TSTP Solution File: NUN015_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN015_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 : n020.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 08:44:53 EDT 2024

% Result   : Theorem 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  275
% Syntax   : Number of formulae    :  778 ( 251 unt;  37 typ;   0 def)
%            Number of atoms       : 1827 ( 450 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 1805 ( 719   ~; 683   |;  92   &)
%                                         ( 228 <=>;  83  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   17 (  10   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :  162 ( 160 usr; 142 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-4 aty)
%            Number of variables   :  988 ( 965   !;   0   ?; 988   :)
%                                         (  23  !>;   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(type_def_8,type,
    fun: ( $tType * $tType ) > $tType ).

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

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

tff(func_def_2,type,
    bit0: int > int ).

tff(func_def_3,type,
    bit1: int > int ).

tff(func_def_4,type,
    pls: int ).

tff(func_def_5,type,
    number_number_of: 
      !>[X0: $tType] : ( int > X0 ) ).

tff(func_def_6,type,
    power_power: 
      !>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).

tff(func_def_7,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_8,type,
    fFalse: bool ).

tff(func_def_9,type,
    fTrue: bool ).

tff(func_def_10,type,
    n: nat ).

tff(func_def_11,type,
    tn: nat ).

tff(func_def_12,type,
    v: int ).

tff(func_def_13,type,
    w: int ).

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

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

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

tff(pred_def_7,type,
    semiring_1: 
      !>[X0: $tType] : $o ).

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

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

tff(pred_def_10,type,
    linordered_idom: 
      !>[X0: $tType] : $o ).

tff(pred_def_11,type,
    no_zero_divisors: 
      !>[X0: $tType] : $o ).

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

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

tff(pred_def_14,type,
    ring_11004092258visors: 
      !>[X0: $tType] : $o ).

tff(pred_def_15,type,
    linord219039673up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_16,type,
    ordere236663937imp_le: 
      !>[X0: $tType] : $o ).

tff(pred_def_17,type,
    ord_less: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_18,type,
    pp: bool > $o ).

tff(pred_def_19,type,
    sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).

tff(f1802,plain,
    $false,
    inference(avatar_sat_refutation,[],[f611,f616,f621,f626,f631,f636,f641,f646,f651,f656,f661,f666,f671,f676,f681,f686,f691,f696,f701,f706,f711,f716,f721,f726,f731,f736,f741,f746,f752,f757,f762,f767,f771,f775,f781,f786,f791,f795,f799,f804,f808,f812,f816,f822,f826,f830,f834,f844,f848,f852,f856,f861,f865,f874,f878,f882,f886,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f960,f964,f969,f973,f977,f981,f1001,f1005,f1009,f1013,f1017,f1021,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1077,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1255,f1259,f1263,f1267,f1271,f1275,f1279,f1283,f1287,f1291,f1295,f1419,f1423,f1427,f1431,f1435,f1439,f1463,f1467,f1487,f1491,f1497,f1512,f1516,f1520,f1524,f1614,f1618,f1628,f1644,f1656,f1663,f1676,f1680,f1692,f1696,f1716,f1723,f1771,f1801]) ).

tff(f1801,plain,
    ( ~ spl1_5
    | spl1_35
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_136 ),
    inference(avatar_split_clause,[],[f1688,f1678,f1625,f764,f778,f628]) ).

tff(f628,plain,
    ( spl1_5
  <=> linordered_idom(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

tff(f778,plain,
    ( spl1_35
  <=> ( v = pls ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).

tff(f764,plain,
    ( spl1_32
  <=> ( zero_zero(int) = pls ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).

tff(f1625,plain,
    ( spl1_131
  <=> ( pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_131])]) ).

tff(f1678,plain,
    ( spl1_136
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( zero_zero(X0) = X2 )
        | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_136])]) ).

tff(f1688,plain,
    ( ( v = pls )
    | ~ linordered_idom(int)
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_136 ),
    inference(forward_demodulation,[],[f1687,f766]) ).

tff(f766,plain,
    ( ( zero_zero(int) = pls )
    | ~ spl1_32 ),
    inference(avatar_component_clause,[],[f764]) ).

tff(f1687,plain,
    ( ( v = zero_zero(int) )
    | ~ linordered_idom(int)
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_136 ),
    inference(trivial_inequality_removal,[],[f1686]) ).

tff(f1686,plain,
    ( ( pls != pls )
    | ( v = zero_zero(int) )
    | ~ linordered_idom(int)
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_136 ),
    inference(forward_demodulation,[],[f1685,f766]) ).

tff(f1685,plain,
    ( ( zero_zero(int) != pls )
    | ( v = zero_zero(int) )
    | ~ linordered_idom(int)
    | ~ spl1_131
    | ~ spl1_136 ),
    inference(superposition,[],[f1679,f1627]) ).

tff(f1627,plain,
    ( ( pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
    | ~ spl1_131 ),
    inference(avatar_component_clause,[],[f1625]) ).

tff(f1679,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] :
        ( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
        | ( zero_zero(X0) = X2 )
        | ~ linordered_idom(X0) )
    | ~ spl1_136 ),
    inference(avatar_component_clause,[],[f1678]) ).

tff(f1771,plain,
    ( ~ spl1_5
    | spl1_141
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_135 ),
    inference(avatar_split_clause,[],[f1684,f1674,f1625,f764,f1768,f628]) ).

tff(f1768,plain,
    ( spl1_141
  <=> ( pls = w ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).

tff(f1674,plain,
    ( spl1_135
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( zero_zero(X0) = X1 )
        | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).

tff(f1684,plain,
    ( ( pls = w )
    | ~ linordered_idom(int)
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_135 ),
    inference(forward_demodulation,[],[f1683,f766]) ).

tff(f1683,plain,
    ( ( zero_zero(int) = w )
    | ~ linordered_idom(int)
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_135 ),
    inference(trivial_inequality_removal,[],[f1682]) ).

tff(f1682,plain,
    ( ( pls != pls )
    | ( zero_zero(int) = w )
    | ~ linordered_idom(int)
    | ~ spl1_32
    | ~ spl1_131
    | ~ spl1_135 ),
    inference(forward_demodulation,[],[f1681,f766]) ).

tff(f1681,plain,
    ( ( zero_zero(int) != pls )
    | ( zero_zero(int) = w )
    | ~ linordered_idom(int)
    | ~ spl1_131
    | ~ spl1_135 ),
    inference(superposition,[],[f1675,f1627]) ).

tff(f1675,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] :
        ( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
        | ( zero_zero(X0) = X1 )
        | ~ linordered_idom(X0) )
    | ~ spl1_135 ),
    inference(avatar_component_clause,[],[f1674]) ).

tff(f1723,plain,
    ( spl1_140
    | ~ spl1_6
    | ~ spl1_39
    | ~ spl1_42
    | ~ spl1_85
    | ~ spl1_129
    | ~ spl1_139 ),
    inference(avatar_split_clause,[],[f1719,f1714,f1612,f1049,f810,f797,f633,f1721]) ).

tff(f1721,plain,
    ( spl1_140
  <=> ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(bit1(pls))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).

tff(f633,plain,
    ( spl1_6
  <=> number_ring(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).

tff(f797,plain,
    ( spl1_39
  <=> ! [X0: int] : ( number_number_of(int,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).

tff(f810,plain,
    ( spl1_42
  <=> ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).

tff(f1049,plain,
    ( spl1_85
  <=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).

tff(f1612,plain,
    ( spl1_129
  <=> ! [X0: $tType,X3: int,X2: int,X1: X0] :
        ( ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).

tff(f1714,plain,
    ( spl1_139
  <=> ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).

tff(f1719,plain,
    ( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(bit1(pls))))) )
    | ~ spl1_6
    | ~ spl1_39
    | ~ spl1_42
    | ~ spl1_85
    | ~ spl1_129
    | ~ spl1_139 ),
    inference(forward_demodulation,[],[f1718,f811]) ).

tff(f811,plain,
    ( ! [X0: int] : ( plus_plus(int,pls,X0) = X0 )
    | ~ spl1_42 ),
    inference(avatar_component_clause,[],[f810]) ).

tff(f1718,plain,
    ( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(plus_plus(int,pls,bit1(pls)))))) )
    | ~ spl1_6
    | ~ spl1_39
    | ~ spl1_85
    | ~ spl1_129
    | ~ spl1_139 ),
    inference(forward_demodulation,[],[f1717,f1050]) ).

tff(f1050,plain,
    ( ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) )
    | ~ spl1_85 ),
    inference(avatar_component_clause,[],[f1049]) ).

tff(f1717,plain,
    ( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),bit1(pls)))))) )
    | ~ spl1_6
    | ~ spl1_39
    | ~ spl1_129
    | ~ spl1_139 ),
    inference(forward_demodulation,[],[f1715,f1622]) ).

tff(f1622,plain,
    ( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)) )
    | ~ spl1_6
    | ~ spl1_39
    | ~ spl1_129 ),
    inference(forward_demodulation,[],[f1621,f798]) ).

tff(f798,plain,
    ( ! [X0: int] : ( number_number_of(int,X0) = X0 )
    | ~ spl1_39 ),
    inference(avatar_component_clause,[],[f797]) ).

tff(f1621,plain,
    ( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,number_number_of(int,X0),plus_plus(int,X1,X2)) )
    | ~ spl1_6
    | ~ spl1_39
    | ~ spl1_129 ),
    inference(forward_demodulation,[],[f1620,f798]) ).

tff(f1620,plain,
    ( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,number_number_of(int,X0),plus_plus(int,number_number_of(int,X1),X2)) )
    | ~ spl1_6
    | ~ spl1_39
    | ~ spl1_129 ),
    inference(forward_demodulation,[],[f1619,f798]) ).

tff(f1619,plain,
    ( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X0),plus_plus(int,number_number_of(int,X1),X2)) = plus_plus(int,number_number_of(int,plus_plus(int,X0,X1)),X2) )
    | ~ spl1_6
    | ~ spl1_129 ),
    inference(resolution,[],[f1613,f635]) ).

tff(f635,plain,
    ( number_ring(int)
    | ~ spl1_6 ),
    inference(avatar_component_clause,[],[f633]) ).

tff(f1613,plain,
    ( ! [X0: $tType,X2: int,X3: int,X1: X0] :
        ( ~ number_ring(X0)
        | ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) )
    | ~ spl1_129 ),
    inference(avatar_component_clause,[],[f1612]) ).

tff(f1715,plain,
    ( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))))) )
    | ~ spl1_139 ),
    inference(avatar_component_clause,[],[f1714]) ).

tff(f1716,plain,
    spl1_139,
    inference(avatar_split_clause,[],[f517,f1714]) ).

tff(f517,plain,
    ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))))) ),
    inference(definition_unfolding,[],[f376,f375,f375,f375,f375]) ).

tff(f375,plain,
    ! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
    inference(cnf_transformation,[],[f140]) ).

tff(f140,plain,
    ! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
    inference(rectify,[],[f75]) ).

tff(f75,axiom,
    ! [X8: int] : ( bit0(X8) = plus_plus(int,X8,X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Bit0__def) ).

tff(f376,plain,
    ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X0,number_number_of(nat,bit0(bit0(bit1(pls))))) ),
    inference(cnf_transformation,[],[f141]) ).

tff(f141,plain,
    ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X0,number_number_of(nat,bit0(bit0(bit1(pls))))) ),
    inference(rectify,[],[f49]) ).

tff(f49,axiom,
    ! [X16: int] : ( power_power(int,power_power(int,X16,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X16,number_number_of(nat,bit0(bit0(bit1(pls))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_quartic__square__square) ).

tff(f1696,plain,
    spl1_138,
    inference(avatar_split_clause,[],[f528,f1694]) ).

tff(f1694,plain,
    ( spl1_138
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
        | ( zero_zero(X0) = X2 )
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).

tff(f528,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
      | ( zero_zero(X0) = X2 )
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f398,f375,f375]) ).

tff(f398,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
      | ( zero_zero(X0) = X2 )
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f276,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
            | ( ( zero_zero(X0) = X1 )
              & ( zero_zero(X0) = X2 ) ) )
          & ( ( zero_zero(X0) != X1 )
            | ( zero_zero(X0) != X2 )
            | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))) ) )
      | ~ linordered_idom(X0) ),
    inference(flattening,[],[f275]) ).

tff(f275,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
            | ( ( zero_zero(X0) = X1 )
              & ( zero_zero(X0) = X2 ) ) )
          & ( ( zero_zero(X0) != X1 )
            | ( zero_zero(X0) != X2 )
            | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))) ) )
      | ~ linordered_idom(X0) ),
    inference(nnf_transformation,[],[f224]) ).

