_58
    | ~ spl2_7
    | ~ spl2_38 ),
    inference(avatar_split_clause,[],[f795,f716,f560,f802]) ).

tff(f560,plain,
    ( spl2_7
  <=> number_ring(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

tff(f716,plain,
    ( spl2_38
  <=> ! [X0: $tType] :
        ( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).

tff(f795,plain,
    ( ( one_one(int) = number_number_of(int,bit1(pls)) )
    | ~ spl2_7
    | ~ spl2_38 ),
    inference(resolution,[],[f717,f562]) ).

tff(f562,plain,
    ( number_ring(int)
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f560]) ).

tff(f717,plain,
    ( ! [X0: $tType] :
        ( ~ number_ring(X0)
        | ( one_one(X0) = number_number_of(X0,bit1(pls)) ) )
    | ~ spl2_38 ),
    inference(avatar_component_clause,[],[f716]) ).

tff(f794,plain,
    spl2_57,
    inference(avatar_split_clause,[],[f499,f792]) ).

tff(f792,plain,
    ( spl2_57
  <=> ! [X0: int] :
        ( ord_less(int,pls,X0)
        | ~ ord_less_eq(int,one_one(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_57])]) ).

tff(f499,plain,
    ! [X0: int] :
      ( ord_less(int,pls,X0)
      | ~ ord_less_eq(int,one_one(int),X0) ),
    inference(forward_demodulation,[],[f399,f324]) ).

tff(f399,plain,
    ! [X0: int] :
      ( ord_less(int,zero_zero(int),X0)
      | ~ ord_less_eq(int,one_one(int),X0) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f270,plain,
    ! [X0: int] :
      ( ( ord_less_eq(int,one_one(int),X0)
        | ~ ord_less(int,zero_zero(int),X0) )
      & ( ord_less(int,zero_zero(int),X0)
        | ~ ord_less_eq(int,one_one(int),X0) ) ),
    inference(nnf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: int] :
      ( ord_less_eq(int,one_one(int),X0)
    <=> ord_less(int,zero_zero(int),X0) ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X15: int] :
      ( ord_less_eq(int,one_one(int),X15)
    <=> ord_less(int,zero_zero(int),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_int__one__le__iff__zero__less) ).

tff(f790,plain,
    spl2_56,
    inference(avatar_split_clause,[],[f498,f788]) ).

tff(f788,plain,
    ( spl2_56
  <=> ! [X0: int] :
        ( ~ ord_less(int,pls,X0)
        | ord_less_eq(int,one_one(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_56])]) ).

tff(f498,plain,
    ! [X0: int] :
      ( ~ ord_less(int,pls,X0)
      | ord_less_eq(int,one_one(int),X0) ),
    inference(forward_demodulation,[],[f400,f324]) ).

tff(f400,plain,
    ! [X0: int] :
      ( ord_less_eq(int,one_one(int),X0)
      | ~ ord_less(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f786,plain,
    spl2_55,
    inference(avatar_split_clause,[],[f412,f784]) ).

tff(f784,plain,
    ( spl2_55
  <=> ! [X0: int] :
        ( ord_less(int,bit0(X0),pls)
        | ~ ord_less(int,X0,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_55])]) ).

tff(f412,plain,
    ! [X0: int] :
      ( ord_less(int,bit0(X0),pls)
      | ~ ord_less(int,X0,pls) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f276,plain,
    ! [X0: int] :
      ( ( ord_less(int,bit0(X0),pls)
        | ~ ord_less(int,X0,pls) )
      & ( ord_less(int,X0,pls)
        | ~ ord_less(int,bit0(X0),pls) ) ),
    inference(nnf_transformation,[],[f158]) ).

tff(f158,plain,
    ! [X0: int] :
      ( ord_less(int,bit0(X0),pls)
    <=> ord_less(int,X0,pls) ),
    inference(rectify,[],[f51]) ).

tff(f51,axiom,
    ! [X8: int] :
      ( ord_less(int,bit0(X8),pls)
    <=> ord_less(int,X8,pls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_rel__simps_I10_J) ).

tff(f782,plain,
    ( spl2_54
    | ~ spl2_33
    | ~ spl2_36 ),
    inference(avatar_split_clause,[],[f714,f697,f685,f780]) ).

tff(f780,plain,
    ( spl2_54
  <=> ! [X0: int] : ord_less_eq(int,X0,plus_plus(int,X0,one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).

