%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SCT264_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 : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 14:57:31 EDT 2024

% Result   : Theorem 1.26s 0.72s
% Output   : Refutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  499
% Syntax   : Number of formulae    : 1390 ( 321 unt;  85 typ;   0 def)
%            Number of atoms       : 4304 ( 701 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives : 4781 (1782   ~;2035   |; 291   &)
%                                         ( 384 <=>; 278  =>;   0  <=;  11 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  111 (  46   >;  65   *;   0   +;   0  <<)
%            Number of predicates  :  307 ( 305 usr; 278 prp; 0-5 aty)
%            Number of functors    :   53 (  53 usr;  22 con; 0-6 aty)
%            Number of variables   : 2803 (2693   !;  60   ?;2803   :)
%                                         (  50  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    arrow_411405190le_alt: $tType ).

tff(type_def_6,type,
    arrow_159774573e_indi: $tType ).

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

tff(type_def_8,type,
    nat: $tType ).

tff(type_def_9,type,
    fun: ( $tType * $tType ) > $tType ).

tff(type_def_10,type,
    product_prod: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).

tff(func_def_1,type,
    arrow_610318064e_Prof: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),bool) ).

tff(func_def_2,type,
    arrow_1158827142_above: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))) ).

tff(func_def_3,type,
    arrow_276188178_mkbot: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ).

tff(func_def_4,type,
    arrow_424895264_mktop: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ).

tff(func_def_5,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).

tff(func_def_6,type,
    combc: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).

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

tff(func_def_8,type,
    combk: 
      !>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).

tff(func_def_9,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).

tff(func_def_10,type,
    finite_card: 
      !>[X0: $tType] : ( fun(X0,bool) > nat ) ).

tff(func_def_11,type,
    pi: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * fun(X0,fun(X1,bool)) ) > fun(fun(X0,X1),bool) ) ).

tff(func_def_12,type,
    one_one: 
      !>[X0: $tType] : X0 ).

tff(func_def_13,type,
    plus_plus: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_14,type,
    hilbert_inv_into: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * fun(X0,X1) * X1 ) > X0 ) ).

tff(func_def_15,type,
    if: 
      !>[X0: $tType] : fun(bool,fun(X0,fun(X0,X0))) ).

tff(func_def_16,type,
    ord_less: 
      !>[X0: $tType] : fun(X0,fun(X0,bool)) ).

tff(func_def_17,type,
    top_top: 
      !>[X0: $tType] : X0 ).

tff(func_def_18,type,
    product_Pair: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).

tff(func_def_19,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_20,type,
    fFalse: bool ).

tff(func_def_21,type,
    fTrue: bool ).

tff(func_def_22,type,
    fequal: 
      !>[X0: $tType] : fun(X0,fun(X0,bool)) ).

tff(func_def_23,type,
    f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_24,type,
    lab: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_25,type,
    lba: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_26,type,
    p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_27,type,
    a: arrow_411405190le_alt ).

tff(func_def_28,type,
    b: arrow_411405190le_alt ).

tff(func_def_29,type,
    c: arrow_411405190le_alt ).

tff(func_def_30,type,
    d: arrow_411405190le_alt ).

tff(func_def_31,type,
    e: arrow_411405190le_alt ).

tff(func_def_32,type,
    h: fun(arrow_159774573e_indi,nat) ).

tff(func_def_33,type,
    n: nat ).

tff(func_def_34,type,
    sK15: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_35,type,
    sK16: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_36,type,
    sK17: nat ).

tff(func_def_37,type,
    sK18: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_38,type,
    sK19: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_39,type,
    sK20: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_40,type,
    sK21: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_41,type,
    sK22: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_42,type,
    sK23: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_43,type,
    sK24: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_44,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_45,type,
    sK26: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_46,type,
    sK27: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_47,type,
    sK28: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_48,type,
    sK29: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_49,type,
    sK30: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_50,type,
    sK31: nat ).

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

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

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

tff(pred_def_4,type,
    cancel146912293up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_5,type,
    ordere779506340up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_6,type,
    ordere236663937imp_le: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    ordere223160158up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_9,type,
    arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_10,type,
    inj_on: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > $o ) ).

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

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

tff(pred_def_13,type,
    pp: bool > $o ).

tff(pred_def_14,type,
    sP0: arrow_159774573e_indi > $o ).

tff(pred_def_15,type,
    sP1: arrow_159774573e_indi > $o ).

tff(pred_def_16,type,
    sP2: arrow_159774573e_indi > $o ).

tff(pred_def_17,type,
    sP3: arrow_159774573e_indi > $o ).

tff(pred_def_18,type,
    sP4: arrow_159774573e_indi > $o ).

tff(pred_def_19,type,
    sP5: arrow_159774573e_indi > $o ).

tff(pred_def_20,type,
    sP6: arrow_159774573e_indi > $o ).

tff(pred_def_21,type,
    sP7: arrow_159774573e_indi > $o ).

tff(pred_def_22,type,
    sP8: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).

tff(pred_def_23,type,
    sP9: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_24,type,
    sP10: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_25,type,
    sP11: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_26,type,
    sP12: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_27,type,
    sP13: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).