tff(f224,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
        <=> ( ( zero_zero(X0) != X1 )
            | ( zero_zero(X0) != X2 ) ) )
      | ~ linordered_idom(X0) ),
    inference(ennf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0,X2: X0] :
          ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
        <=> ( ( zero_zero(X0) != X1 )
            | ( zero_zero(X0) != X2 ) ) ) ),
    inference(rectify,[],[f87]) ).

tff(f87,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X3: X0,X4: X0] :
          ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X3,number_number_of(nat,bit0(bit1(pls))))))
        <=> ( ( zero_zero(X0) != X3 )
            | ( zero_zero(X0) != X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_sum__power2__gt__zero__iff) ).

tff(f1692,plain,
    spl1_137,
    inference(avatar_split_clause,[],[f527,f1690]) ).

tff(f1690,plain,
    ( spl1_137
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
        | ( zero_zero(X0) = X1 )
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).

tff(f527,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
      | ( zero_zero(X0) = X1 )
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f399,f375,f375]) ).

tff(f399,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
      | ( zero_zero(X0) = X1 )
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f1680,plain,
    spl1_136,
    inference(avatar_split_clause,[],[f526,f1678]) ).

tff(f526,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) = X2 )
      | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f394,f375,f375]) ).

tff(f394,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) = X2 )
      | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f274,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
            | ( zero_zero(X0) != X1 )
            | ( zero_zero(X0) != X2 ) )
          & ( ( ( zero_zero(X0) = X1 )
              & ( zero_zero(X0) = X2 ) )
            | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ) )
      | ~ linordered_idom(X0) ),
    inference(flattening,[],[f273]) ).

tff(f273,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
            | ( zero_zero(X0) != X1 )
            | ( zero_zero(X0) != X2 ) )
          & ( ( ( zero_zero(X0) = X1 )
              & ( zero_zero(X0) = X2 ) )
            | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ) )
      | ~ linordered_idom(X0) ),
    inference(nnf_transformation,[],[f223]) ).

tff(f223,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
        <=> ( ( zero_zero(X0) = X1 )
            & ( zero_zero(X0) = X2 ) ) )
      | ~ linordered_idom(X0) ),
    inference(ennf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0,X2: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
        <=> ( ( zero_zero(X0) = X1 )
            & ( zero_zero(X0) = X2 ) ) ) ),
    inference(rectify,[],[f84]) ).

tff(f84,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X3: X0,X4: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X3,number_number_of(nat,bit0(bit1(pls))))) )
        <=> ( ( zero_zero(X0) = X3 )
            & ( zero_zero(X0) = X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_sum__power2__eq__zero__iff) ).

tff(f1676,plain,
    spl1_135,
    inference(avatar_split_clause,[],[f525,f1674]) ).

tff(f525,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) = X1 )
      | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f395,f375,f375]) ).

tff(f395,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) = X1 )
      | ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f1663,plain,
    spl1_134,
    inference(avatar_split_clause,[],[f564,f1661]) ).

tff(f1661,plain,
    ( spl1_134
  <=> ! [X0: $tType] :
        ( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).

tff(f564,plain,
    ! [X0: $tType] :
      ( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
      | ~ linordered_idom(X0) ),
    inference(equality_resolution,[],[f563]) ).

tff(f563,plain,
    ! [X0: $tType,X2: X0] :
      ( ( zero_zero(X0) != X2 )
      | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
      | ~ linordered_idom(X0) ),
    inference(equality_resolution,[],[f529]) ).

tff(f529,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) != X1 )
      | ( zero_zero(X0) != X2 )
      | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f397,f375,f375]) ).

tff(f397,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) != X1 )
      | ( zero_zero(X0) != X2 )
      | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f1656,plain,
    spl1_133,
    inference(avatar_split_clause,[],[f562,f1654]) ).

tff(f1654,plain,
    ( spl1_133
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).

tff(f562,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
      | ~ linordered_idom(X0) ),
    inference(equality_resolution,[],[f561]) ).

tff(f561,plain,
    ! [X0: $tType,X2: X0] :
      ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
      | ( zero_zero(X0) != X2 )
      | ~ linordered_idom(X0) ),
    inference(equality_resolution,[],[f524]) ).

tff(f524,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
      | ( zero_zero(X0) != X1 )
      | ( zero_zero(X0) != X2 )
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f396,f375,f375]) ).

tff(f396,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
      | ( zero_zero(X0) != X1 )
      | ( zero_zero(X0) != X2 )
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f1644,plain,
    spl1_132,
    inference(avatar_split_clause,[],[f523,f1642]) ).

tff(f1642,plain,
    ( spl1_132
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).

tff(f523,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f393,f375,f375]) ).

tff(f393,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f222]) ).

tff(f222,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(ennf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0,X2: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X22: X0,X16: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X16,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X22,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_not__sum__power2__lt__zero) ).

tff(f1628,plain,
    spl1_131,
    inference(avatar_split_clause,[],[f590,f1625]) ).

tff(f590,plain,
    pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
    inference(forward_demodulation,[],[f516,f356]) ).

tff(f356,plain,
    zero_zero(int) = pls,
    inference(cnf_transformation,[],[f38]) ).

tff(f38,axiom,
    zero_zero(int) = pls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Pls__def) ).

tff(f516,plain,
    zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
    inference(definition_unfolding,[],[f364,f375,f375]) ).

tff(f364,plain,
    zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f51]) ).

tff(f51,axiom,
    zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_calculation) ).

tff(f1618,plain,
    spl1_130,
    inference(avatar_split_clause,[],[f507,f1616]) ).

tff(f1616,plain,
    ( spl1_130
  <=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_130])]) ).

tff(f507,plain,
    ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ord_less(nat,X1,X2)
      | ( X1 = X2 )
      | sP0(X2,X1,X0) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f265,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X1,X2) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ( X1 = X2 ) )
      | sP0(X2,X1,X0) ),
    inference(definition_folding,[],[f263,f264]) ).

tff(f264,plain,
    ! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) )
      | ~ sP0(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f263,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X1,X2) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ( X1 = X2 ) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) ) ),
    inference(flattening,[],[f262]) ).

tff(f262,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X1,X2) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ( X1 = X2 ) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) ) ),
    inference(ennf_transformation,[],[f209]) ).

tff(f209,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( ( ord_less(nat,X2,X1)
       => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
     => ( ( ( X1 = X2 )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
       => ( ( ord_less(nat,X1,X2)
           => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) ) ) ),
    inference(rectify,[],[f72]) ).

tff(f72,axiom,
    ! [X26: fun(nat,fun(nat,bool)),X12: nat,X21: nat] :
      ( ( ord_less(nat,X21,X12)
       => pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) )
     => ( ( ( X12 = X21 )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) )
       => ( ( ord_less(nat,X12,X21)
           => pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_nat__less__cases) ).

tff(f1614,plain,
    spl1_129,
    inference(avatar_split_clause,[],[f407,f1612]) ).

tff(f407,plain,
    ! [X0: $tType,X2: int,X3: int,X1: X0] :
      ( ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f232]) ).

tff(f232,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f159]) ).

tff(f159,plain,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X20: X0,X18: int,X19: int] : ( plus_plus(X0,number_number_of(X0,X19),plus_plus(X0,number_number_of(X0,X18),X20)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X19,X18)),X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__number__of__left) ).

tff(f1524,plain,
    spl1_128,
    inference(avatar_split_clause,[],[f546,f1522]) ).

tff(f1522,plain,
    ( spl1_128
  <=> ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_128])]) ).

tff(f546,plain,
    ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ),
    inference(definition_unfolding,[],[f458,f375,f375,f375]) ).

tff(f458,plain,
    ! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
    inference(cnf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X9: int,X8: int] : ( plus_plus(int,bit0(X8),bit0(X9)) = bit0(plus_plus(int,X8,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__Bit0__Bit0) ).

tff(f1520,plain,
    spl1_127,
    inference(avatar_split_clause,[],[f530,f1518]) ).

tff(f1518,plain,
    ( spl1_127
  <=> ! [X0: $tType,X1: int] :
        ( ( plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_127])]) ).

tff(f530,plain,
    ! [X0: $tType,X1: int] :
      ( ( plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
      | ~ number_ring(X0) ),
    inference(definition_unfolding,[],[f404,f375]) ).

tff(f404,plain,
    ! [X0: $tType,X1: int] :
      ( ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f229]) ).

tff(f229,plain,
    ! [X0: $tType] :
      ( ! [X1: int] : ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f156]) ).

tff(f156,plain,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X1: int] : ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) ) ),
    inference(rectify,[],[f79]) ).

tff(f79,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X18: int] : ( number_number_of(X0,bit0(X18)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X18)),number_number_of(X0,X18)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_number__of__Bit0) ).

tff(f1516,plain,
    spl1_126,
    inference(avatar_split_clause,[],[f521,f1514]) ).

tff(f1514,plain,
    ( spl1_126
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
        | ( zero_zero(X0) = X1 )
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).

tff(f521,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
      | ( zero_zero(X0) = X1 )
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f392,f375]) ).

tff(f392,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
      | ( zero_zero(X0) = X1 )
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f272]) ).

tff(f272,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
            | ( zero_zero(X0) = X1 ) )
          & ( ( zero_zero(X0) != X1 )
            | ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) )
      | ~ linordered_idom(X0) ),
    inference(nnf_transformation,[],[f221]) ).

tff(f221,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
        <=> ( zero_zero(X0) != X1 ) )
      | ~ linordered_idom(X0) ),
    inference(ennf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0] :
          ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
        <=> ( zero_zero(X0) != X1 ) ) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X2: X0] :
          ( ord_less(X0,zero_zero(X0),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
        <=> ( zero_zero(X0) != X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_zero__less__power2) ).

tff(f1512,plain,
    ( ~ spl1_123
    | ~ spl1_124
    | spl1_125
    | ~ spl1_82
    | ~ spl1_101 ),
    inference(avatar_split_clause,[],[f1304,f1252,f1037,f1510,f1506,f1502]) ).

tff(f1502,plain,
    ( spl1_123
  <=> number_ring(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_123])]) ).

tff(f1506,plain,
    ( spl1_124
  <=> ring_char_0(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).

tff(f1510,plain,
    ( spl1_125
  <=> ! [X0: int] :
        ( ( zero_zero(nat) != number_number_of(nat,X0) )
        | ( power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).

tff(f1037,plain,
    ( spl1_82
  <=> ! [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,[spl1_82])]) ).

tff(f1252,plain,
    ( spl1_101
  <=> ( zero_zero(nat) = number_number_of(nat,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).

tff(f1304,plain,
    ( ! [X0: int] :
        ( ( zero_zero(nat) != number_number_of(nat,X0) )
        | ( power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = X0 )
        | ~ ring_char_0(nat)
        | ~ number_ring(nat) )
    | ~ spl1_82
    | ~ spl1_101 ),
    inference(superposition,[],[f1038,f1254]) ).

tff(f1254,plain,
    ( ( zero_zero(nat) = number_number_of(nat,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
    | ~ spl1_101 ),
    inference(avatar_component_clause,[],[f1252]) ).

tff(f1038,plain,
    ( ! [X0: $tType,X2: int,X1: int] :
        ( ( number_number_of(X0,X1) != number_number_of(X0,X2) )
        | ( X1 = X2 )
        | ~ ring_char_0(X0)
        | ~ number_ring(X0) )
    | ~ spl1_82 ),
    inference(avatar_component_clause,[],[f1037]) ).

tff(f1497,plain,
    spl1_122,
    inference(avatar_split_clause,[],[f570,f1495]) ).

tff(f1495,plain,
    ( spl1_122
  <=> ! [X0: $tType,X1: nat] :
        ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),X1) )
        | ( zero_zero(nat) = X1 )
        | ~ zero_neq_one(X0)
        | ~ no_zero_divisors(X0)
        | ~ mult_zero(X0)
        | ~ power(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_122])]) ).

tff(f570,plain,
    ! [X0: $tType,X1: nat] :
      ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),X1) )
      | ( zero_zero(nat) = X1 )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(equality_resolution,[],[f432]) ).

tff(f432,plain,
    ! [X0: $tType,X2: X0,X1: nat] :
      ( ( zero_zero(X0) = power_power(X0,X2,X1) )
      | ( zero_zero(nat) = X1 )
      | ( zero_zero(X0) != X2 )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f287,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: X0] :
          ( ( ( zero_zero(X0) = power_power(X0,X2,X1) )
            | ( zero_zero(nat) = X1 )
            | ( zero_zero(X0) != X2 ) )
          & ( ( ( zero_zero(nat) != X1 )
              & ( zero_zero(X0) = X2 ) )
            | ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(flattening,[],[f286]) ).