tff(f685,plain,
    ( spl2_33
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).

tff(f697,plain,
    ( spl2_36
  <=> ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).

tff(f714,plain,
    ( ! [X0: int] : ord_less_eq(int,X0,plus_plus(int,X0,one_one(int)))
    | ~ spl2_33
    | ~ spl2_36 ),
    inference(resolution,[],[f698,f686]) ).

tff(f686,plain,
    ( ! [X0: int,X1: int] :
        ( ~ ord_less(int,X1,X0)
        | ord_less_eq(int,X1,X0) )
    | ~ spl2_33 ),
    inference(avatar_component_clause,[],[f685]) ).

tff(f698,plain,
    ( ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int)))
    | ~ spl2_36 ),
    inference(avatar_component_clause,[],[f697]) ).

tff(f778,plain,
    spl2_53,
    inference(avatar_split_clause,[],[f411,f776]) ).

tff(f776,plain,
    ( spl2_53
  <=> ! [X0: int] :
        ( ord_less(int,X0,pls)
        | ~ ord_less(int,bit0(X0),pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).

tff(f411,plain,
    ! [X0: int] :
      ( ord_less(int,X0,pls)
      | ~ ord_less(int,bit0(X0),pls) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f774,plain,
    spl2_52,
    inference(avatar_split_clause,[],[f410,f772]) ).

tff(f772,plain,
    ( spl2_52
  <=> ! [X0: int] :
        ( ord_less(int,bit1(X0),pls)
        | ~ ord_less(int,X0,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).

tff(f410,plain,
    ! [X0: int] :
      ( ord_less(int,bit1(X0),pls)
      | ~ ord_less(int,X0,pls) ),
    inference(cnf_transformation,[],[f275]) ).

tff(f275,plain,
    ! [X0: int] :
      ( ( ord_less(int,bit1(X0),pls)
        | ~ ord_less(int,X0,pls) )
      & ( ord_less(int,X0,pls)
        | ~ ord_less(int,bit1(X0),pls) ) ),
    inference(nnf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X0: int] :
      ( ord_less(int,bit1(X0),pls)
    <=> ord_less(int,X0,pls) ),
    inference(rectify,[],[f49]) ).

tff(f49,axiom,
    ! [X8: int] :
      ( ord_less(int,bit1(X8),pls)
    <=> ord_less(int,X8,pls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I12_J) ).

tff(f770,plain,
    spl2_51,
    inference(avatar_split_clause,[],[f409,f768]) ).

tff(f768,plain,
    ( spl2_51
  <=> ! [X0: int] :
        ( ord_less(int,X0,pls)
        | ~ ord_less(int,bit1(X0),pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_51])]) ).

tff(f409,plain,
    ! [X0: int] :
      ( ord_less(int,X0,pls)
      | ~ ord_less(int,bit1(X0),pls) ),
    inference(cnf_transformation,[],[f275]) ).

tff(f766,plain,
    spl2_50,
    inference(avatar_split_clause,[],[f408,f764]) ).

tff(f764,plain,
    ( spl2_50
  <=> ! [X0: int] :
        ( ord_less(int,pls,bit0(X0))
        | ~ ord_less(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).

tff(f408,plain,
    ! [X0: int] :
      ( ord_less(int,pls,bit0(X0))
      | ~ ord_less(int,pls,X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f274,plain,
    ! [X0: int] :
      ( ( ord_less(int,pls,bit0(X0))
        | ~ ord_less(int,pls,X0) )
      & ( ord_less(int,pls,X0)
        | ~ ord_less(int,pls,bit0(X0)) ) ),
    inference(nnf_transformation,[],[f156]) ).

tff(f156,plain,
    ! [X0: int] :
      ( ord_less(int,pls,bit0(X0))
    <=> ord_less(int,pls,X0) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X8: int] :
      ( ord_less(int,pls,bit0(X8))
    <=> ord_less(int,pls,X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I4_J) ).

tff(f762,plain,
    spl2_49,
    inference(avatar_split_clause,[],[f407,f760]) ).

tff(f760,plain,
    ( spl2_49
  <=> ! [X0: int] :
        ( ord_less(int,pls,X0)
        | ~ ord_less(int,pls,bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_49])]) ).

tff(f407,plain,
    ! [X0: int] :
      ( ord_less(int,pls,X0)
      | ~ ord_less(int,pls,bit0(X0)) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f758,plain,
    spl2_48,
    inference(avatar_split_clause,[],[f406,f756]) ).