tff(pred_def_28,type,
    sP14: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(f3606,plain,
    $false,
    inference(avatar_sat_refutation,[],[f696,f701,f706,f711,f716,f721,f726,f731,f736,f741,f746,f751,f756,f760,f764,f768,f772,f776,f780,f784,f788,f792,f796,f800,f807,f812,f817,f822,f827,f831,f835,f839,f844,f852,f860,f864,f869,f874,f879,f884,f889,f894,f899,f904,f908,f912,f916,f929,f936,f940,f944,f948,f952,f956,f975,f980,f987,f992,f996,f1002,f1006,f1010,f1014,f1018,f1057,f1061,f1065,f1155,f1159,f1163,f1167,f1171,f1175,f1179,f1183,f1188,f1200,f1205,f1209,f1214,f1222,f1227,f1235,f1239,f1243,f1247,f1283,f1371,f1375,f1380,f1384,f1389,f1402,f1408,f1412,f1420,f1426,f1433,f1437,f1441,f1450,f1454,f1460,f1464,f1468,f1472,f1510,f1514,f1519,f1526,f1531,f1538,f1543,f1550,f1555,f1559,f1566,f1571,f1578,f1583,f1590,f1594,f1600,f1604,f1628,f1633,f1640,f1647,f1655,f1659,f1663,f1695,f1699,f1722,f1727,f1731,f1741,f1745,f1751,f1755,f1821,f1828,f1832,f1836,f1851,f1856,f1869,f1874,f1882,f1888,f1892,f1910,f1914,f1950,f1956,f1974,f1980,f1984,f2007,f2013,f2035,f2040,f2047,f2052,f2064,f2068,f2074,f2096,f2102,f2127,f2133,f2159,f2165,f2169,f2197,f2203,f2232,f2238,f2264,f2268,f2272,f2276,f2280,f2310,f2314,f2322,f2326,f2330,f2344,f2351,f2358,f2383,f2387,f2391,f2395,f2399,f2403,f2449,f2454,f2459,f2464,f2470,f2475,f2489,f2499,f2504,f2518,f2523,f2532,f2537,f2551,f2556,f2565,f2570,f2584,f2589,f2593,f2602,f2607,f2611,f2616,f2620,f2625,f2629,f2633,f2638,f2642,f2647,f2651,f2656,f2660,f2665,f2671,f2675,f2680,f2687,f2692,f2703,f2708,f2716,f2720,f2725,f2729,f2733,f2738,f2794,f2798,f2802,f2806,f2874,f2878,f2882,f2886,f2938,f2942,f2946,f2950,f2995,f3000,f3004,f3008,f3056,f3060,f3064,f3448,f3452,f3456,f3524,f3528,f3533,f3570,f3579,f3589,f3594,f3599,f3605]) ).

tff(f3605,plain,
    ( ~ spl32_14
    | spl32_276 ),
    inference(avatar_contradiction_clause,[],[f3602]) ).

tff(f3602,plain,
    ( $false
    | ~ spl32_14
    | spl32_276 ),
    inference(resolution,[],[f3593,f759]) ).

tff(f759,plain,
    ( ! [X0: nat] : ord_less_eq(nat,X0,X0)
    | ~ spl32_14 ),
    inference(avatar_component_clause,[],[f758]) ).

tff(f758,plain,
    ( spl32_14
  <=> ! [X0: nat] : ord_less_eq(nat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_14])]) ).

tff(f3593,plain,
    ( ~ ord_less_eq(nat,n,n)
    | spl32_276 ),
    inference(avatar_component_clause,[],[f3591]) ).

tff(f3591,plain,
    ( spl32_276
  <=> ord_less_eq(nat,n,n) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_276])]) ).

tff(f3599,plain,
    ( ~ spl32_277
    | ~ spl32_242
    | spl32_274 ),
    inference(avatar_split_clause,[],[f3582,f3576,f2718,f3596]) ).

tff(f3596,plain,
    ( spl32_277
  <=> ord_less_eq(nat,n,sK17) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_277])]) ).

tff(f2718,plain,
    ( spl32_242
  <=> ! [X1: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
        | ~ ord_less_eq(nat,X1,sK17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_242])]) ).

tff(f3576,plain,
    ( spl32_274
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),lab),lba))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_274])]) ).

tff(f3582,plain,
    ( ~ ord_less_eq(nat,n,sK17)
    | ~ spl32_242
    | spl32_274 ),
    inference(resolution,[],[f3578,f2719]) ).

tff(f2719,plain,
    ( ! [X1: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
        | ~ ord_less_eq(nat,X1,sK17) )
    | ~ spl32_242 ),
    inference(avatar_component_clause,[],[f2718]) ).

tff(f3578,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),lab),lba)))
    | spl32_274 ),
    inference(avatar_component_clause,[],[f3576]) ).

tff(f3594,plain,
    ( ~ spl32_276
    | ~ spl32_244
    | spl32_274 ),
    inference(avatar_split_clause,[],[f3581,f3576,f2727,f3591]) ).