tff(f286,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: X0] :
          ( ( ( zero_zero(X0) = power_power(X0,X2,X1) )
            | ( zero_zero(nat) = X1 )
            | ( zero_zero(X0) != X2 ) )
          & ( ( ( zero_zero(nat) != X1 )
              & ( zero_zero(X0) = X2 ) )
            | ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(nnf_transformation,[],[f251]) ).

tff(f251,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: X0] :
          ( ( zero_zero(X0) = power_power(X0,X2,X1) )
        <=> ( ( zero_zero(nat) != X1 )
            & ( zero_zero(X0) = X2 ) ) )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(flattening,[],[f250]) ).

tff(f250,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: X0] :
          ( ( zero_zero(X0) = power_power(X0,X2,X1) )
        <=> ( ( zero_zero(nat) != X1 )
            & ( zero_zero(X0) = X2 ) ) )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(ennf_transformation,[],[f171]) ).

tff(f171,plain,
    ! [X0: $tType] :
      ( ( zero_neq_one(X0)
        & no_zero_divisors(X0)
        & mult_zero(X0)
        & power(X0) )
     => ! [X1: nat,X2: X0] :
          ( ( zero_zero(X0) = power_power(X0,X2,X1) )
        <=> ( ( zero_zero(nat) != X1 )
            & ( zero_zero(X0) = X2 ) ) ) ),
    inference(rectify,[],[f48]) ).

tff(f48,axiom,
    ! [X0: $tType] :
      ( ( zero_neq_one(X0)
        & no_zero_divisors(X0)
        & mult_zero(X0)
        & power(X0) )
     => ! [X12: nat,X2: X0] :
          ( ( zero_zero(X0) = power_power(X0,X2,X12) )
        <=> ( ( zero_zero(nat) != X12 )
            & ( zero_zero(X0) = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_power__eq__0__iff) ).

tff(f1491,plain,
    spl1_121,
    inference(avatar_split_clause,[],[f504,f1489]) ).

tff(f1489,plain,
    ( spl1_121
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
        | ~ ord_less(nat,zero_zero(nat),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_121])]) ).

tff(f504,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
      | ~ ord_less(nat,zero_zero(nat),X2) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f261,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less(nat,X1,X0)
      | ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
      | ~ ord_less(nat,zero_zero(nat),X2) ),
    inference(flattening,[],[f260]) ).

tff(f260,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less(nat,X1,X0)
      | ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
      | ~ ord_less(nat,zero_zero(nat),X2) ),
    inference(ennf_transformation,[],[f208]) ).

tff(f208,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less(nat,zero_zero(nat),X2)
     => ( ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
       => ord_less(nat,X1,X0) ) ),
    inference(rectify,[],[f82]) ).

tff(f82,axiom,
    ! [X17: nat,X23: nat,X27: nat] :
      ( ord_less(nat,zero_zero(nat),X27)
     => ( ord_less(nat,power_power(nat,X27,X23),power_power(nat,X27,X17))
       => ord_less(nat,X23,X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_nat__power__less__imp__less) ).

tff(f1487,plain,
    spl1_120,
    inference(avatar_split_clause,[],[f430,f1485]) ).

tff(f1485,plain,
    ( spl1_120
  <=> ! [X0: $tType,X2: X0,X1: nat] :
        ( ( zero_zero(X0) = X2 )
        | ( zero_zero(X0) != power_power(X0,X2,X1) )
        | ~ zero_neq_one(X0)
        | ~ no_zero_divisors(X0)
        | ~ mult_zero(X0)
        | ~ power(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_120])]) ).

tff(f430,plain,
    ! [X0: $tType,X2: X0,X1: nat] :
      ( ( zero_zero(X0) = X2 )
      | ( zero_zero(X0) != power_power(X0,X2,X1) )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f1467,plain,
    spl1_119,
    inference(avatar_split_clause,[],[f560,f1465]) ).

tff(f1465,plain,
    ( spl1_119
  <=> ! [X0: $tType] :
        ( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_119])]) ).

tff(f560,plain,
    ! [X0: $tType] :
      ( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
      | ~ linordered_idom(X0) ),
    inference(equality_resolution,[],[f522]) ).

tff(f522,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) != X1 )
      | ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f391,f375]) ).

tff(f391,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) != X1 )
      | ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f272]) ).

tff(f1463,plain,
    spl1_118,
    inference(avatar_split_clause,[],[f494,f1461]) ).

tff(f1461,plain,
    ( spl1_118
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ord_less(nat,zero_zero(nat),X1)
        | ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_118])]) ).

tff(f494,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ord_less(nat,zero_zero(nat),X1)
      | ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ),
    inference(cnf_transformation,[],[f317]) ).

tff(f317,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
        | ( ~ ord_less(nat,zero_zero(nat),X0)
          & ~ ord_less(nat,zero_zero(nat),X1) ) )
      & ( ord_less(nat,zero_zero(nat),X0)
        | ord_less(nat,zero_zero(nat),X1)
        | ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ) ),
    inference(flattening,[],[f316]) ).

tff(f316,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
        | ( ~ ord_less(nat,zero_zero(nat),X0)
          & ~ ord_less(nat,zero_zero(nat),X1) ) )
      & ( ord_less(nat,zero_zero(nat),X0)
        | ord_less(nat,zero_zero(nat),X1)
        | ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ) ),
    inference(nnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
    <=> ( ord_less(nat,zero_zero(nat),X0)
        | ord_less(nat,zero_zero(nat),X1) ) ),
    inference(rectify,[],[f97]) ).

tff(f97,axiom,
    ! [X12: nat,X21: nat] :
      ( ord_less(nat,zero_zero(nat),plus_plus(nat,X21,X12))
    <=> ( ord_less(nat,zero_zero(nat),X12)
        | ord_less(nat,zero_zero(nat),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__gr__0) ).

tff(f1439,plain,
    spl1_117,
    inference(avatar_split_clause,[],[f557,f1437]) ).

tff(f1437,plain,
    ( spl1_117
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
        | ~ ring_11004092258visors(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_117])]) ).

tff(f557,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
      | ~ ring_11004092258visors(X0) ),
    inference(equality_resolution,[],[f518]) ).

tff(f518,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
      | ( zero_zero(X0) != X1 )
      | ~ ring_11004092258visors(X0) ),
    inference(definition_unfolding,[],[f378,f375]) ).

tff(f378,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
      | ( zero_zero(X0) != X1 )
      | ~ ring_11004092258visors(X0) ),
    inference(cnf_transformation,[],[f266]) ).

tff(f266,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
            | ( zero_zero(X0) != X1 ) )
          & ( ( zero_zero(X0) = X1 )
            | ( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) ) )
      | ~ ring_11004092258visors(X0) ),
    inference(nnf_transformation,[],[f213]) ).

tff(f213,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
        <=> ( zero_zero(X0) = X1 ) )
      | ~ ring_11004092258visors(X0) ),
    inference(ennf_transformation,[],[f142]) ).

tff(f142,plain,
    ! [X0: $tType] :
      ( ring_11004092258visors(X0)
     => ! [X1: X0] :
          ( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
        <=> ( zero_zero(X0) = X1 ) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X0: $tType] :
      ( ring_11004092258visors(X0)
     => ! [X2: X0] :
          ( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))) )
        <=> ( zero_zero(X0) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_zero__eq__power2) ).

tff(f1435,plain,
    spl1_116,
    inference(avatar_split_clause,[],[f531,f1433]) ).

tff(f1433,plain,
    ( spl1_116
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
        | ~ semiring_1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).

tff(f531,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
      | ~ semiring_1(X0) ),
    inference(definition_unfolding,[],[f409,f375]) ).

tff(f409,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) )
      | ~ semiring_1(X0) ),
    inference(cnf_transformation,[],[f234]) ).

tff(f234,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) )
      | ~ semiring_1(X0) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,axiom,
    ! [X0: $tType] :
      ( semiring_1(X0)
     => ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_zero__power2) ).

tff(f1431,plain,
    spl1_115,
    inference(avatar_split_clause,[],[f520,f1429]) ).

tff(f1429,plain,
    ( spl1_115
  <=> ! [X0: $tType,X1: X0] :
        ( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),zero_zero(X0))
        | ~ linordered_idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_115])]) ).

tff(f520,plain,
    ! [X0: $tType,X1: X0] :
      ( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(definition_unfolding,[],[f388,f375]) ).

tff(f388,plain,
    ! [X0: $tType,X1: X0] :
      ( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(cnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
      | ~ linordered_idom(X0) ),
    inference(ennf_transformation,[],[f148]) ).

tff(f148,plain,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X1: X0] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X15: X0] : ~ ord_less(X0,power_power(X0,X15,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_power2__less__0) ).

tff(f1427,plain,
    spl1_114,
    inference(avatar_split_clause,[],[f488,f1425]) ).

tff(f1425,plain,
    ( spl1_114
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),X1)
        | ( zero_zero(nat) = X0 )
        | ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_114])]) ).

tff(f488,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),X1)
      | ( zero_zero(nat) = X0 )
      | ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ),
    inference(cnf_transformation,[],[f313]) ).

tff(f313,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
        | ( ~ ord_less(nat,zero_zero(nat),X1)
          & ( zero_zero(nat) != X0 ) ) )
      & ( ord_less(nat,zero_zero(nat),X1)
        | ( zero_zero(nat) = X0 )
        | ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ) ),
    inference(flattening,[],[f312]) ).

tff(f312,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
        | ( ~ ord_less(nat,zero_zero(nat),X1)
          & ( zero_zero(nat) != X0 ) ) )
      & ( ord_less(nat,zero_zero(nat),X1)
        | ( zero_zero(nat) = X0 )
        | ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ) ),
    inference(nnf_transformation,[],[f203]) ).

tff(f203,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
    <=> ( ord_less(nat,zero_zero(nat),X1)
        | ( zero_zero(nat) = X0 ) ) ),
    inference(rectify,[],[f33]) ).

tff(f33,axiom,
    ! [X12: nat,X4: nat] :
      ( ord_less(nat,zero_zero(nat),power_power(nat,X4,X12))
    <=> ( ord_less(nat,zero_zero(nat),X4)
        | ( zero_zero(nat) = X12 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zero__less__power__nat__eq) ).

tff(f1423,plain,
    spl1_113,
    inference(avatar_split_clause,[],[f405,f1421]) ).

tff(f1421,plain,
    ( spl1_113
  <=> ! [X0: $tType,X2: int,X1: int] :
        ( ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).

tff(f405,plain,
    ! [X0: $tType,X2: int,X1: int] :
      ( ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f230]) ).

tff(f230,plain,
    ! [X0: $tType] :
      ( ! [X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) ) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X18: int,X19: int] : ( plus_plus(X0,number_number_of(X0,X19),number_number_of(X0,X18)) = number_number_of(X0,plus_plus(int,X19,X18)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_add__number__of__eq) ).

tff(f1419,plain,
    ( spl1_112
    | ~ spl1_69
    | ~ spl1_101 ),
    inference(avatar_split_clause,[],[f1297,f1252,f962,f1417]) ).

tff(f1417,plain,
    ( spl1_112
  <=> ! [X0: int] :
        ( ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
        | ord_less(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).

tff(f962,plain,
    ( spl1_69
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).

tff(f1297,plain,
    ( ! [X0: int] :
        ( ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
        | ord_less(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),X0) )
    | ~ spl1_69
    | ~ spl1_101 ),
    inference(superposition,[],[f963,f1254]) ).

tff(f963,plain,
    ( ! [X0: int,X1: int] :
        ( ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
        | ord_less(int,X1,X0) )
    | ~ spl1_69 ),
    inference(avatar_component_clause,[],[f962]) ).

tff(f1295,plain,
    spl1_111,
    inference(avatar_split_clause,[],[f571,f1293]) ).

tff(f1293,plain,
    ( spl1_111
  <=> ! [X0: $tType,X2: X0] :
        ( ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
        | ~ zero_neq_one(X0)
        | ~ no_zero_divisors(X0)
        | ~ mult_zero(X0)
        | ~ power(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).

tff(f571,plain,
    ! [X0: $tType,X2: X0] :
      ( ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(equality_resolution,[],[f431]) ).

tff(f431,plain,
    ! [X0: $tType,X2: X0,X1: nat] :
      ( ( zero_zero(nat) != X1 )
      | ( zero_zero(X0) != power_power(X0,X2,X1) )
      | ~ zero_neq_one(X0)
      | ~ no_zero_divisors(X0)
      | ~ mult_zero(X0)
      | ~ power(X0) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f1291,plain,
    spl1_110,
    inference(avatar_split_clause,[],[f506,f1289]) ).

tff(f1289,plain,
    ( spl1_110
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_110])]) ).

tff(f506,plain,
    ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
      ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f323]) ).