tff(f756,plain,
    ( spl2_48
  <=> ! [X0: int] :
        ( ord_less(int,pls,bit1(X0))
        | ~ ord_less_eq(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).

tff(f406,plain,
    ! [X0: int] :
      ( ord_less(int,pls,bit1(X0))
      | ~ ord_less_eq(int,pls,X0) ),
    inference(cnf_transformation,[],[f273]) ).

tff(f273,plain,
    ! [X0: int] :
      ( ( ord_less(int,pls,bit1(X0))
        | ~ ord_less_eq(int,pls,X0) )
      & ( ord_less_eq(int,pls,X0)
        | ~ ord_less(int,pls,bit1(X0)) ) ),
    inference(nnf_transformation,[],[f155]) ).

tff(f155,plain,
    ! [X0: int] :
      ( ord_less(int,pls,bit1(X0))
    <=> ord_less_eq(int,pls,X0) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X8: int] :
      ( ord_less(int,pls,bit1(X8))
    <=> ord_less_eq(int,pls,X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rel__simps_I5_J) ).

tff(f754,plain,
    spl2_47,
    inference(avatar_split_clause,[],[f405,f752]) ).

tff(f752,plain,
    ( spl2_47
  <=> ! [X0: int] :
        ( ord_less_eq(int,pls,X0)
        | ~ ord_less(int,pls,bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_47])]) ).

tff(f405,plain,
    ! [X0: int] :
      ( ord_less_eq(int,pls,X0)
      | ~ ord_less(int,pls,bit1(X0)) ),
    inference(cnf_transformation,[],[f273]) ).

tff(f750,plain,
    spl2_46,
    inference(avatar_split_clause,[],[f404,f748]) ).

tff(f748,plain,
    ( spl2_46
  <=> ! [X0: int] :
        ( ord_less_eq(int,bit0(X0),pls)
        | ~ ord_less_eq(int,X0,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_46])]) ).

tff(f404,plain,
    ! [X0: int] :
      ( ord_less_eq(int,bit0(X0),pls)
      | ~ ord_less_eq(int,X0,pls) ),
    inference(cnf_transformation,[],[f272]) ).

tff(f272,plain,
    ! [X0: int] :
      ( ( ord_less_eq(int,bit0(X0),pls)
        | ~ ord_less_eq(int,X0,pls) )
      & ( ord_less_eq(int,X0,pls)
        | ~ ord_less_eq(int,bit0(X0),pls) ) ),
    inference(nnf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: int] :
      ( ord_less_eq(int,bit0(X0),pls)
    <=> ord_less_eq(int,X0,pls) ),
    inference(rectify,[],[f55]) ).

tff(f55,axiom,
    ! [X8: int] :
      ( ord_less_eq(int,bit0(X8),pls)
    <=> ord_less_eq(int,X8,pls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I27_J) ).

tff(f746,plain,
    spl2_45,
    inference(avatar_split_clause,[],[f403,f744]) ).

tff(f744,plain,
    ( spl2_45
  <=> ! [X0: int] :
        ( ord_less_eq(int,X0,pls)
        | ~ ord_less_eq(int,bit0(X0),pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_45])]) ).

tff(f403,plain,
    ! [X0: int] :
      ( ord_less_eq(int,X0,pls)
      | ~ ord_less_eq(int,bit0(X0),pls) ),
    inference(cnf_transformation,[],[f272]) ).

tff(f742,plain,
    spl2_44,
    inference(avatar_split_clause,[],[f402,f740]) ).

tff(f740,plain,
    ( spl2_44
  <=> ! [X0: int] :
        ( ord_less_eq(int,bit1(X0),pls)
        | ~ ord_less(int,X0,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).

tff(f402,plain,
    ! [X0: int] :
      ( ord_less_eq(int,bit1(X0),pls)
      | ~ ord_less(int,X0,pls) ),
    inference(cnf_transformation,[],[f271]) ).

tff(f271,plain,
    ! [X0: int] :
      ( ( ord_less_eq(int,bit1(X0),pls)
        | ~ ord_less(int,X0,pls) )
      & ( ord_less(int,X0,pls)
        | ~ ord_less_eq(int,bit1(X0),pls) ) ),
    inference(nnf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X0: int] :
      ( ord_less_eq(int,bit1(X0),pls)
    <=> ord_less(int,X0,pls) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X8: int] :
      ( ord_less_eq(int,bit1(X8),pls)
    <=> ord_less(int,X8,pls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rel__simps_I29_J) ).