tff(f2727,plain,
    ( spl32_244
  <=> ! [X0: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba)))
        | ~ ord_less_eq(nat,X0,n) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_244])]) ).

tff(f3581,plain,
    ( ~ ord_less_eq(nat,n,n)
    | ~ spl32_244
    | spl32_274 ),
    inference(resolution,[],[f3578,f2728]) ).

tff(f2728,plain,
    ( ! [X0: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba)))
        | ~ ord_less_eq(nat,X0,n) )
    | ~ spl32_244 ),
    inference(avatar_component_clause,[],[f2727]) ).

tff(f3589,plain,
    ( ~ spl32_275
    | ~ spl32_245
    | spl32_274 ),
    inference(avatar_split_clause,[],[f3580,f3576,f2731,f3586]) ).

tff(f3586,plain,
    ( spl32_275
  <=> ord_less_eq(nat,n,sK31) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_275])]) ).

tff(f2731,plain,
    ( spl32_245
  <=> ! [X1: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
        | ~ ord_less_eq(nat,X1,sK31) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_245])]) ).

tff(f3580,plain,
    ( ~ ord_less_eq(nat,n,sK31)
    | ~ spl32_245
    | spl32_274 ),
    inference(resolution,[],[f3578,f2732]) ).

tff(f2732,plain,
    ( ! [X1: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
        | ~ ord_less_eq(nat,X1,sK31) )
    | ~ spl32_245 ),
    inference(avatar_component_clause,[],[f2731]) ).

tff(f3579,plain,
    ( ~ spl32_274
    | spl32_233 ),
    inference(avatar_split_clause,[],[f440,f2662,f3576]) ).

tff(f2662,plain,
    ( spl32_233
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_233])]) ).

tff(f440,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e)))))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),lab),lba))) ),
    inference(cnf_transformation,[],[f311]) ).

tff(f311,plain,
    ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e)))))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),lab),lba))) )
    & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),lab),lba)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))) ) ),
    inference(nnf_transformation,[],[f10]) ).

tff(f10,axiom,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e)))))
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),lab),lba))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).

tff(f3570,plain,
    ( ~ spl32_272
    | spl32_273 ),
    inference(avatar_split_clause,[],[f435,f3567,f3563]) ).

tff(f3563,plain,
    ( spl32_272
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_272])]) ).

tff(f3567,plain,
    ( spl32_273
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_273])]) ).

tff(f435,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e)))))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f309,plain,
    ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))) )
    & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e)))))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ) ),
    inference(nnf_transformation,[],[f13]) ).

tff(f13,axiom,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_PW) ).

tff(f3533,plain,
    spl32_271,
    inference(avatar_split_clause,[],[f434,f3530]) ).

tff(f3530,plain,
    ( spl32_271
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_271])]) ).

tff(f434,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))),
    inference(cnf_transformation,[],[f12]) ).

tff(f12,axiom,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096) ).

tff(f3528,plain,
    ( spl32_270
    | spl32_1
    | ~ spl32_48 ),
    inference(avatar_split_clause,[],[f3252,f914,f693,f3526]) ).

tff(f3526,plain,
    ( spl32_270
  <=> ! [X0: bool,X1: bool] :
        ( ~ pp(X0)
        | ( X0 = X1 )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_270])]) ).

tff(f693,plain,
    ( spl32_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_1])]) ).

tff(f914,plain,
    ( spl32_48
  <=> ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_48])]) ).

tff(f3252,plain,
    ( ! [X0: bool,X1: bool] :
        ( ~ pp(X0)
        | ( X0 = X1 )
        | ( fFalse = X1 ) )
    | spl32_1
    | ~ spl32_48 ),
    inference(superposition,[],[f695,f915]) ).

tff(f915,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) )
    | ~ spl32_48 ),
    inference(avatar_component_clause,[],[f914]) ).

tff(f695,plain,
    ( ~ pp(fFalse)
    | spl32_1 ),
    inference(avatar_component_clause,[],[f693]) ).

tff(f3524,plain,
    spl32_269,
    inference(avatar_split_clause,[],[f433,f3521]) ).

tff(f3521,plain,
    ( spl32_269
  <=> member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))),arrow_610318064e_Prof) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_269])]) ).

tff(f433,plain,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))),arrow_610318064e_Prof),
    inference(cnf_transformation,[],[f16]) ).

tff(f16,axiom,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))),arrow_610318064e_Prof),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096) ).

tff(f3456,plain,
    spl32_268,
    inference(avatar_split_clause,[],[f642,f3454]) ).

tff(f3454,plain,
    ( spl32_268
  <=> ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X3 = X4 )
        | ( X2 = X5 )
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_268])]) ).

tff(f642,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f399]) ).

tff(f399,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5))) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f397,f398]) ).

tff(f398,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ? [X6: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) ) )
     => ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f397,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ? [X6: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(nnf_transformation,[],[f276]) ).

tff(f276,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X6: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(flattening,[],[f275]) ).

tff(f275,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X6: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(ennf_transformation,[],[f201]) ).