tff(f323,plain,
    ! [X0: nat,X1: nat,X2: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        & ord_less(nat,X0,X1) )
      | ~ sP0(X0,X1,X2) ),
    inference(rectify,[],[f322]) ).

tff(f322,plain,
    ! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) )
      | ~ sP0(X2,X1,X0) ),
    inference(nnf_transformation,[],[f264]) ).

tff(f1287,plain,
    spl1_109,
    inference(avatar_split_clause,[],[f500,f1285]) ).

tff(f1285,plain,
    ( spl1_109
  <=> ! [X0: int,X1: int] :
        ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
        | ~ ord_less(int,X1,X0)
        | ~ ord_less(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_109])]) ).

tff(f500,plain,
    ! [X0: int,X1: int] :
      ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
      | ~ ord_less(int,X1,X0)
      | ~ ord_less(int,pls,X0) ),
    inference(cnf_transformation,[],[f319]) ).

tff(f319,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
        | ~ ord_less(int,X1,X0)
        | ( ~ ord_less(int,pls,X0)
          & ord_less(int,X1,X0) ) )
      & ( ( ord_less(int,X1,X0)
          & ( ord_less(int,pls,X0)
            | ~ ord_less(int,X1,X0) ) )
        | ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
    inference(flattening,[],[f318]) ).

tff(f318,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
        | ~ ord_less(int,X1,X0)
        | ( ~ ord_less(int,pls,X0)
          & ord_less(int,X1,X0) ) )
      & ( ( ord_less(int,X1,X0)
          & ( ord_less(int,pls,X0)
            | ~ ord_less(int,X1,X0) ) )
        | ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
    inference(nnf_transformation,[],[f259]) ).

tff(f259,plain,
    ! [X0: int,X1: int] :
      ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
    <=> ( ord_less(int,X1,X0)
        & ( ord_less(int,pls,X0)
          | ~ ord_less(int,X1,X0) ) ) ),
    inference(ennf_transformation,[],[f206]) ).

tff(f206,plain,
    ! [X0: int,X1: int] :
      ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
    <=> ( ord_less(int,X1,X0)
        & ( ord_less(int,X1,X0)
         => ord_less(int,pls,X0) ) ) ),
    inference(rectify,[],[f31]) ).

tff(f31,axiom,
    ! [X10: int,X11: int] :
      ( ord_less(nat,number_number_of(nat,X11),number_number_of(nat,X10))
    <=> ( ord_less(int,X11,X10)
        & ( ord_less(int,X11,X10)
         => ord_less(int,pls,X10) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_less__nat__number__of) ).

tff(f1283,plain,
    spl1_108,
    inference(avatar_split_clause,[],[f497,f1281]) ).

tff(f1281,plain,
    ( spl1_108
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,pls,X0)
        | ~ ord_less(int,X1,X0)
        | ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).

tff(f497,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,pls,X0)
      | ~ ord_less(int,X1,X0)
      | ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ),
    inference(cnf_transformation,[],[f319]) ).

tff(f1279,plain,
    spl1_107,
    inference(avatar_split_clause,[],[f429,f1277]) ).

tff(f1277,plain,
    ( spl1_107
  <=> ! [X0: $tType,X2: int,X1: int] :
        ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
        | ~ ord_less(int,X2,X1)
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).

tff(f429,plain,
    ! [X0: $tType,X2: int,X1: int] :
      ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
      | ~ ord_less(int,X2,X1)
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: $tType] :
      ( ! [X1: int,X2: int] :
          ( ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
            | ~ ord_less(int,X2,X1) )
          & ( ord_less(int,X2,X1)
            | ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(nnf_transformation,[],[f249]) ).

tff(f249,plain,
    ! [X0: $tType] :
      ( ! [X1: int,X2: int] :
          ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
        <=> ord_less(int,X2,X1) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(flattening,[],[f248]) ).

tff(f248,plain,
    ! [X0: $tType] :
      ( ! [X1: int,X2: int] :
          ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
        <=> ord_less(int,X2,X1) )
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f170]) ).

tff(f170,plain,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X1: int,X2: int] :
          ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
        <=> ord_less(int,X2,X1) ) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X0: $tType] :
      ( ( linordered_idom(X0)
        & number_ring(X0) )
     => ! [X3: int,X4: int] :
          ( ord_less(X0,number_number_of(X0,X4),number_number_of(X0,X3))
        <=> ord_less(int,X4,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_less__number__of) ).

tff(f1275,plain,
    spl1_106,
    inference(avatar_split_clause,[],[f428,f1273]) ).

tff(f1273,plain,
    ( spl1_106
  <=> ! [X0: $tType,X2: int,X1: int] :
        ( ord_less(int,X2,X1)
        | ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
        | ~ linordered_idom(X0)
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).

tff(f428,plain,
    ! [X0: $tType,X2: int,X1: int] :
      ( ord_less(int,X2,X1)
      | ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
      | ~ linordered_idom(X0)
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f1271,plain,
    spl1_105,
    inference(avatar_split_clause,[],[f420,f1269]) ).

tff(f1269,plain,
    ( spl1_105
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        | ~ ord_less(X0,X3,X1)
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_105])]) ).

tff(f420,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
      | ~ ord_less(X0,X3,X1)
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f281]) ).

tff(f281,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
            | ~ ord_less(X0,X3,X1) )
          & ( ord_less(X0,X3,X1)
            | ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) ) )
      | ~ ordere236663937imp_le(X0) ),
    inference(nnf_transformation,[],[f240]) ).

tff(f240,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        <=> ord_less(X0,X3,X1) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        <=> ord_less(X0,X3,X1) ) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X28: X0,X29: X0,X2: X0] :
          ( ord_less(X0,plus_plus(X0,X2,X29),plus_plus(X0,X28,X29))
        <=> ord_less(X0,X2,X28) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_add__less__cancel__right) ).

tff(f1267,plain,
    spl1_104,
    inference(avatar_split_clause,[],[f419,f1265]) ).

tff(f1265,plain,
    ( spl1_104
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less(X0,X3,X1)
        | ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_104])]) ).

tff(f419,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less(X0,X3,X1)
      | ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f281]) ).

tff(f1263,plain,
    spl1_103,
    inference(avatar_split_clause,[],[f418,f1261]) ).

tff(f1261,plain,
    ( spl1_103
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        | ~ ord_less(X0,X2,X1)
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_103])]) ).

tff(f418,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
      | ~ ord_less(X0,X2,X1)
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f280]) ).

tff(f280,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
            | ~ ord_less(X0,X2,X1) )
          & ( ord_less(X0,X2,X1)
            | ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1)) ) )
      | ~ ordere236663937imp_le(X0) ),
    inference(nnf_transformation,[],[f239]) ).

tff(f239,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        <=> ord_less(X0,X2,X1) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f164]) ).

tff(f164,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        <=> ord_less(X0,X2,X1) ) ),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X28: X0,X2: X0,X29: X0] :
          ( ord_less(X0,plus_plus(X0,X29,X2),plus_plus(X0,X29,X28))
        <=> ord_less(X0,X2,X28) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__less__cancel__left) ).

tff(f1259,plain,
    spl1_102,
    inference(avatar_split_clause,[],[f417,f1257]) ).

tff(f1257,plain,
    ( spl1_102
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less(X0,X2,X1)
        | ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_102])]) ).

tff(f417,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less(X0,X2,X1)
      | ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f280]) ).

tff(f1255,plain,
    ( spl1_101
    | spl1_29
    | ~ spl1_68 ),
    inference(avatar_split_clause,[],[f1180,f958,f749,f1252]) ).

tff(f749,plain,
    ( spl1_29
  <=> ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).

tff(f958,plain,
    ( spl1_68
  <=> ! [X0: int] :
        ( ord_less(int,pls,X0)
        | ( zero_zero(nat) = number_number_of(nat,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_68])]) ).

tff(f1180,plain,
    ( ( zero_zero(nat) = number_number_of(nat,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
    | spl1_29
    | ~ spl1_68 ),
    inference(resolution,[],[f959,f751]) ).

tff(f751,plain,
    ( ~ ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
    | spl1_29 ),
    inference(avatar_component_clause,[],[f749]) ).

tff(f959,plain,
    ( ! [X0: int] :
        ( ord_less(int,pls,X0)
        | ( zero_zero(nat) = number_number_of(nat,X0) ) )
    | ~ spl1_68 ),
    inference(avatar_component_clause,[],[f958]) ).

tff(f1170,plain,
    spl1_100,
    inference(avatar_split_clause,[],[f427,f1168]) ).

tff(f1168,plain,
    ( spl1_100
  <=> ! [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,[spl1_100])]) ).

tff(f427,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,[],[f284]) ).

tff(f284,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,[],[f247]) ).

tff(f247,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,[],[f246]) ).

tff(f246,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,[],[f169]) ).

tff(f169,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,[],[f6]) ).

tff(f6,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/sandbox/benchmark/theBenchmark.p',fact_5_less__special_I3_J) ).

tff(f1166,plain,
    spl1_99,
    inference(avatar_split_clause,[],[f426,f1164]) ).

tff(f1164,plain,
    ( spl1_99
  <=> ! [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,[spl1_99])]) ).

tff(f426,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,[],[f284]) ).

tff(f1162,plain,
    spl1_98,
    inference(avatar_split_clause,[],[f425,f1160]) ).

tff(f1160,plain,
    ( spl1_98
  <=> ! [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,[spl1_98])]) ).

tff(f425,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,[],[f283]) ).

tff(f283,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,[],[f245]) ).

tff(f245,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,[],[f244]) ).

tff(f244,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,[],[f168]) ).

tff(f168,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,[],[f5]) ).

tff(f5,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/sandbox/benchmark/theBenchmark.p',fact_4_less__special_I1_J) ).

tff(f1158,plain,
    spl1_97,
    inference(avatar_split_clause,[],[f424,f1156]) ).

tff(f1156,plain,
    ( spl1_97
  <=> ! [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,[spl1_97])]) ).

tff(f424,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,[],[f283]) ).

tff(f1154,plain,
    spl1_96,
    inference(avatar_split_clause,[],[f410,f1152]) ).

tff(f1152,plain,
    ( spl1_96
  <=> ! [X0: $tType,X2: X0,X1: nat] :
        ( ord_less(X0,zero_zero(X0),power_power(X0,X2,X1))
        | ~ ord_less(X0,zero_zero(X0),X2)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).

tff(f410,plain,
    ! [X0: $tType,X2: X0,X1: nat] :
      ( ord_less(X0,zero_zero(X0),power_power(X0,X2,X1))
      | ~ ord_less(X0,zero_zero(X0),X2)
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f235]) ).

tff(f235,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: X0] :
          ( ord_less(X0,zero_zero(X0),power_power(X0,X2,X1))
          | ~ ord_less(X0,zero_zero(X0),X2) )
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f160]) ).

tff(f160,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat,X2: X0] :
          ( ord_less(X0,zero_zero(X0),X2)
         => ord_less(X0,zero_zero(X0),power_power(X0,X2,X1)) ) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X17: nat,X15: X0] :
          ( ord_less(X0,zero_zero(X0),X15)
         => ord_less(X0,zero_zero(X0),power_power(X0,X15,X17)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zero__less__power) ).

tff(f1150,plain,
    spl1_95,
    inference(avatar_split_clause,[],[f390,f1148]) ).

tff(f1148,plain,
    ( spl1_95
  <=> ! [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,[spl1_95])]) ).

tff(f390,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,[],[f271]) ).

tff(f271,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,[],[f220]) ).

tff(f220,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,[],[f149]) ).

tff(f149,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,[],[f76]) ).

tff(f76,axiom,
    ! [X0: $tType] :
      ( linordered_idom(X0)
     => ! [X2: X0] :
          ( ord_less(X0,plus_plus(X0,X2,X2),zero_zero(X0))
        <=> ord_less(X0,X2,zero_zero(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_even__less__0__iff) ).

tff(f1146,plain,
    spl1_94,
    inference(avatar_split_clause,[],[f389,f1144]) ).

tff(f1144,plain,
    ( spl1_94
  <=> ! [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,[spl1_94])]) ).

tff(f389,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,[],[f271]) ).

tff(f1142,plain,
    spl1_93,
    inference(avatar_split_clause,[],[f387,f1140]) ).

tff(f1140,plain,
    ( spl1_93
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        | ~ ord_less(X0,X1,zero_zero(X0))
        | ~ linord219039673up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_93])]) ).

tff(f387,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
      | ~ ord_less(X0,X1,zero_zero(X0))
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f270,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)) ) )
      | ~ linord219039673up_add(X0) ),
    inference(nnf_transformation,[],[f218]) ).