tff(f738,plain,
    spl2_43,
    inference(avatar_split_clause,[],[f401,f736]) ).

tff(f736,plain,
    ( spl2_43
  <=> ! [X0: int] :
        ( ord_less(int,X0,pls)
        | ~ ord_less_eq(int,bit1(X0),pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).

tff(f401,plain,
    ! [X0: int] :
      ( ord_less(int,X0,pls)
      | ~ ord_less_eq(int,bit1(X0),pls) ),
    inference(cnf_transformation,[],[f271]) ).

tff(f734,plain,
    spl2_42,
    inference(avatar_split_clause,[],[f398,f732]) ).

tff(f732,plain,
    ( spl2_42
  <=> ! [X0: int] :
        ( ord_less_eq(int,pls,bit0(X0))
        | ~ ord_less_eq(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).

tff(f398,plain,
    ! [X0: int] :
      ( ord_less_eq(int,pls,bit0(X0))
      | ~ ord_less_eq(int,pls,X0) ),
    inference(cnf_transformation,[],[f269]) ).

tff(f269,plain,
    ! [X0: int] :
      ( ( ord_less_eq(int,pls,bit0(X0))
        | ~ ord_less_eq(int,pls,X0) )
      & ( ord_less_eq(int,pls,X0)
        | ~ ord_less_eq(int,pls,bit0(X0)) ) ),
    inference(nnf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X0: int] :
      ( ord_less_eq(int,pls,bit0(X0))
    <=> ord_less_eq(int,pls,X0) ),
    inference(rectify,[],[f56]) ).

tff(f56,axiom,
    ! [X8: int] :
      ( ord_less_eq(int,pls,bit0(X8))
    <=> ord_less_eq(int,pls,X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I21_J) ).

tff(f730,plain,
    spl2_41,
    inference(avatar_split_clause,[],[f397,f728]) ).

tff(f728,plain,
    ( spl2_41
  <=> ! [X0: int] :
        ( ord_less_eq(int,pls,X0)
        | ~ ord_less_eq(int,pls,bit0(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).

tff(f397,plain,
    ! [X0: int] :
      ( ord_less_eq(int,pls,X0)
      | ~ ord_less_eq(int,pls,bit0(X0)) ),
    inference(cnf_transformation,[],[f269]) ).

tff(f726,plain,
    spl2_40,
    inference(avatar_split_clause,[],[f396,f724]) ).

tff(f724,plain,
    ( spl2_40
  <=> ! [X0: int] :
        ( ord_less_eq(int,pls,bit1(X0))
        | ~ ord_less_eq(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).

tff(f396,plain,
    ! [X0: int] :
      ( ord_less_eq(int,pls,bit1(X0))
      | ~ ord_less_eq(int,pls,X0) ),
    inference(cnf_transformation,[],[f268]) ).

tff(f268,plain,
    ! [X0: int] :
      ( ( ord_less_eq(int,pls,bit1(X0))
        | ~ ord_less_eq(int,pls,X0) )
      & ( ord_less_eq(int,pls,X0)
        | ~ ord_less_eq(int,pls,bit1(X0)) ) ),
    inference(nnf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: int] :
      ( ord_less_eq(int,pls,bit1(X0))
    <=> ord_less_eq(int,pls,X0) ),
    inference(rectify,[],[f53]) ).

tff(f53,axiom,
    ! [X8: int] :
      ( ord_less_eq(int,pls,bit1(X8))
    <=> ord_less_eq(int,pls,X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rel__simps_I22_J) ).

tff(f722,plain,
    spl2_39,
    inference(avatar_split_clause,[],[f395,f720]) ).

tff(f720,plain,
    ( spl2_39
  <=> ! [X0: int] :
        ( ord_less_eq(int,pls,X0)
        | ~ ord_less_eq(int,pls,bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).

tff(f395,plain,
    ! [X0: int] :
      ( ord_less_eq(int,pls,X0)
      | ~ ord_less_eq(int,pls,bit1(X0)) ),
    inference(cnf_transformation,[],[f268]) ).

tff(f718,plain,
    spl2_38,
    inference(avatar_split_clause,[],[f350,f716]) ).