tff(f201,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( X4 != X5 )
     => ( ( X2 != X3 )
       => ( ( X2 != X5 )
         => ( ( X3 != X4 )
           => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
             => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
               => ( ! [X6: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
                    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X17: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X13: arrow_411405190le_alt,X14: arrow_411405190le_alt,X15: arrow_411405190le_alt,X16: arrow_411405190le_alt] :
      ( ( X15 != X16 )
     => ( ( X13 != X14 )
       => ( ( X13 != X16 )
         => ( ( X14 != X15 )
           => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9,arrow_610318064e_Prof)
             => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X17,arrow_610318064e_Prof)
               => ( ! [X18: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X9,X18))
                    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X14,X13),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X17,X18)) )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X9))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X14,X13),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X17)) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__C2_C) ).

tff(f3452,plain,
    spl32_267,
    inference(avatar_split_clause,[],[f641,f3450]) ).

tff(f3450,plain,
    ( spl32_267
  <=> ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X3 = X4 )
        | ( X2 = X5 )
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_267])]) ).

tff(f641,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f399]) ).

tff(f3448,plain,
    spl32_266,
    inference(avatar_split_clause,[],[f640,f3446]) ).

tff(f3446,plain,
    ( spl32_266
  <=> ! [X5: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X3 = X4 )
        | ( X2 = X5 )
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_266])]) ).

tff(f640,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f399]) ).

tff(f3064,plain,
    spl32_265,
    inference(avatar_split_clause,[],[f639,f3062]) ).

tff(f3062,plain,
    ( spl32_265
  <=> ! [X5: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X3 = X4 )
        | ( X2 = X5 )
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_265])]) ).

tff(f639,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK29(X0,X1,X2,X3,X4,X5)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK29(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f399]) ).

tff(f3060,plain,
    spl32_264,
    inference(avatar_split_clause,[],[f638,f3058]) ).

tff(f3058,plain,
    ( spl32_264
  <=> ! [X5: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X3 = X4 )
        | ( X2 = X5 )
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_264])]) ).

tff(f638,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f396]) ).

tff(f396,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5))) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f394,f395]) ).

tff(f395,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ? [X6: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) ) )
     => ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f394,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ? [X6: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(nnf_transformation,[],[f274]) ).

tff(f274,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ? [X6: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(flattening,[],[f273]) ).

tff(f273,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ? [X6: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(ennf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( X4 != X5 )
     => ( ( X2 != X3 )
       => ( ( X2 != X5 )
         => ( ( X3 != X4 )
           => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
             => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
               => ( ! [X6: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
                    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
                   => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X17: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X13: arrow_411405190le_alt,X14: arrow_411405190le_alt,X15: arrow_411405190le_alt,X16: arrow_411405190le_alt] :
      ( ( X15 != X16 )
     => ( ( X13 != X14 )
       => ( ( X13 != X16 )
         => ( ( X14 != X15 )
           => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9,arrow_610318064e_Prof)
             => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X17,arrow_610318064e_Prof)
               => ( ! [X18: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X9,X18))
                    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X14,X13),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X17,X18)) )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X9))
                   => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X14,X13),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X17)) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__C1_C) ).

tff(f3056,plain,
    spl32_263,
    inference(avatar_split_clause,[],[f637,f3054]) ).

tff(f3054,plain,
    ( spl32_263
  <=> ! [X5: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X3 = X4 )
        | ( X2 = X5 )
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_263])]) ).

tff(f637,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK28(X0,X1,X2,X3,X4,X5)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK28(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X3 = X4 )
      | ( X2 = X5 )
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f396]) ).

tff(f3008,plain,
    spl32_262,
    inference(avatar_split_clause,[],[f616,f3006]) ).

tff(f3006,plain,
    ( spl32_262
  <=> ! [X2: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X4 )
        | ( X2 = X3 )
        | ( X3 = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_262])]) ).

tff(f616,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(cnf_transformation,[],[f382]) ).

tff(f382,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4))) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f380,f381]) ).

tff(f381,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ? [X5: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X5))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X5))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) ) )
     => ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f380,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ? [X5: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X5))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X5))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(nnf_transformation,[],[f270]) ).

tff(f270,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X5: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X5)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(flattening,[],[f269]) ).

tff(f269,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X5: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X5)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(ennf_transformation,[],[f195]) ).

tff(f195,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( X3 != X4 )
     => ( ( X2 != X3 )
       => ( ( X2 != X4 )
         => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
           => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
             => ( ! [X5: arrow_159774573e_indi] :
                    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X5)) )
               => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
                <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ) ) ) ) ) ) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X17: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X19: arrow_411405190le_alt,X15: arrow_411405190le_alt,X16: arrow_411405190le_alt] :
      ( ( X15 != X16 )
     => ( ( X15 != X19 )
       => ( ( X16 != X19 )
         => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9,arrow_610318064e_Prof)
           => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X17,arrow_610318064e_Prof)
             => ( ! [X18: arrow_159774573e_indi] :
                    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X9,X18))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X15,X19),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X17,X18)) )
               => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X9))
                <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X15,X19),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X17)) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__C4_C) ).

tff(f3004,plain,
    spl32_261,
    inference(avatar_split_clause,[],[f615,f3002]) ).