tff(f218,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        <=> ord_less(X0,X1,zero_zero(X0)) )
      | ~ linord219039673up_add(X0) ),
    inference(ennf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X1: X0] :
          ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        <=> ord_less(X0,X1,zero_zero(X0)) ) ),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X2: X0] :
          ( ord_less(X0,plus_plus(X0,X2,X2),zero_zero(X0))
        <=> ord_less(X0,X2,zero_zero(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_double__add__less__zero__iff__single__add__less__zero) ).

tff(f1138,plain,
    spl1_92,
    inference(avatar_split_clause,[],[f386,f1136]) ).

tff(f1136,plain,
    ( spl1_92
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,X1,zero_zero(X0))
        | ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
        | ~ linord219039673up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_92])]) ).

tff(f386,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,X1,zero_zero(X0))
      | ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f1134,plain,
    spl1_91,
    inference(avatar_split_clause,[],[f385,f1132]) ).

tff(f1132,plain,
    ( spl1_91
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
        | ~ ord_less(X0,zero_zero(X0),X1)
        | ~ linord219039673up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_91])]) ).

tff(f385,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
      | ~ ord_less(X0,zero_zero(X0),X1)
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f269]) ).

tff(f269,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
            | ~ ord_less(X0,zero_zero(X0),X1) )
          & ( ord_less(X0,zero_zero(X0),X1)
            | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1)) ) )
      | ~ linord219039673up_add(X0) ),
    inference(nnf_transformation,[],[f217]) ).

tff(f217,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
        <=> ord_less(X0,zero_zero(X0),X1) )
      | ~ linord219039673up_add(X0) ),
    inference(ennf_transformation,[],[f146]) ).

tff(f146,plain,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X1: X0] :
          ( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
        <=> ord_less(X0,zero_zero(X0),X1) ) ),
    inference(rectify,[],[f88]) ).

tff(f88,axiom,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X2: X0] :
          ( ord_less(X0,zero_zero(X0),plus_plus(X0,X2,X2))
        <=> ord_less(X0,zero_zero(X0),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__less__double__add__iff__zero__less__single__add) ).

tff(f1130,plain,
    spl1_90,
    inference(avatar_split_clause,[],[f384,f1128]) ).

tff(f1128,plain,
    ( spl1_90
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,zero_zero(X0),X1)
        | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
        | ~ linord219039673up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_90])]) ).

tff(f384,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,zero_zero(X0),X1)
      | ~ ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f269]) ).

tff(f1077,plain,
    ( spl1_89
    | ~ spl1_64
    | ~ spl1_74 ),
    inference(avatar_split_clause,[],[f1027,f998,f917,f1074]) ).

tff(f1074,plain,
    ( spl1_89
  <=> ord_less(int,pls,bit1(pls)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).

tff(f917,plain,
    ( spl1_64
  <=> ! [X0: int] :
        ( ord_less(int,pls,X0)
        | ~ ord_less(int,pls,plus_plus(int,X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).

tff(f998,plain,
    ( spl1_74
  <=> ord_less(int,pls,plus_plus(int,bit1(pls),bit1(pls))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_74])]) ).

tff(f1027,plain,
    ( ord_less(int,pls,bit1(pls))
    | ~ spl1_64
    | ~ spl1_74 ),
    inference(resolution,[],[f1000,f918]) ).

tff(f918,plain,
    ( ! [X0: int] :
        ( ~ ord_less(int,pls,plus_plus(int,X0,X0))
        | ord_less(int,pls,X0) )
    | ~ spl1_64 ),
    inference(avatar_component_clause,[],[f917]) ).

tff(f1000,plain,
    ( ord_less(int,pls,plus_plus(int,bit1(pls),bit1(pls)))
    | ~ spl1_74 ),
    inference(avatar_component_clause,[],[f998]) ).

tff(f1063,plain,
    spl1_88,
    inference(avatar_split_clause,[],[f554,f1061]) ).

tff(f1061,plain,
    ( spl1_88
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).

tff(f554,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ),
    inference(definition_unfolding,[],[f479,f375,f375]) ).

tff(f479,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,bit0(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f307]) ).

tff(f307,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,[],[f199]) ).

tff(f199,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit0(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X13: int,X14: int] :
      ( ord_less(int,bit0(X14),bit0(X13))
    <=> ord_less(int,X14,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_less__int__code_I13_J) ).

tff(f1059,plain,
    spl1_87,
    inference(avatar_split_clause,[],[f553,f1057]) ).

tff(f1057,plain,
    ( spl1_87
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).

tff(f553,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
      | ~ ord_less(int,X1,X0) ),
    inference(definition_unfolding,[],[f480,f375,f375]) ).

tff(f480,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit0(X1),bit0(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f307]) ).

tff(f1055,plain,
    spl1_86,
    inference(avatar_split_clause,[],[f545,f1053]) ).

tff(f1053,plain,
    ( spl1_86
  <=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).

tff(f545,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) ),
    inference(definition_unfolding,[],[f457,f375]) ).

tff(f457,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f185]) ).

tff(f185,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
    inference(rectify,[],[f61]) ).

tff(f61,axiom,
    ! [X9: int,X8: int] : ( plus_plus(int,bit0(X8),bit1(X9)) = bit1(plus_plus(int,X8,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__Bit0__Bit1) ).

tff(f1051,plain,
    spl1_85,
    inference(avatar_split_clause,[],[f544,f1049]) ).

tff(f544,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) ),
    inference(definition_unfolding,[],[f456,f375]) ).

tff(f456,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
    inference(rectify,[],[f62]) ).

tff(f62,axiom,
    ! [X9: int,X8: int] : ( bit1(plus_plus(int,X8,X9)) = plus_plus(int,bit1(X8),bit0(X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_add__Bit1__Bit0) ).

tff(f1047,plain,
    spl1_84,
    inference(avatar_split_clause,[],[f512,f1045]) ).

tff(f1045,plain,
    ( spl1_84
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
        | ~ ord_less(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_84])]) ).

tff(f512,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
      | ~ ord_less(nat,X1,X0) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f324,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
        | ~ ord_less(nat,X1,X0) )
      & ( ord_less(nat,X1,X0)
        | ~ ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ) ),
    inference(nnf_transformation,[],[f210]) ).

tff(f210,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
    <=> ord_less(nat,X1,X0) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X12: nat,X21: nat,X5: nat] :
      ( ord_less(nat,plus_plus(nat,X5,X21),plus_plus(nat,X5,X12))
    <=> ord_less(nat,X21,X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat__add__left__cancel__less) ).

tff(f1043,plain,
    spl1_83,
    inference(avatar_split_clause,[],[f511,f1041]) ).

tff(f1041,plain,
    ( spl1_83
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ~ ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_83])]) ).

tff(f511,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ~ ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f1039,plain,
    spl1_82,
    inference(avatar_split_clause,[],[f422,f1037]) ).

tff(f422,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,[],[f282]) ).

tff(f282,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,[],[f243]) ).

tff(f243,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,[],[f242]) ).

tff(f242,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,[],[f167]) ).

tff(f167,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,[],[f15]) ).

tff(f15,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/sandbox/benchmark/theBenchmark.p',fact_14_eq__number__of) ).

tff(f1035,plain,
    spl1_81,
    inference(avatar_split_clause,[],[f415,f1033]) ).

tff(f1033,plain,
    ( spl1_81
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ( X1 = X3 )
        | ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) )
        | ~ cancel_semigroup_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_81])]) ).

tff(f415,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ( X1 = X3 )
      | ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) )
      | ~ cancel_semigroup_add(X0) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f279,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
            | ( X1 != X3 ) )
          & ( ( X1 = X3 )
            | ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) ) ) )
      | ~ cancel_semigroup_add(X0) ),
    inference(nnf_transformation,[],[f238]) ).

tff(f238,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
        <=> ( X1 = X3 ) )
      | ~ cancel_semigroup_add(X0) ),
    inference(ennf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: $tType] :
      ( cancel_semigroup_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
        <=> ( X1 = X3 ) ) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X0: $tType] :
      ( cancel_semigroup_add(X0)
     => ! [X29: X0,X2: X0,X28: X0] :
          ( ( plus_plus(X0,X28,X2) = plus_plus(X0,X29,X2) )
        <=> ( X28 = X29 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__right__cancel) ).

tff(f1031,plain,
    spl1_80,
    inference(avatar_split_clause,[],[f413,f1029]) ).

tff(f1029,plain,
    ( spl1_80
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ( plus_plus(X0,X3,X1) != plus_plus(X0,X3,X2) )
        | ~ cancel_semigroup_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).

tff(f413,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ( X1 = X2 )
      | ( plus_plus(X0,X3,X1) != plus_plus(X0,X3,X2) )
      | ~ cancel_semigroup_add(X0) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f278,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( ( plus_plus(X0,X3,X1) = plus_plus(X0,X3,X2) )
            | ( X1 != X2 ) )
          & ( ( X1 = X2 )
            | ( plus_plus(X0,X3,X1) != plus_plus(X0,X3,X2) ) ) )
      | ~ cancel_semigroup_add(X0) ),
    inference(nnf_transformation,[],[f237]) ).

tff(f237,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( plus_plus(X0,X3,X1) = plus_plus(X0,X3,X2) )
        <=> ( X1 = X2 ) )
      | ~ cancel_semigroup_add(X0) ),
    inference(ennf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: $tType] :
      ( cancel_semigroup_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ( plus_plus(X0,X3,X1) = plus_plus(X0,X3,X2) )
        <=> ( X1 = X2 ) ) ),
    inference(rectify,[],[f91]) ).

tff(f91,axiom,
    ! [X0: $tType] :
      ( cancel_semigroup_add(X0)
     => ! [X29: X0,X28: X0,X2: X0] :
          ( ( plus_plus(X0,X2,X29) = plus_plus(X0,X2,X28) )
        <=> ( X28 = X29 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__left__cancel) ).

tff(f1021,plain,
    spl1_79,
    inference(avatar_split_clause,[],[f496,f1019]) ).

tff(f1019,plain,
    ( spl1_79
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
        | ~ ord_less(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).

tff(f496,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
      | ~ ord_less(nat,zero_zero(nat),X0) ),
    inference(cnf_transformation,[],[f317]) ).

tff(f1017,plain,
    spl1_78,
    inference(avatar_split_clause,[],[f495,f1015]) ).

tff(f1015,plain,
    ( spl1_78
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
        | ~ ord_less(nat,zero_zero(nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).

tff(f495,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
      | ~ ord_less(nat,zero_zero(nat),X1) ),
    inference(cnf_transformation,[],[f317]) ).

tff(f1013,plain,
    spl1_77,
    inference(avatar_split_clause,[],[f490,f1011]) ).

tff(f1011,plain,
    ( spl1_77
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
        | ~ ord_less(nat,zero_zero(nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).

tff(f490,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
      | ~ ord_less(nat,zero_zero(nat),X1) ),
    inference(cnf_transformation,[],[f313]) ).

tff(f1009,plain,
    spl1_76,
    inference(avatar_split_clause,[],[f380,f1007]) ).

tff(f1007,plain,
    ( spl1_76
  <=> ! [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,[spl1_76])]) ).

tff(f380,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) = X1 )
      | ( zero_zero(X0) != plus_plus(X0,X1,X1) )
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f267,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,[],[f215]) ).

tff(f215,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
        <=> ( zero_zero(X0) = X1 ) )
      | ~ linord219039673up_add(X0) ),
    inference(ennf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X1: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
        <=> ( zero_zero(X0) = X1 ) ) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X0: $tType] :
      ( linord219039673up_add(X0)
     => ! [X2: X0] :
          ( ( zero_zero(X0) = plus_plus(X0,X2,X2) )
        <=> ( zero_zero(X0) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_double__eq__0__iff) ).

tff(f1005,plain,
    spl1_75,
    inference(avatar_split_clause,[],[f379,f1003]) ).

tff(f1003,plain,
    ( spl1_75
  <=> ! [X0: $tType,X2: X0,X1: nat] :
        ( ( zero_zero(X0) != power_power(X0,X2,X1) )
        | ( zero_zero(X0) = X2 )
        | ~ ring_11004092258visors(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).

tff(f379,plain,
    ! [X0: $tType,X2: X0,X1: nat] :
      ( ( zero_zero(X0) != power_power(X0,X2,X1) )
      | ( zero_zero(X0) = X2 )
      | ~ ring_11004092258visors(X0) ),
    inference(cnf_transformation,[],[f214]) ).

tff(f214,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: X0] :
          ( ( zero_zero(X0) != power_power(X0,X2,X1) )
          | ( zero_zero(X0) = X2 ) )
      | ~ ring_11004092258visors(X0) ),
    inference(ennf_transformation,[],[f143]) ).