tff(f350,plain,
    ! [X0: $tType] :
      ( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: $tType] :
      ( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f11,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).

tff(f709,plain,
    ( spl2_37
    | ~ spl2_8
    | ~ spl2_32 ),
    inference(avatar_split_clause,[],[f702,f681,f565,f706]) ).

tff(f706,plain,
    ( spl2_37
  <=> ( zero_zero(nat) = number_number_of(nat,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).

tff(f565,plain,
    ( spl2_8
  <=> number_semiring(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

tff(f681,plain,
    ( spl2_32
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = number_number_of(X0,pls) )
        | ~ number_semiring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).

tff(f702,plain,
    ( ( zero_zero(nat) = number_number_of(nat,pls) )
    | ~ spl2_8
    | ~ spl2_32 ),
    inference(resolution,[],[f682,f567]) ).

tff(f567,plain,
    ( number_semiring(nat)
    | ~ spl2_8 ),
    inference(avatar_component_clause,[],[f565]) ).

tff(f682,plain,
    ( ! [X0: $tType] :
        ( ~ number_semiring(X0)
        | ( zero_zero(X0) = number_number_of(X0,pls) ) )
    | ~ spl2_32 ),
    inference(avatar_component_clause,[],[f681]) ).

tff(f699,plain,
    spl2_36,
    inference(avatar_split_clause,[],[f488,f697]) ).

tff(f488,plain,
    ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
    inference(equality_resolution,[],[f469]) ).

tff(f469,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f695,plain,
    spl2_35,
    inference(avatar_split_clause,[],[f439,f693]) ).

tff(f693,plain,
    ( spl2_35
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ( bit0(X1) != bit0(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).

tff(f439,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( bit0(X1) != bit0(X0) ) ),
    inference(cnf_transformation,[],[f286]) ).

tff(f286,plain,
    ! [X0: int,X1: int] :
      ( ( ( bit0(X1) = bit0(X0) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( bit0(X1) != bit0(X0) ) ) ),
    inference(nnf_transformation,[],[f176]) ).

tff(f176,plain,
    ! [X0: int,X1: int] :
      ( ( bit0(X1) = bit0(X0) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X7: int,X8: int] :
      ( ( bit0(X8) = bit0(X7) )
    <=> ( X7 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I48_J) ).

tff(f691,plain,
    spl2_34,
    inference(avatar_split_clause,[],[f437,f689]) ).

tff(f689,plain,
    ( spl2_34
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ( bit1(X0) != bit1(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).

tff(f437,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( bit1(X0) != bit1(X1) ) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: int,X1: int] :
      ( ( ( bit1(X0) = bit1(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( bit1(X0) != bit1(X1) ) ) ),
    inference(nnf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: int,X1: int] :
      ( ( bit1(X0) = bit1(X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f18]) ).

tff(f18,axiom,
    ! [X7: int,X8: int] :
      ( ( bit1(X8) = bit1(X7) )
    <=> ( X7 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I51_J) ).

tff(f687,plain,
    spl2_33,
    inference(avatar_split_clause,[],[f434,f685]) ).

tff(f434,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f284]) ).

tff(f683,plain,
    spl2_32,
    inference(avatar_split_clause,[],[f359,f681]) ).

tff(f359,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_semiring(X0) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f209,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_semiring(X0) ),
    inference(ennf_transformation,[],[f93]) ).

tff(f93,axiom,
    ! [X0: $tType] :
      ( number_semiring(X0)
     => ( zero_zero(X0) = number_number_of(X0,pls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_semiring__numeral__0__eq__0) ).

tff(f679,plain,
    spl2_31,
    inference(avatar_split_clause,[],[f349,f677]) ).

tff(f677,plain,
    ( spl2_31
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = number_number_of(X0,pls) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).

tff(f349,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f199]) ).

tff(f199,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f40]) ).

tff(f40,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ( zero_zero(X0) = number_number_of(X0,pls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_number__of__Pls) ).

tff(f674,plain,
    spl2_30,
    inference(avatar_split_clause,[],[f391,f672]) ).

tff(f672,plain,
    ( spl2_30
  <=> ! [X0: int] :
        ( ( pls = X0 )
        | ( pls != bit0(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).

tff(f391,plain,
    ! [X0: int] :
      ( ( pls = X0 )
      | ( pls != bit0(X0) ) ),
    inference(cnf_transformation,[],[f266]) ).