tff(f3002,plain,
    ( spl32_261
  <=> ! [X2: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X4 )
        | ( X2 = X3 )
        | ( X3 = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_261])]) ).

tff(f615,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(cnf_transformation,[],[f382]) ).

tff(f3000,plain,
    spl32_260,
    inference(avatar_split_clause,[],[f614,f2998]) ).

tff(f2998,plain,
    ( spl32_260
  <=> ! [X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X4 )
        | ( X2 = X3 )
        | ( X3 = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_260])]) ).

tff(f614,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(cnf_transformation,[],[f382]) ).

tff(f2995,plain,
    spl32_259,
    inference(avatar_split_clause,[],[f613,f2993]) ).

tff(f2993,plain,
    ( spl32_259
  <=> ! [X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X4 )
        | ( X2 = X3 )
        | ( X3 = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_259])]) ).

tff(f613,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK27(X0,X1,X2,X3,X4)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK27(X0,X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ( X3 = X4 ) ),
    inference(cnf_transformation,[],[f382]) ).

tff(f2950,plain,
    spl32_258,
    inference(avatar_split_clause,[],[f646,f2948]) ).

tff(f2948,plain,
    ( spl32_258
  <=> ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_258])]) ).

tff(f646,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f402]) ).

tff(f402,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5))) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f400,f401]) ).

tff(f401,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ? [X6: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) ) )
     => ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f400,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ? [X6: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6)) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(nnf_transformation,[],[f278]) ).

tff(f278,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X6: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(flattening,[],[f277]) ).

tff(f277,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X6: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(ennf_transformation,[],[f202]) ).

tff(f202,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ( X4 != X5 )
     => ( ( X2 != X3 )
       => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
         => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
           => ( ! [X6: arrow_159774573e_indi] :
                  ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X6))
                <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X6)) )
             => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
              <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ) ) ) ) ) ),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X17: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X13: arrow_411405190le_alt,X14: arrow_411405190le_alt,X15: arrow_411405190le_alt,X16: arrow_411405190le_alt] :
      ( ( X15 != X16 )
     => ( ( X13 != X14 )
       => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9,arrow_610318064e_Prof)
         => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X17,arrow_610318064e_Prof)
           => ( ! [X18: arrow_159774573e_indi] :
                  ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X9,X18))
                <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X14,X13),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X17,X18)) )
             => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X9))
              <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X14,X13),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X17)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_pairwise__neutrality) ).

tff(f2946,plain,
    spl32_257,
    inference(avatar_split_clause,[],[f645,f2944]) ).

tff(f2944,plain,
    ( spl32_257
  <=> ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_257])]) ).

tff(f645,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f402]) ).

tff(f2942,plain,
    spl32_256,
    inference(avatar_split_clause,[],[f644,f2940]) ).

tff(f2940,plain,
    ( spl32_256
  <=> ! [X5: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_256])]) ).

tff(f644,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f402]) ).

tff(f2938,plain,
    spl32_255,
    inference(avatar_split_clause,[],[f643,f2936]) ).

tff(f2936,plain,
    ( spl32_255
  <=> ! [X5: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 )
        | ( X4 = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_255])]) ).

tff(f643,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK30(X0,X1,X2,X3,X4,X5)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X5,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK30(X0,X1,X2,X3,X4,X5)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f402]) ).

tff(f2886,plain,
    spl32_254,
    inference(avatar_split_clause,[],[f594,f2884]) ).

tff(f2884,plain,
    ( spl32_254
  <=> ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_254])]) ).

tff(f594,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f371]) ).

tff(f371,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3))) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f369,f370]) ).

tff(f370,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ? [X4: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4)) ) )
     => ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f369,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ? [X4: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4)) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(nnf_transformation,[],[f266]) ).

tff(f266,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X4: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(flattening,[],[f265]) ).

tff(f265,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X4: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(ennf_transformation,[],[f192]) ).

tff(f192,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( X2 != X3 )
     => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
       => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
         => ( ! [X4: arrow_159774573e_indi] :
                ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
              <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4)) )
           => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
            <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ) ) ) ) ),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X17: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X15: arrow_411405190le_alt,X16: arrow_411405190le_alt] :
      ( ( X15 != X16 )
     => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X9,arrow_610318064e_Prof)
       => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X17,arrow_610318064e_Prof)
         => ( ! [X18: arrow_159774573e_indi] :
                ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X9,X18))
              <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X15,X16),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X17,X18)) )
           => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X9))
            <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X15,X16),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X17)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__C3_C) ).

tff(f2882,plain,
    spl32_253,
    inference(avatar_split_clause,[],[f593,f2880]) ).

tff(f2880,plain,
    ( spl32_253
  <=> ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_253])]) ).

tff(f593,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f371]) ).

tff(f2878,plain,
    spl32_252,
    inference(avatar_split_clause,[],[f592,f2876]) ).

tff(f2876,plain,
    ( spl32_252
  <=> ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_252])]) ).

tff(f592,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f371]) ).

tff(f2874,plain,
    spl32_251,
    inference(avatar_split_clause,[],[f591,f2872]) ).

tff(f2872,plain,
    ( spl32_251
  <=> ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_251])]) ).