tff(f143,plain,
    ! [X0: $tType] :
      ( ring_11004092258visors(X0)
     => ! [X1: nat,X2: X0] :
          ( ( zero_zero(X0) != X2 )
         => ( zero_zero(X0) != power_power(X0,X2,X1) ) ) ),
    inference(rectify,[],[f85]) ).

tff(f85,axiom,
    ! [X0: $tType] :
      ( ring_11004092258visors(X0)
     => ! [X17: nat,X15: X0] :
          ( ( zero_zero(X0) != X15 )
         => ( zero_zero(X0) != power_power(X0,X15,X17) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_field__power__not__zero) ).

tff(f1001,plain,
    ( spl1_74
    | ~ spl1_58
    | ~ spl1_70 ),
    inference(avatar_split_clause,[],[f986,f966,f893,f998]) ).

tff(f893,plain,
    ( spl1_58
  <=> ! [X0: int] :
        ( ord_less(int,pls,X0)
        | ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).

tff(f966,plain,
    ( spl1_70
  <=> ord_less(nat,zero_zero(nat),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).

tff(f986,plain,
    ( ord_less(int,pls,plus_plus(int,bit1(pls),bit1(pls)))
    | ~ spl1_58
    | ~ spl1_70 ),
    inference(resolution,[],[f968,f894]) ).

tff(f894,plain,
    ( ! [X0: int] :
        ( ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
        | ord_less(int,pls,X0) )
    | ~ spl1_58 ),
    inference(avatar_component_clause,[],[f893]) ).

tff(f968,plain,
    ( ord_less(nat,zero_zero(nat),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))
    | ~ spl1_70 ),
    inference(avatar_component_clause,[],[f966]) ).

tff(f981,plain,
    spl1_73,
    inference(avatar_split_clause,[],[f550,f979]) ).

tff(f979,plain,
    ( spl1_73
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).

tff(f550,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,bit1(X1),plus_plus(int,X0,X0)) ),
    inference(definition_unfolding,[],[f475,f375]) ).

tff(f475,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,bit1(X1),bit0(X0)) ),
    inference(cnf_transformation,[],[f305]) ).

tff(f305,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,[],[f197]) ).

tff(f197,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit0(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X6: int,X5: int] :
      ( ord_less(int,bit1(X5),bit0(X6))
    <=> ord_less(int,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_rel__simps_I16_J) ).

tff(f977,plain,
    spl1_72,
    inference(avatar_split_clause,[],[f549,f975]) ).

tff(f975,plain,
    ( spl1_72
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,bit1(X1),plus_plus(int,X0,X0))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).

tff(f549,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),plus_plus(int,X0,X0))
      | ~ ord_less(int,X1,X0) ),
    inference(definition_unfolding,[],[f476,f375]) ).

tff(f476,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit0(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f305]) ).

tff(f973,plain,
    spl1_71,
    inference(avatar_split_clause,[],[f548,f971]) ).

tff(f971,plain,
    ( spl1_71
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).

tff(f548,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ),
    inference(definition_unfolding,[],[f469,f375,f375]) ).

tff(f469,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( bit0(X0) != bit0(X1) ) ),
    inference(cnf_transformation,[],[f302]) ).

tff(f302,plain,
    ! [X0: int,X1: int] :
      ( ( ( bit0(X0) = bit0(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( bit0(X0) != bit0(X1) ) ) ),
    inference(nnf_transformation,[],[f194]) ).

tff(f194,plain,
    ! [X0: int,X1: int] :
      ( ( bit0(X0) = bit0(X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f17]) ).

tff(f17,axiom,
    ! [X6: int,X5: int] :
      ( ( bit0(X5) = bit0(X6) )
    <=> ( X5 = X6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rel__simps_I48_J) ).

tff(f969,plain,
    spl1_70,
    inference(avatar_split_clause,[],[f515,f966]) ).

tff(f515,plain,
    ord_less(nat,zero_zero(nat),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),
    inference(definition_unfolding,[],[f363,f375]) ).

tff(f363,plain,
    ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))),
    inference(cnf_transformation,[],[f50]) ).

tff(f50,axiom,
    ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pos2) ).

tff(f964,plain,
    spl1_69,
    inference(avatar_split_clause,[],[f498,f962]) ).

tff(f498,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ),
    inference(cnf_transformation,[],[f319]) ).

tff(f960,plain,
    ( spl1_68
    | ~ spl1_48
    | ~ spl1_58 ),
    inference(avatar_split_clause,[],[f932,f893,f842,f958]) ).

tff(f842,plain,
    ( spl1_48
  <=> ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).

tff(f932,plain,
    ( ! [X0: int] :
        ( ord_less(int,pls,X0)
        | ( zero_zero(nat) = number_number_of(nat,X0) ) )
    | ~ spl1_48
    | ~ spl1_58 ),
    inference(resolution,[],[f894,f843]) ).

tff(f843,plain,
    ( ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) )
    | ~ spl1_48 ),
    inference(avatar_component_clause,[],[f842]) ).

tff(f931,plain,
    spl1_67,
    inference(avatar_split_clause,[],[f558,f929]) ).

tff(f929,plain,
    ( spl1_67
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
        | ~ linord219039673up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_67])]) ).

tff(f558,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
      | ~ linord219039673up_add(X0) ),
    inference(equality_resolution,[],[f381]) ).

tff(f381,plain,
    ! [X0: $tType,X1: X0] :
      ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
      | ( zero_zero(X0) != X1 )
      | ~ linord219039673up_add(X0) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f927,plain,
    spl1_66,
    inference(avatar_split_clause,[],[f539,f925]) ).

tff(f925,plain,
    ( spl1_66
  <=> ! [X0: int] :
        ( ord_less(int,X0,pls)
        | ~ ord_less(int,plus_plus(int,X0,X0),pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).

tff(f539,plain,
    ! [X0: int] :
      ( ord_less(int,X0,pls)
      | ~ ord_less(int,plus_plus(int,X0,X0),pls) ),
    inference(definition_unfolding,[],[f446,f375]) ).

tff(f446,plain,
    ! [X0: int] :
      ( ord_less(int,X0,pls)
      | ~ ord_less(int,bit0(X0),pls) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f295,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,[],[f178]) ).

tff(f178,plain,
    ! [X0: int] :
      ( ord_less(int,bit0(X0),pls)
    <=> ord_less(int,X0,pls) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X5: int] :
      ( ord_less(int,bit0(X5),pls)
    <=> ord_less(int,X5,pls) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rel__simps_I10_J) ).

tff(f923,plain,
    spl1_65,
    inference(avatar_split_clause,[],[f538,f921]) ).

tff(f921,plain,
    ( spl1_65
  <=> ! [X0: int] :
        ( ord_less(int,plus_plus(int,X0,X0),pls)
        | ~ ord_less(int,X0,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).

tff(f538,plain,
    ! [X0: int] :
      ( ord_less(int,plus_plus(int,X0,X0),pls)
      | ~ ord_less(int,X0,pls) ),
    inference(definition_unfolding,[],[f447,f375]) ).

tff(f447,plain,
    ! [X0: int] :
      ( ord_less(int,bit0(X0),pls)
      | ~ ord_less(int,X0,pls) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f919,plain,
    spl1_64,
    inference(avatar_split_clause,[],[f537,f917]) ).

tff(f537,plain,
    ! [X0: int] :
      ( ord_less(int,pls,X0)
      | ~ ord_less(int,pls,plus_plus(int,X0,X0)) ),
    inference(definition_unfolding,[],[f442,f375]) ).

tff(f442,plain,
    ! [X0: int] :
      ( ord_less(int,pls,X0)
      | ~ ord_less(int,pls,bit0(X0)) ),
    inference(cnf_transformation,[],[f293]) ).

tff(f293,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,[],[f176]) ).

tff(f176,plain,
    ! [X0: int] :
      ( ord_less(int,pls,bit0(X0))
    <=> ord_less(int,pls,X0) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X5: int] :
      ( ord_less(int,pls,bit0(X5))
    <=> ord_less(int,pls,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_rel__simps_I4_J) ).

tff(f915,plain,
    spl1_63,
    inference(avatar_split_clause,[],[f536,f913]) ).

tff(f913,plain,
    ( spl1_63
  <=> ! [X0: int] :
        ( ord_less(int,pls,plus_plus(int,X0,X0))
        | ~ ord_less(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).

tff(f536,plain,
    ! [X0: int] :
      ( ord_less(int,pls,plus_plus(int,X0,X0))
      | ~ ord_less(int,pls,X0) ),
    inference(definition_unfolding,[],[f443,f375]) ).

tff(f443,plain,
    ! [X0: int] :
      ( ord_less(int,pls,bit0(X0))
      | ~ ord_less(int,pls,X0) ),
    inference(cnf_transformation,[],[f293]) ).

tff(f911,plain,
    spl1_62,
    inference(avatar_split_clause,[],[f484,f909]) ).

tff(f909,plain,
    ( spl1_62
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero(nat) = X0 )
        | ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).

tff(f484,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero(nat) = X0 )
      | ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
    inference(cnf_transformation,[],[f310]) ).

tff(f310,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
        | ( zero_zero(nat) != X0 )
        | ( zero_zero(nat) != X1 ) )
      & ( ( ( zero_zero(nat) = X0 )
          & ( zero_zero(nat) = X1 ) )
        | ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
    inference(flattening,[],[f309]) ).

tff(f309,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
        | ( zero_zero(nat) != X0 )
        | ( zero_zero(nat) != X1 ) )
      & ( ( ( zero_zero(nat) = X0 )
          & ( zero_zero(nat) = X1 ) )
        | ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
    inference(nnf_transformation,[],[f201]) ).

tff(f201,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
    <=> ( ( zero_zero(nat) = X0 )
        & ( zero_zero(nat) = X1 ) ) ),
    inference(rectify,[],[f93]) ).

tff(f93,axiom,
    ! [X12: nat,X21: nat] :
      ( ( zero_zero(nat) = plus_plus(nat,X21,X12) )
    <=> ( ( zero_zero(nat) = X12 )
        & ( zero_zero(nat) = X21 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__is__0) ).

tff(f907,plain,
    spl1_61,
    inference(avatar_split_clause,[],[f483,f905]) ).

tff(f905,plain,
    ( spl1_61
  <=> ! [X0: nat,X1: nat] :
        ( ( zero_zero(nat) = X1 )
        | ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).

tff(f483,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero(nat) = X1 )
      | ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
    inference(cnf_transformation,[],[f310]) ).

tff(f903,plain,
    spl1_60,
    inference(avatar_split_clause,[],[f460,f901]) ).

tff(f901,plain,
    ( spl1_60
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ord_less(nat,X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).

tff(f460,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f255]) ).

tff(f255,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(flattening,[],[f254]) ).

tff(f254,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f188]) ).

tff(f188,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ~ ord_less(nat,X1,X0)
       => ord_less(nat,X0,X1) ) ),
    inference(rectify,[],[f68]) ).

tff(f68,axiom,
    ! [X22: nat,X16: nat] :
      ( ( X16 != X22 )
     => ( ~ ord_less(nat,X16,X22)
       => ord_less(nat,X22,X16) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_linorder__neqE__nat) ).

tff(f899,plain,
    spl1_59,
    inference(avatar_split_clause,[],[f453,f897]) ).

tff(f897,plain,
    ( spl1_59
  <=> ! [X0: int] :
        ( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
        | ~ ord_less(int,pls,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).

tff(f453,plain,
    ! [X0: int] :
      ( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
      | ~ ord_less(int,pls,X0) ),
    inference(cnf_transformation,[],[f298]) ).

tff(f298,plain,
    ! [X0: int] :
      ( ( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
        | ~ ord_less(int,pls,X0) )
      & ( ord_less(int,pls,X0)
        | ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ) ),
    inference(nnf_transformation,[],[f181]) ).

tff(f181,plain,
    ! [X0: int] :
      ( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
    <=> ord_less(int,pls,X0) ),
    inference(rectify,[],[f32]) ).

tff(f32,axiom,
    ! [X11: int] :
      ( ord_less(nat,zero_zero(nat),number_number_of(nat,X11))
    <=> ord_less(int,pls,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_less__0__number__of) ).

tff(f895,plain,
    spl1_58,
    inference(avatar_split_clause,[],[f452,f893]) ).

tff(f452,plain,
    ! [X0: int] :
      ( ord_less(int,pls,X0)
      | ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ),
    inference(cnf_transformation,[],[f298]) ).

tff(f886,plain,
    spl1_57,
    inference(avatar_split_clause,[],[f472,f884]) ).

tff(f884,plain,
    ( spl1_57
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,bit1(X1),bit1(X0))
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).

tff(f472,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit1(X0))
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f303]) ).

tff(f303,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,[],[f195]) ).