tff(f266,plain,
    ! [X0: int] :
      ( ( ( pls = bit0(X0) )
        | ( pls != X0 ) )
      & ( ( pls = X0 )
        | ( pls != bit0(X0) ) ) ),
    inference(nnf_transformation,[],[f148]) ).

tff(f148,plain,
    ! [X0: int] :
      ( ( pls = bit0(X0) )
    <=> ( pls = X0 ) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X8: int] :
      ( ( pls = bit0(X8) )
    <=> ( pls = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_rel__simps_I44_J) ).

tff(f670,plain,
    spl2_29,
    inference(avatar_split_clause,[],[f342,f668]) ).

tff(f668,plain,
    ( spl2_29
  <=> ! [X0: int] : ( pls = times_times(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).

tff(f342,plain,
    ! [X0: int] : ( pls = times_times(int,pls,X0) ),
    inference(cnf_transformation,[],[f122]) ).

tff(f122,plain,
    ! [X0: int] : ( pls = times_times(int,pls,X0) ),
    inference(rectify,[],[f34]) ).

tff(f34,axiom,
    ! [X1: int] : ( pls = times_times(int,pls,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_mult__Pls) ).

tff(f665,plain,
    spl2_28,
    inference(avatar_split_clause,[],[f419,f663]) ).

tff(f663,plain,
    ( spl2_28
  <=> ! [X0: int,X1: int] : ( bit0(X1) != bit1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).

tff(f419,plain,
    ! [X0: int,X1: int] : ( bit0(X1) != bit1(X0) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: int,X1: int] : ( bit0(X1) != bit1(X0) ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X5: int,X6: int] : ( bit1(X5) != bit0(X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I49_J) ).

tff(f661,plain,
    spl2_27,
    inference(avatar_split_clause,[],[f341,f659]) ).

tff(f657,plain,
    ( ~ spl2_26
    | spl2_25 ),
    inference(avatar_split_clause,[],[f652,f648,f654]) ).

tff(f648,plain,
    ( spl2_25
  <=> ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).

tff(f652,plain,
    ( ~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),one_one(int)))
    | spl2_25 ),
    inference(forward_demodulation,[],[f650,f341]) ).

tff(f650,plain,
    ( ~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)))
    | spl2_25 ),
    inference(avatar_component_clause,[],[f648]) ).

tff(f651,plain,
    ~ spl2_25,
    inference(avatar_split_clause,[],[f305,f648]) ).

tff(f305,plain,
    ~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,plain,
    ~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
    inference(flattening,[],[f116]) ).

tff(f116,negated_conjecture,
    ~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
    inference(negated_conjecture,[],[f115]) ).

tff(f115,conjecture,
    ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f646,plain,
    spl2_24,
    inference(avatar_split_clause,[],[f528,f643]) ).

tff(f643,plain,
    ( spl2_24
  <=> ord_less_eq(int,pls,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).

tff(f528,plain,
    ord_less_eq(int,pls,sK1),
    inference(forward_demodulation,[],[f473,f324]) ).

tff(f473,plain,
    ord_less_eq(int,zero_zero(int),sK1),
    inference(cnf_transformation,[],[f304]) ).

tff(f641,plain,
    spl2_23,
    inference(avatar_split_clause,[],[f494,f638]) ).

tff(f638,plain,
    ( spl2_23
  <=> ord_less_eq(int,pls,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).

tff(f494,plain,
    ord_less_eq(int,pls,sK0),
    inference(forward_demodulation,[],[f336,f324]) ).

tff(f336,plain,
    ord_less_eq(int,zero_zero(int),sK0),
    inference(cnf_transformation,[],[f250]) ).

tff(f250,plain,
    ( zcong(s1,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    & ord_less(int,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
    & ord_less_eq(int,zero_zero(int),sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f196,f249]) ).

tff(f249,plain,
    ( ? [X0: int] :
        ( zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
        & ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
        & ord_less_eq(int,zero_zero(int),X0) )
   => ( zcong(s1,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less(int,sK0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less_eq(int,zero_zero(int),sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f196,plain,
    ? [X0: int] :
      ( zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
      & ord_less_eq(int,zero_zero(int),X0) ),
    inference(ennf_transformation,[],[f118]) ).

tff(f118,plain,
    ~ ! [X0: int] :
        ~ ( zcong(s1,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          & ord_less(int,X0,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          & ord_less_eq(int,zero_zero(int),X0) ),
    inference(rectify,[],[f71]) ).