tff(f591,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK26(X0,X1,X2,X3)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK26(X0,X1,X2,X3)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f371]) ).

tff(f2806,plain,
    spl32_250,
    inference(avatar_split_clause,[],[f486,f2804]) ).

tff(f2804,plain,
    ( spl32_250
  <=> ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ~ arrow_1958449194le_IIA(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_250])]) ).

tff(f486,plain,
    ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ~ arrow_1958449194le_IIA(X0) ),
    inference(cnf_transformation,[],[f327]) ).

tff(f327,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
              ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
                  ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
                      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2)) )
                    & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
                      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) )
                  | ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
                      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4))) )
                    & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
                      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4))) ) ) )
              | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof) )
          | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof) )
      | ~ arrow_1958449194le_IIA(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f325,f326]) ).

tff(f326,plain,
    ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ? [X5: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,X5))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,X5))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) ) )
     => ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f325,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
              ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
                  ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
                      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2)) )
                    & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
                      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) )
                  | ? [X5: arrow_159774573e_indi] :
                      ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,X5))
                        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) )
                      & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,X5))
                        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5)) ) ) )
              | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof) )
          | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof) )
      | ~ arrow_1958449194le_IIA(X0) ),
    inference(nnf_transformation,[],[f241]) ).

tff(f241,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
              ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
                  ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2)) )
                  | ? [X5: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5))
                    <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,X5)) ) )
              | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof) )
          | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof) )
      | ~ arrow_1958449194le_IIA(X0) ),
    inference(ennf_transformation,[],[f210]) ).

tff(f210,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( arrow_1958449194le_IIA(X0)
     => ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
         => ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
              ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
             => ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
                  ( ! [X5: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5))
                    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,X5)) )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2)) ) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f153]) ).

tff(f153,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( arrow_1958449194le_IIA(X0)
    <=> ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
         => ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
              ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
             => ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
                  ( ! [X5: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X5))
                    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,X5)) )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2)) ) ) ) ) ),
    inference(rectify,[],[f45]) ).

tff(f45,axiom,
    ! [X27: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( arrow_1958449194le_IIA(X27)
    <=> ! [X28: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X28,arrow_610318064e_Prof)
         => ! [X29: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
              ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X29,arrow_610318064e_Prof)
             => ! [X11: arrow_411405190le_alt,X12: arrow_411405190le_alt] :
                  ( ! [X30: arrow_159774573e_indi] :
                      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X11,X12),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X28,X30))
                    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X11,X12),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X29,X30)) )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X11,X12),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X27,X28))
                  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X11,X12),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X27,X29)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_IIA__def) ).

tff(f2802,plain,
    spl32_249,
    inference(avatar_split_clause,[],[f485,f2800]) ).

tff(f2800,plain,
    ( spl32_249
  <=> ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ~ arrow_1958449194le_IIA(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_249])]) ).

tff(f485,plain,
    ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ~ arrow_1958449194le_IIA(X0) ),
    inference(cnf_transformation,[],[f327]) ).

tff(f2798,plain,
    spl32_248,
    inference(avatar_split_clause,[],[f484,f2796]) ).

tff(f2796,plain,
    ( spl32_248
  <=> ! [X4: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ~ arrow_1958449194le_IIA(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_248])]) ).

tff(f484,plain,
    ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ~ arrow_1958449194le_IIA(X0) ),
    inference(cnf_transformation,[],[f327]) ).

tff(f2794,plain,
    spl32_247,
    inference(avatar_split_clause,[],[f483,f2792]) ).

tff(f2792,plain,
    ( spl32_247
  <=> ! [X4: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ~ arrow_1958449194le_IIA(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_247])]) ).

tff(f483,plain,
    ! [X2: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X2))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,sK18(X1,X2,X3,X4)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK18(X1,X2,X3,X4)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ~ arrow_1958449194le_IIA(X0) ),
    inference(cnf_transformation,[],[f327]) ).

tff(f2738,plain,
    spl32_246,
    inference(avatar_split_clause,[],[f657,f2735]) ).

tff(f2735,plain,
    ( spl32_246
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK31,one_one(nat)))),lab),lba))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_246])]) ).

tff(f657,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK31,one_one(nat)))),lab),lba))),
    inference(cnf_transformation,[],[f406]) ).

tff(f406,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK31,one_one(nat)))),lab),lba)))
    & ! [X1: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
        | ~ ord_less_eq(nat,X1,sK31) )
    & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK31),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f286,f405]) ).

tff(f405,plain,
    ( ? [X0: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X0,one_one(nat)))),lab),lba)))
        & ! [X1: nat] :
            ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
            | ~ ord_less_eq(nat,X1,X0) )
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) )
   => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK31,one_one(nat)))),lab),lba)))
      & ! [X1: nat] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
          | ~ ord_less_eq(nat,X1,sK31) )
      & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK31),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ) ),
    introduced(choice_axiom,[]) ).

tff(f286,plain,
    ? [X0: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X0,one_one(nat)))),lab),lba)))
      & ! [X1: nat] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
          | ~ ord_less_eq(nat,X1,X0) )
      & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    inference(ennf_transformation,[],[f208]) ).