tff(f195,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,bit1(X1),bit1(X0))
    <=> ord_less(int,X1,X0) ),
    inference(rectify,[],[f39]) ).

tff(f39,axiom,
    ! [X13: int,X14: int] :
      ( ord_less(int,bit1(X14),bit1(X13))
    <=> ord_less(int,X14,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__int__code_I16_J) ).

tff(f882,plain,
    spl1_56,
    inference(avatar_split_clause,[],[f471,f880]) ).

tff(f880,plain,
    ( spl1_56
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).

tff(f471,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ~ ord_less(int,bit1(X1),bit1(X0)) ),
    inference(cnf_transformation,[],[f303]) ).

tff(f878,plain,
    spl1_55,
    inference(avatar_split_clause,[],[f403,f876]) ).

tff(f876,plain,
    ( spl1_55
  <=> ! [X0: $tType,X1: X0] :
        ( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).

tff(f403,plain,
    ! [X0: $tType,X1: X0] :
      ( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f228]) ).

tff(f228,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f155]) ).

tff(f155,plain,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
    inference(rectify,[],[f78]) ).

tff(f78,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X15: X0] : ( plus_plus(X0,number_number_of(X0,pls),X15) = X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__numeral__0) ).

tff(f874,plain,
    spl1_54,
    inference(avatar_split_clause,[],[f402,f872]) ).

tff(f872,plain,
    ( spl1_54
  <=> ! [X0: $tType,X1: X0] :
        ( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).

tff(f402,plain,
    ! [X0: $tType,X1: X0] :
      ( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f227]) ).

tff(f227,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 ) ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ! [X15: X0] : ( plus_plus(X0,X15,number_number_of(X0,pls)) = X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__numeral__0__right) ).

tff(f865,plain,
    spl1_53,
    inference(avatar_split_clause,[],[f585,f863]) ).

tff(f863,plain,
    ( spl1_53
  <=> ! [X1: nat] : ord_less(nat,zero_zero(nat),power_power(nat,X1,zero_zero(nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).

tff(f585,plain,
    ! [X1: nat] : ord_less(nat,zero_zero(nat),power_power(nat,X1,zero_zero(nat))),
    inference(equality_resolution,[],[f489]) ).

tff(f489,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
      | ( zero_zero(nat) != X0 ) ),
    inference(cnf_transformation,[],[f313]) ).

tff(f861,plain,
    spl1_52,
    inference(avatar_split_clause,[],[f584,f858]) ).

tff(f858,plain,
    ( spl1_52
  <=> ( zero_zero(nat) = plus_plus(nat,zero_zero(nat),zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).

tff(f584,plain,
    zero_zero(nat) = plus_plus(nat,zero_zero(nat),zero_zero(nat)),
    inference(equality_resolution,[],[f583]) ).

tff(f583,plain,
    ! [X1: nat] :
      ( ( zero_zero(nat) = plus_plus(nat,X1,zero_zero(nat)) )
      | ( zero_zero(nat) != X1 ) ),
    inference(equality_resolution,[],[f485]) ).

tff(f485,plain,
    ! [X0: nat,X1: nat] :
      ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
      | ( zero_zero(nat) != X0 )
      | ( zero_zero(nat) != X1 ) ),
    inference(cnf_transformation,[],[f310]) ).

tff(f856,plain,
    spl1_51,
    inference(avatar_split_clause,[],[f533,f854]) ).

tff(f854,plain,
    ( spl1_51
  <=> ! [X0: int] :
        ( ( pls = X0 )
        | ( pls != plus_plus(int,X0,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).

tff(f533,plain,
    ! [X0: int] :
      ( ( pls = X0 )
      | ( pls != plus_plus(int,X0,X0) ) ),
    inference(definition_unfolding,[],[f438,f375]) ).

tff(f438,plain,
    ! [X0: int] :
      ( ( pls = X0 )
      | ( pls != bit0(X0) ) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f291,plain,
    ! [X0: int] :
      ( ( ( pls = bit0(X0) )
        | ( pls != X0 ) )
      & ( ( pls = X0 )
        | ( pls != bit0(X0) ) ) ),
    inference(nnf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: int] :
      ( ( pls = bit0(X0) )
    <=> ( pls = X0 ) ),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X5: int] :
      ( ( pls = bit0(X5) )
    <=> ( pls = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I44_J) ).

tff(f852,plain,
    spl1_50,
    inference(avatar_split_clause,[],[f445,f850]) ).

tff(f850,plain,
    ( spl1_50
  <=> ! [X0: int] :
        ( ord_less(int,bit1(X0),pls)
        | ~ ord_less(int,X0,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).

tff(f445,plain,
    ! [X0: int] :
      ( ord_less(int,bit1(X0),pls)
      | ~ ord_less(int,X0,pls) ),
    inference(cnf_transformation,[],[f294]) ).

tff(f294,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,[],[f177]) ).

tff(f177,plain,
    ! [X0: int] :
      ( ord_less(int,bit1(X0),pls)
    <=> ord_less(int,X0,pls) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X5: int] :
      ( ord_less(int,bit1(X5),pls)
    <=> ord_less(int,X5,pls) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rel__simps_I12_J) ).

tff(f848,plain,
    spl1_49,
    inference(avatar_split_clause,[],[f444,f846]) ).

tff(f846,plain,
    ( spl1_49
  <=> ! [X0: int] :
        ( ord_less(int,X0,pls)
        | ~ ord_less(int,bit1(X0),pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).

tff(f444,plain,
    ! [X0: int] :
      ( ord_less(int,X0,pls)
      | ~ ord_less(int,bit1(X0),pls) ),
    inference(cnf_transformation,[],[f294]) ).

tff(f844,plain,
    spl1_48,
    inference(avatar_split_clause,[],[f421,f842]) ).

tff(f421,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ( zero_zero(nat) = X0 ) ),
    inference(cnf_transformation,[],[f241]) ).

tff(f241,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ( zero_zero(nat) = X0 ) ),
    inference(ennf_transformation,[],[f166]) ).

tff(f166,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) != X0 )
     => ord_less(nat,zero_zero(nat),X0) ),
    inference(rectify,[],[f80]) ).

tff(f80,axiom,
    ! [X17: nat] :
      ( ( zero_zero(nat) != X17 )
     => ord_less(nat,zero_zero(nat),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_gr0I) ).

tff(f834,plain,
    spl1_47,
    inference(avatar_split_clause,[],[f505,f832]) ).

tff(f832,plain,
    ( spl1_47
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).

tff(f505,plain,
    ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f323]) ).

tff(f830,plain,
    spl1_46,
    inference(avatar_split_clause,[],[f467,f828]) ).

tff(f828,plain,
    ( spl1_46
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ( bit1(X0) != bit1(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).

tff(f467,plain,
    ! [X0: int,X1: int] :
      ( ( X0 = X1 )
      | ( bit1(X0) != bit1(X1) ) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f301,plain,
    ! [X0: int,X1: int] :
      ( ( ( bit1(X0) = bit1(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( bit1(X0) != bit1(X1) ) ) ),
    inference(nnf_transformation,[],[f193]) ).

tff(f193,plain,
    ! [X0: int,X1: int] :
      ( ( bit1(X0) = bit1(X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ! [X6: int,X5: int] :
      ( ( bit1(X5) = bit1(X6) )
    <=> ( X5 = X6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rel__simps_I51_J) ).

tff(f826,plain,
    spl1_45,
    inference(avatar_split_clause,[],[f408,f824]) ).

tff(f824,plain,
    ( spl1_45
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = number_number_of(X0,pls) )
        | ~ number_semiring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).

tff(f408,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_semiring(X0) ),
    inference(cnf_transformation,[],[f233]) ).

tff(f233,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_semiring(X0) ),
    inference(ennf_transformation,[],[f41]) ).

tff(f41,axiom,
    ! [X0: $tType] :
      ( number_semiring(X0)
     => ( zero_zero(X0) = number_number_of(X0,pls) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_semiring__numeral__0__eq__0) ).

tff(f822,plain,
    spl1_44,
    inference(avatar_split_clause,[],[f400,f820]) ).

tff(f820,plain,
    ( spl1_44
  <=> ! [X0: $tType] :
        ( ( zero_zero(X0) = number_number_of(X0,pls) )
        | ~ number_ring(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).

tff(f400,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_ring(X0) ),
    inference(cnf_transformation,[],[f225]) ).

tff(f225,plain,
    ! [X0: $tType] :
      ( ( zero_zero(X0) = number_number_of(X0,pls) )
      | ~ number_ring(X0) ),
    inference(ennf_transformation,[],[f42]) ).

tff(f42,axiom,
    ! [X0: $tType] :
      ( number_ring(X0)
     => ( zero_zero(X0) = number_number_of(X0,pls) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_semiring__norm_I112_J) ).

tff(f816,plain,
    spl1_43,
    inference(avatar_split_clause,[],[f542,f814]) ).

tff(f814,plain,
    ( spl1_43
  <=> ! [X0: int,X1: int] : ( bit1(X0) != plus_plus(int,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).

tff(f542,plain,
    ! [X0: int,X1: int] : ( bit1(X0) != plus_plus(int,X1,X1) ),
    inference(definition_unfolding,[],[f454,f375]) ).

tff(f454,plain,
    ! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
    inference(cnf_transformation,[],[f182]) ).

tff(f182,plain,
    ! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
    inference(rectify,[],[f22]) ).

tff(f22,axiom,
    ! [X9: int,X8: int] : ( bit1(X9) != bit0(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).

tff(f812,plain,
    spl1_42,
    inference(avatar_split_clause,[],[f374,f810]) ).

tff(f374,plain,
    ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
    inference(cnf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X8: int] : ( plus_plus(int,pls,X8) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__Pls) ).

tff(f808,plain,
    spl1_41,
    inference(avatar_split_clause,[],[f373,f806]) ).

tff(f806,plain,
    ( spl1_41
  <=> ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).

tff(f373,plain,
    ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
    inference(cnf_transformation,[],[f138]) ).

tff(f138,plain,
    ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
    inference(rectify,[],[f74]) ).

tff(f74,axiom,
    ! [X8: int] : ( plus_plus(int,X8,pls) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_add__Pls__right) ).

tff(f804,plain,
    spl1_40,
    inference(avatar_split_clause,[],[f361,f801]) ).

tff(f801,plain,
    ( spl1_40
  <=> ( zero_zero(nat) = number_number_of(nat,pls) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).

tff(f361,plain,
    zero_zero(nat) = number_number_of(nat,pls),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,axiom,
    zero_zero(nat) = number_number_of(nat,pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_semiring__norm_I113_J) ).

tff(f799,plain,
    spl1_39,
    inference(avatar_split_clause,[],[f372,f797]) ).

tff(f372,plain,
    ! [X0: int] : ( number_number_of(int,X0) = X0 ),
    inference(cnf_transformation,[],[f137]) ).

tff(f137,plain,
    ! [X0: int] : ( number_number_of(int,X0) = X0 ),
    inference(rectify,[],[f64]) ).

tff(f64,axiom,
    ! [X8: int] : ( number_number_of(int,X8) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_number__of__is__id) ).

tff(f795,plain,
    spl1_38,
    inference(avatar_split_clause,[],[f369,f793]) ).

tff(f793,plain,
    ( spl1_38
  <=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).

tff(f369,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(cnf_transformation,[],[f134]) ).

tff(f134,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(rectify,[],[f83]) ).

tff(f83,axiom,
    ! [X17: nat] : ~ ord_less(nat,X17,zero_zero(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_not__less0) ).

tff(f791,plain,
    spl1_37,
    inference(avatar_split_clause,[],[f359,f788]) ).

tff(f788,plain,
    ( spl1_37
  <=> ord_less(nat,zero_zero(nat),n) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).

tff(f359,plain,
    ord_less(nat,zero_zero(nat),n),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,axiom,
    ord_less(nat,zero_zero(nat),n),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_n0) ).

tff(f786,plain,
    spl1_36,
    inference(avatar_split_clause,[],[f358,f783]) ).

tff(f783,plain,
    ( spl1_36
  <=> ord_less(nat,zero_zero(nat),tn) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).

tff(f358,plain,
    ord_less(nat,zero_zero(nat),tn),
    inference(cnf_transformation,[],[f14]) ).

tff(f14,axiom,
    ord_less(nat,zero_zero(nat),tn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_tn0) ).

tff(f781,plain,
    ( ~ spl1_35
    | spl1_30
    | ~ spl1_32 ),
    inference(avatar_split_clause,[],[f776,f764,f754,f778]) ).

tff(f754,plain,
    ( spl1_30
  <=> ( v = zero_zero(int) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).

tff(f776,plain,
    ( ( v != pls )
    | spl1_30
    | ~ spl1_32 ),
    inference(superposition,[],[f756,f766]) ).