tff(f71,axiom,
    ~ ! [X17: int] :
        ~ ( zcong(s1,X17,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          & ord_less(int,X17,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
          & ord_less_eq(int,zero_zero(int),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1_A_061_As_093_A_Imod_A4_A_K_Am_A_L_A1_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

tff(f636,plain,
    spl2_22,
    inference(avatar_split_clause,[],[f493,f633]) ).

tff(f633,plain,
    ( spl2_22
  <=> ord_less_eq(int,pls,s) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).

tff(f493,plain,
    ord_less_eq(int,pls,s),
    inference(forward_demodulation,[],[f333,f324]) ).

tff(f333,plain,
    ord_less_eq(int,zero_zero(int),s),
    inference(cnf_transformation,[],[f1]) ).

tff(f631,plain,
    spl2_21,
    inference(avatar_split_clause,[],[f485,f629]) ).

tff(f629,plain,
    ( spl2_21
  <=> ! [X1: int] : ~ ord_less(int,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).

tff(f485,plain,
    ! [X1: int] : ~ ord_less(int,X1,X1),
    inference(equality_resolution,[],[f435]) ).

tff(f435,plain,
    ! [X0: int,X1: int] :
      ( ( X0 != X1 )
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f284]) ).

tff(f627,plain,
    spl2_20,
    inference(avatar_split_clause,[],[f339,f625]) ).

tff(f339,plain,
    ! [X0: int] : ( pls != bit1(X0) ),
    inference(cnf_transformation,[],[f119]) ).

tff(f119,plain,
    ! [X0: int] : ( pls != bit1(X0) ),
    inference(rectify,[],[f22]) ).

tff(f22,axiom,
    ! [X5: int] : ( pls != bit1(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I39_J) ).

tff(f623,plain,
    spl2_19,
    inference(avatar_split_clause,[],[f325,f620]) ).

tff(f620,plain,
    ( spl2_19
  <=> ord_less_eq(int,pls,pls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).

tff(f325,plain,
    ord_less_eq(int,pls,pls),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,axiom,
    ord_less_eq(int,pls,pls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I19_J) ).

tff(f618,plain,
    spl2_18,
    inference(avatar_split_clause,[],[f324,f615]) ).

tff(f615,plain,
    ( spl2_18
  <=> ( zero_zero(int) = pls ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).

tff(f613,plain,
    spl2_17,
    inference(avatar_split_clause,[],[f323,f610]) ).

tff(f610,plain,
    ( spl2_17
  <=> ( pls = bit0(pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).

tff(f323,plain,
    pls = bit0(pls),
    inference(cnf_transformation,[],[f27]) ).

tff(f27,axiom,
    pls = bit0(pls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Bit0__Pls) ).

tff(f608,plain,
    spl2_16,
    inference(avatar_split_clause,[],[f321,f605]) ).

tff(f605,plain,
    ( spl2_16
  <=> linorder(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).

tff(f321,plain,
    linorder(int),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    linorder(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).

tff(f603,plain,
    spl2_15,
    inference(avatar_split_clause,[],[f320,f600]) ).

tff(f600,plain,
    ( spl2_15
  <=> linorder(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).

tff(f320,plain,
    linorder(nat),
    inference(cnf_transformation,[],[f109]) ).

tff(f109,axiom,
    linorder(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).

tff(f598,plain,
    spl2_14,
    inference(avatar_split_clause,[],[f319,f595]) ).

tff(f595,plain,
    ( spl2_14
  <=> linorder(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).

tff(f319,plain,
    linorder(bool),
    inference(cnf_transformation,[],[f112]) ).

tff(f112,axiom,
    linorder(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).

tff(f593,plain,
    spl2_13,
    inference(avatar_split_clause,[],[f318,f590]) ).

tff(f590,plain,
    ( spl2_13
  <=> number(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).

tff(f318,plain,
    number(int),
    inference(cnf_transformation,[],[f107]) ).

tff(f107,axiom,
    number(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).

tff(f588,plain,
    spl2_12,
    inference(avatar_split_clause,[],[f317,f585]) ).

tff(f585,plain,
    ( spl2_12
  <=> number(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).

tff(f317,plain,
    number(nat),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,axiom,
    number(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).

tff(f583,plain,
    spl2_11,
    inference(avatar_split_clause,[],[f316,f580]) ).