tff(f208,plain,
    ? [X0: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X0,one_one(nat)))),lab),lba)))
      & ! [X1: nat] :
          ( ord_less_eq(nat,X1,X0)
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba))) )
      & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    inference(rectify,[],[f49]) ).

tff(f49,axiom,
    ? [X31: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X31,one_one(nat)))),lab),lba)))
      & ! [X3: nat] :
          ( ord_less_eq(nat,X3,X31)
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X3)),lab),lba))) )
      & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X31),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096) ).

tff(f2733,plain,
    spl32_245,
    inference(avatar_split_clause,[],[f656,f2731]) ).

tff(f656,plain,
    ! [X1: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
      | ~ ord_less_eq(nat,X1,sK31) ),
    inference(cnf_transformation,[],[f406]) ).

tff(f2729,plain,
    spl32_244,
    inference(avatar_split_clause,[],[f481,f2727]) ).

tff(f481,plain,
    ! [X0: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba)))
      | ~ ord_less_eq(nat,X0,n) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f239,plain,
    ! [X0: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba)))
      | ~ ord_less_eq(nat,X0,n) ),
    inference(ennf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X0: nat] :
      ( ord_less_eq(nat,X0,n)
     => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba))) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X3: nat] :
      ( ord_less_eq(nat,X3,n)
     => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X3)),lab),lba))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_n_I2_J) ).

tff(f2725,plain,
    spl32_243,
    inference(avatar_split_clause,[],[f447,f2722]) ).

tff(f2722,plain,
    ( spl32_243
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK17,one_one(nat)))),lab),lba))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_243])]) ).

tff(f447,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK17,one_one(nat)))),lab),lba))),
    inference(cnf_transformation,[],[f317]) ).

tff(f317,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK17,one_one(nat)))),lab),lba)))
    & ! [X1: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
        | ~ ord_less_eq(nat,X1,sK17) )
    & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK17),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f215,f316]) ).

tff(f316,plain,
    ( ? [X0: nat] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X0,one_one(nat)))),lab),lba)))
        & ! [X1: nat] :
            ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
            | ~ ord_less_eq(nat,X1,X0) )
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) )
   => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,sK17,one_one(nat)))),lab),lba)))
      & ! [X1: nat] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
          | ~ ord_less_eq(nat,X1,sK17) )
      & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK17),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ) ),
    introduced(choice_axiom,[]) ).

tff(f215,plain,
    ? [X0: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X0,one_one(nat)))),lab),lba)))
      & ! [X1: nat] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
          | ~ ord_less_eq(nat,X1,X0) )
      & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    inference(flattening,[],[f214]) ).

tff(f214,plain,
    ? [X0: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X0,one_one(nat)))),lab),lba)))
      & ! [X1: nat] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
          | ~ ord_less_eq(nat,X1,X0) )
      & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    inference(ennf_transformation,[],[f124]) ).

tff(f124,plain,
    ~ ! [X0: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))))
       => ( ! [X1: nat] :
              ( ord_less_eq(nat,X1,X0)
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba))) )
         => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X0,one_one(nat)))),lab),lba))) ) ),
    inference(rectify,[],[f50]) ).

tff(f50,axiom,
    ~ ! [X31: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X31),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))))
       => ( ! [X3: nat] :
              ( ord_less_eq(nat,X3,X31)
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X3)),lab),lba))) )
         => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,X31,one_one(nat)))),lab),lba))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

tff(f2720,plain,
    spl32_242,
    inference(avatar_split_clause,[],[f446,f2718]) ).

tff(f446,plain,
    ! [X1: nat] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X1)),lab),lba)))
      | ~ ord_less_eq(nat,X1,sK17) ),
    inference(cnf_transformation,[],[f317]) ).

tff(f2716,plain,
    spl32_241,
    inference(avatar_split_clause,[],[f432,f2713]) ).

tff(f2713,plain,
    ( spl32_241
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,n,one_one(nat)))),lab),lba))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_241])]) ).

tff(f432,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,n,one_one(nat)))),lab),lba))),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,axiom,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),plus_plus(nat,n,one_one(nat)))),lab),lba))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_n_I3_J) ).

tff(f2708,plain,
    ( spl32_240
    | ~ spl32_132
    | ~ spl32_239 ),
    inference(avatar_split_clause,[],[f2704,f2701,f1661,f2706]) ).

tff(f2706,plain,
    ( spl32_240
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP5(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_240])]) ).

tff(f1661,plain,
    ( spl32_132
  <=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_132])]) ).

tff(f2701,plain,
    ( spl32_239
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP5(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_239])]) ).

tff(f2704,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP5(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_132
    | ~ spl32_239 ),
    inference(forward_demodulation,[],[f2702,f1662]) ).

tff(f1662,plain,
    ( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
    | ~ spl32_132 ),
    inference(avatar_component_clause,[],[f1661]) ).

tff(f2702,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP5(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) )
    | ~ spl32_239 ),
    inference(avatar_component_clause,[],[f2701]) ).

tff(f2703,plain,
    spl32_239,
    inference(avatar_split_clause,[],[f539,f2701]) ).