tff(f756,plain,
    ( ( v != zero_zero(int) )
    | spl1_30 ),
    inference(avatar_component_clause,[],[f754]) ).

tff(f775,plain,
    spl1_34,
    inference(avatar_split_clause,[],[f367,f773]) ).

tff(f773,plain,
    ( spl1_34
  <=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).

tff(f367,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,X0),
    inference(cnf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,X0),
    inference(rectify,[],[f69]) ).

tff(f69,axiom,
    ! [X17: nat] : ~ ord_less(nat,X17,X17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__irrefl__nat) ).

tff(f771,plain,
    spl1_33,
    inference(avatar_split_clause,[],[f365,f769]) ).

tff(f769,plain,
    ( spl1_33
  <=> ! [X0: int] : ( pls != bit1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).

tff(f365,plain,
    ! [X0: int] : ( pls != bit1(X0) ),
    inference(cnf_transformation,[],[f130]) ).

tff(f130,plain,
    ! [X0: int] : ( pls != bit1(X0) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X8: int] : ( pls != bit1(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).

tff(f767,plain,
    spl1_32,
    inference(avatar_split_clause,[],[f356,f764]) ).

tff(f762,plain,
    ~ spl1_31,
    inference(avatar_split_clause,[],[f354,f759]) ).

tff(f759,plain,
    ( spl1_31
  <=> ord_less(int,pls,pls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).

tff(f354,plain,
    ~ ord_less(int,pls,pls),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,axiom,
    ~ ord_less(int,pls,pls),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I2_J) ).

tff(f757,plain,
    ~ spl1_30,
    inference(avatar_split_clause,[],[f353,f754]) ).

tff(f353,plain,
    v != zero_zero(int),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    v != zero_zero(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096v_A_126_061_A0_096) ).

tff(f752,plain,
    ( ~ spl1_29
    | spl1_28 ),
    inference(avatar_split_clause,[],[f747,f743,f749]) ).

tff(f743,plain,
    ( spl1_28
  <=> ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).

tff(f747,plain,
    ( ~ ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
    | spl1_28 ),
    inference(forward_demodulation,[],[f745,f356]) ).

tff(f745,plain,
    ( ~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
    | spl1_28 ),
    inference(avatar_component_clause,[],[f743]) ).

tff(f746,plain,
    ~ spl1_28,
    inference(avatar_split_clause,[],[f513,f743]) ).

tff(f513,plain,
    ~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
    inference(definition_unfolding,[],[f325,f375]) ).

tff(f325,plain,
    ~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
    inference(cnf_transformation,[],[f129]) ).

tff(f129,plain,
    ~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
    inference(flattening,[],[f128]) ).

tff(f128,negated_conjecture,
    ~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
    inference(negated_conjecture,[],[f127]) ).

tff(f127,conjecture,
    ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f741,plain,
    spl1_27,
    inference(avatar_split_clause,[],[f352,f738]) ).

tff(f738,plain,
    ( spl1_27
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).

tff(f352,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f126]) ).

tff(f126,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f736,plain,
    spl1_26,
    inference(avatar_split_clause,[],[f351,f733]) ).

tff(f733,plain,
    ( spl1_26
  <=> ordere236663937imp_le(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).

tff(f351,plain,
    ordere236663937imp_le(nat),
    inference(cnf_transformation,[],[f114]) ).

tff(f114,axiom,
    ordere236663937imp_le(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).

tff(f731,plain,
    spl1_25,
    inference(avatar_split_clause,[],[f350,f728]) ).

tff(f728,plain,
    ( spl1_25
  <=> power(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).

tff(f350,plain,
    power(nat),
    inference(cnf_transformation,[],[f122]) ).

tff(f122,axiom,
    power(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).

tff(f726,plain,
    spl1_24,
    inference(avatar_split_clause,[],[f349,f723]) ).

tff(f723,plain,
    ( spl1_24
  <=> mult_zero(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).

tff(f349,plain,
    mult_zero(nat),
    inference(cnf_transformation,[],[f121]) ).

tff(f121,axiom,
    mult_zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).

tff(f721,plain,
    spl1_23,
    inference(avatar_split_clause,[],[f348,f718]) ).

tff(f718,plain,
    ( spl1_23
  <=> zero_neq_one(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).

tff(f348,plain,
    zero_neq_one(nat),
    inference(cnf_transformation,[],[f119]) ).

tff(f119,axiom,
    zero_neq_one(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).

tff(f716,plain,
    spl1_22,
    inference(avatar_split_clause,[],[f347,f713]) ).

tff(f713,plain,
    ( spl1_22
  <=> no_zero_divisors(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).

tff(f347,plain,
    no_zero_divisors(nat),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,axiom,
    no_zero_divisors(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).

tff(f711,plain,
    spl1_21,
    inference(avatar_split_clause,[],[f346,f708]) ).

tff(f708,plain,
    ( spl1_21
  <=> cancel_semigroup_add(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).

tff(f346,plain,
    cancel_semigroup_add(nat),
    inference(cnf_transformation,[],[f115]) ).

tff(f115,axiom,
    cancel_semigroup_add(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).

tff(f706,plain,
    spl1_20,
    inference(avatar_split_clause,[],[f345,f703]) ).

tff(f703,plain,
    ( spl1_20
  <=> no_zero_divisors(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).

tff(f345,plain,
    no_zero_divisors(int),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    no_zero_divisors(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).

tff(f701,plain,
    spl1_19,
    inference(avatar_split_clause,[],[f344,f698]) ).

tff(f698,plain,
    ( spl1_19
  <=> power(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).

tff(f344,plain,
    power(int),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,axiom,
    power(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).

tff(f696,plain,
    spl1_18,
    inference(avatar_split_clause,[],[f343,f693]) ).

tff(f693,plain,
    ( spl1_18
  <=> cancel_semigroup_add(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).

tff(f343,plain,
    cancel_semigroup_add(int),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,axiom,
    cancel_semigroup_add(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).

tff(f691,plain,
    spl1_17,
    inference(avatar_split_clause,[],[f342,f688]) ).

tff(f688,plain,
    ( spl1_17
  <=> ordere236663937imp_le(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).

tff(f342,plain,
    ordere236663937imp_le(int),
    inference(cnf_transformation,[],[f98]) ).

tff(f98,axiom,
    ordere236663937imp_le(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).

tff(f686,plain,
    spl1_16,
    inference(avatar_split_clause,[],[f341,f683]) ).

tff(f683,plain,
    ( spl1_16
  <=> mult_zero(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).

tff(f341,plain,
    mult_zero(int),
    inference(cnf_transformation,[],[f108]) ).

tff(f108,axiom,
    mult_zero(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).

tff(f681,plain,
    spl1_15,
    inference(avatar_split_clause,[],[f340,f678]) ).

tff(f678,plain,
    ( spl1_15
  <=> zero_neq_one(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).

tff(f340,plain,
    zero_neq_one(int),
    inference(cnf_transformation,[],[f106]) ).

tff(f106,axiom,
    zero_neq_one(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).

tff(f676,plain,
    spl1_14,
    inference(avatar_split_clause,[],[f339,f673]) ).

tff(f673,plain,
    ( spl1_14
  <=> number_semiring(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).

tff(f339,plain,
    number_semiring(nat),
    inference(cnf_transformation,[],[f118]) ).

tff(f118,axiom,
    number_semiring(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).

tff(f671,plain,
    spl1_13,
    inference(avatar_split_clause,[],[f338,f668]) ).

tff(f668,plain,
    ( spl1_13
  <=> linordered_semidom(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).

tff(f338,plain,
    linordered_semidom(nat),
    inference(cnf_transformation,[],[f116]) ).

tff(f116,axiom,
    linordered_semidom(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).

tff(f666,plain,
    spl1_12,
    inference(avatar_split_clause,[],[f337,f663]) ).

tff(f663,plain,
    ( spl1_12
  <=> semiring_1(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).

tff(f337,plain,
    semiring_1(nat),
    inference(cnf_transformation,[],[f120]) ).

tff(f120,axiom,
    semiring_1(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).

tff(f661,plain,
    spl1_11,
    inference(avatar_split_clause,[],[f336,f658]) ).

tff(f658,plain,
    ( spl1_11
  <=> number(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).

tff(f336,plain,
    number(nat),
    inference(cnf_transformation,[],[f124]) ).

tff(f124,axiom,
    number(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).

tff(f656,plain,
    spl1_10,
    inference(avatar_split_clause,[],[f335,f653]) ).

tff(f653,plain,
    ( spl1_10
  <=> semiring_1(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).

tff(f335,plain,
    semiring_1(int),
    inference(cnf_transformation,[],[f107]) ).

tff(f107,axiom,
    semiring_1(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).

tff(f651,plain,
    spl1_9,
    inference(avatar_split_clause,[],[f334,f648]) ).

tff(f648,plain,
    ( spl1_9
  <=> number_semiring(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).

tff(f334,plain,
    number_semiring(int),
    inference(cnf_transformation,[],[f105]) ).

tff(f105,axiom,
    number_semiring(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).

tff(f646,plain,
    spl1_8,
    inference(avatar_split_clause,[],[f333,f643]) ).

tff(f643,plain,
    ( spl1_8
  <=> number(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).

tff(f333,plain,
    number(int),
    inference(cnf_transformation,[],[f113]) ).

tff(f113,axiom,
    number(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).

tff(f641,plain,
    spl1_7,
    inference(avatar_split_clause,[],[f332,f638]) ).

tff(f638,plain,
    ( spl1_7
  <=> linordered_semidom(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).

tff(f332,plain,
    linordered_semidom(int),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    linordered_semidom(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).

tff(f636,plain,
    spl1_6,
    inference(avatar_split_clause,[],[f331,f633]) ).

tff(f331,plain,
    number_ring(int),
    inference(cnf_transformation,[],[f110]) ).

tff(f110,axiom,
    number_ring(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).

tff(f631,plain,
    spl1_5,
    inference(avatar_split_clause,[],[f330,f628]) ).

tff(f330,plain,
    linordered_idom(int),
    inference(cnf_transformation,[],[f104]) ).

tff(f104,axiom,
    linordered_idom(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).

tff(f626,plain,
    spl1_4,
    inference(avatar_split_clause,[],[f329,f623]) ).

tff(f623,plain,
    ( spl1_4
  <=> linord219039673up_add(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

tff(f329,plain,
    linord219039673up_add(int),
    inference(cnf_transformation,[],[f99]) ).

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

tff(f621,plain,
    spl1_3,
    inference(avatar_split_clause,[],[f328,f618]) ).

tff(f618,plain,
    ( spl1_3
  <=> ring_11004092258visors(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f328,plain,
    ring_11004092258visors(int),
    inference(cnf_transformation,[],[f100]) ).

tff(f100,axiom,
    ring_11004092258visors(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).

tff(f616,plain,
    spl1_2,
    inference(avatar_split_clause,[],[f327,f613]) ).

tff(f613,plain,
    ( spl1_2
  <=> ring_char_0(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

tff(f327,plain,
    ring_char_0(int),
    inference(cnf_transformation,[],[f109]) ).

tff(f109,axiom,
    ring_char_0(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).

tff(f611,plain,
    ~ spl1_1,
    inference(avatar_split_clause,[],[f326,f608]) ).

tff(f608,plain,
    ( spl1_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

tff(f326,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f125]) ).

tff(f125,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUN015_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 18:54:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (10330)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (10333)WARNING: value z3 for option sas not known
% 0.14/0.39  % (10334)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  % (10331)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  % (10336)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39  % (10332)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (10333)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39  % (10337)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39  % (10335)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39  % (10337)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39  % Exception at run slice level% Exception at run slice level
% 0.14/0.39  
% 0.14/0.39  User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39  
% 0.14/0.39  % Exception at run slice level
% 0.14/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41  % (10338)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.41  % (10339)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)
% 0.21/0.41  % (10340)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)
% 0.21/0.41  % (10338)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41  % Exception at run slice level
% 0.21/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41  % (10339)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42  % (10335)First to succeed.
% 0.21/0.43  % (10341)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.21/0.43  % (10335)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10330"
% 0.21/0.43  % (10335)Refutation found. Thanks to Tanya!
% 0.21/0.43  % SZS status Theorem for theBenchmark
% 0.21/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44  % (10335)------------------------------
% 0.21/0.44  % (10335)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44  % (10335)Termination reason: Refutation
% 0.21/0.44  
% 0.21/0.44  % (10335)Memory used [KB]: 1514
% 0.21/0.44  % (10335)Time elapsed: 0.047 s
% 0.21/0.44  % (10335)Instructions burned: 74 (million)
% 0.21/0.44  % (10330)Success in time 0.069 s
%------------------------------------------------------------------------------