tff(f580,plain,
    ( spl2_11
  <=> semiring(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).

tff(f316,plain,
    semiring(int),
    inference(cnf_transformation,[],[f105]) ).

tff(f105,axiom,
    semiring(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).

tff(f578,plain,
    spl2_10,
    inference(avatar_split_clause,[],[f315,f575]) ).

tff(f575,plain,
    ( spl2_10
  <=> semiring(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

tff(f315,plain,
    semiring(nat),
    inference(cnf_transformation,[],[f110]) ).

tff(f110,axiom,
    semiring(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).

tff(f573,plain,
    spl2_9,
    inference(avatar_split_clause,[],[f314,f570]) ).

tff(f570,plain,
    ( spl2_9
  <=> number_semiring(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).

tff(f314,plain,
    number_semiring(int),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,axiom,
    number_semiring(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).

tff(f568,plain,
    spl2_8,
    inference(avatar_split_clause,[],[f313,f565]) ).

tff(f313,plain,
    number_semiring(nat),
    inference(cnf_transformation,[],[f108]) ).

tff(f108,axiom,
    number_semiring(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).

tff(f563,plain,
    spl2_7,
    inference(avatar_split_clause,[],[f312,f560]) ).

tff(f312,plain,
    number_ring(int),
    inference(cnf_transformation,[],[f104]) ).

tff(f104,axiom,
    number_ring(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).

tff(f558,plain,
    spl2_6,
    inference(avatar_split_clause,[],[f311,f555]) ).

tff(f555,plain,
    ( spl2_6
  <=> linordered_idom(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

tff(f311,plain,
    linordered_idom(int),
    inference(cnf_transformation,[],[f100]) ).

tff(f100,axiom,
    linordered_idom(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).

tff(f553,plain,
    spl2_5,
    inference(avatar_split_clause,[],[f310,f550]) ).

tff(f550,plain,
    ( spl2_5
  <=> ring(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

tff(f310,plain,
    ring(int),
    inference(cnf_transformation,[],[f106]) ).

tff(f106,axiom,
    ring(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).

tff(f548,plain,
    spl2_4,
    inference(avatar_split_clause,[],[f309,f545]) ).

tff(f545,plain,
    ( spl2_4
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

tff(f309,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f114]) ).

tff(f114,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f543,plain,
    spl2_3,
    inference(avatar_split_clause,[],[f308,f540]) ).

tff(f540,plain,
    ( spl2_3
  <=> linord219039673up_add(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

tff(f308,plain,
    linord219039673up_add(int),
    inference(cnf_transformation,[],[f99]) ).

tff(f99,axiom,
    linord219039673up_add(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).

tff(f538,plain,
    spl2_2,
    inference(avatar_split_clause,[],[f307,f535]) ).

tff(f535,plain,
    ( spl2_2
  <=> ring_char_0(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

tff(f307,plain,
    ring_char_0(int),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    ring_char_0(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).

tff(f533,plain,
    ~ spl2_1,
    inference(avatar_split_clause,[],[f306,f530]) ).

tff(f530,plain,
    ( spl2_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

tff(f306,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f113]) ).

tff(f113,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : NUM960_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri May  3 14:56:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (7097)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (7100)WARNING: value z3 for option sas not known
% 0.13/0.37  % (7101)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (7103)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.37  % (7102)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.37  % (7098)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (7099)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (7100)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (7104)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37  % (7104)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: % Exception at run slice level
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37  % Exception at run slice level
% 0.13/0.37  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39  % (7105)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.39  % (7106)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.13/0.39  % (7107)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.13/0.39  % (7105)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.39  % (7106)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.39  % Exception at run slice level% (7102)First to succeed.
% 0.19/0.39  
% 0.19/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.40  % (7102)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7097"
% 0.19/0.40  % (7102)Refutation found. Thanks to Tanya!
% 0.19/0.40  % SZS status Theorem for theBenchmark
% 0.19/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.41  % (7102)------------------------------
% 0.19/0.41  % (7102)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.41  % (7102)Termination reason: Refutation
% 0.19/0.41  
% 0.19/0.41  % (7102)Memory used [KB]: 1466
% 0.19/0.41  % (7102)Time elapsed: 0.034 s
% 0.19/0.41  % (7102)Instructions burned: 55 (million)
% 0.19/0.41  % (7097)Success in time 0.046 s
%------------------------------------------------------------------------------