tff(f539,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP5(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f347,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP5(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          & ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
            | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
        | ~ sP5(X0) ) ),
    inference(flattening,[],[f346]) ).

tff(f346,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP5(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          & ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
            | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
        | ~ sP5(X0) ) ),
    inference(nnf_transformation,[],[f294]) ).

tff(f294,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP5(X0)
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

tff(f2692,plain,
    ( spl32_238
    | ~ spl32_132
    | ~ spl32_237 ),
    inference(avatar_split_clause,[],[f2688,f2685,f1661,f2690]) ).

tff(f2690,plain,
    ( spl32_238
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP2(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_238])]) ).

tff(f2685,plain,
    ( spl32_237
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP2(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_237])]) ).

tff(f2688,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP2(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_132
    | ~ spl32_237 ),
    inference(forward_demodulation,[],[f2686,f1662]) ).

tff(f2686,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP2(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) )
    | ~ spl32_237 ),
    inference(avatar_component_clause,[],[f2685]) ).

tff(f2687,plain,
    spl32_237,
    inference(avatar_split_clause,[],[f519,f2685]) ).

tff(f519,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP2(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f340,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP2(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          & ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
            | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
        | ~ sP2(X0) ) ),
    inference(flattening,[],[f339]) ).

tff(f339,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP2(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          & ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
            | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
        | ~ sP2(X0) ) ),
    inference(nnf_transformation,[],[f290]) ).

tff(f290,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP2(X0)
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

tff(f2680,plain,
    ( spl32_236
    | ~ spl32_132
    | ~ spl32_235 ),
    inference(avatar_split_clause,[],[f2676,f2673,f1661,f2678]) ).

tff(f2678,plain,
    ( spl32_236
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP0(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_236])]) ).

tff(f2673,plain,
    ( spl32_235
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP0(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_235])]) ).

tff(f2676,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP0(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_132
    | ~ spl32_235 ),
    inference(forward_demodulation,[],[f2674,f1662]) ).

tff(f2674,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP0(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) )
    | ~ spl32_235 ),
    inference(avatar_component_clause,[],[f2673]) ).

tff(f2675,plain,
    spl32_235,
    inference(avatar_split_clause,[],[f499,f2673]) ).

tff(f499,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP0(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ),
    inference(cnf_transformation,[],[f333]) ).

tff(f333,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP0(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          & ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
            | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f332]) ).

tff(f332,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP0(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          & ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
            | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f287]) ).

tff(f287,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP0(X0)
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
          | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f2671,plain,
    spl32_234,
    inference(avatar_split_clause,[],[f451,f2669]) ).

tff(f2669,plain,
    ( spl32_234
  <=> ! [X0: nat] : member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba),arrow_610318064e_Prof) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_234])]) ).

tff(f451,plain,
    ! [X0: nat] : member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba),arrow_610318064e_Prof),
    inference(cnf_transformation,[],[f128]) ).

tff(f128,plain,
    ! [X0: nat] : member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X0)),lab),lba),arrow_610318064e_Prof),
    inference(rectify,[],[f29]) ).

tff(f29,axiom,
    ! [X20: nat] : member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),X20)),lab),lba),arrow_610318064e_Prof),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_PiProf) ).

tff(f2665,plain,
    ~ spl32_233,
    inference(avatar_split_clause,[],[f407,f2662]) ).

tff(f407,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))),
    inference(cnf_transformation,[],[f121]) ).

tff(f121,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))),
    inference(flattening,[],[f120]) ).

tff(f120,negated_conjecture,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))),
    inference(negated_conjecture,[],[f119]) ).

tff(f119,conjecture,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,ord_less(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_424895264_mktop,p),e)),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combs(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(bool,fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,if(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(arrow_159774573e_indi,nat,bool,combb(nat,fun(nat,bool),arrow_159774573e_indi,fequal(nat),h),n)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_1158827142_above,p),c),e)),combc(arrow_159774573e_indi,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,arrow_276188178_mkbot,p),e))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f2660,plain,
    ( spl32_232
    | ~ spl32_54
    | ~ spl32_116 ),
    inference(avatar_split_clause,[],[f1747,f1553,f950,f2658]) ).

tff(f2658,plain,
    ( spl32_232
  <=> ! [X0: arrow_411405190le_alt] : sP12(sK16,X0,a,X0,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_232])]) ).

tff(f950,plain,
    ( spl32_54
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
        ( sP12(X0,X3,X2,X3,X4)
        | ~ sP11(X0,X4,X2,X3,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_54])]) ).

tff(f1553,plain,
    ( spl32_116
  <=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(sK16,b,a,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_116])]) ).

tff(f1747,plain,
    ( ! [X0: arrow_411405190le_alt] : sP12(sK16,X0,a,X0,b)
    | ~ spl32_54
    | ~ spl32_116 ),
    inference(resolution,[],[f1554,f951]) ).

tff(f951,plain,
    ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
        ( ~ sP11(X0,X4,X2,X3,X3)
        | sP12(X0,X3,X2,X3,X4) )
    | ~ spl32_54 ),
    inference(avatar_component_clause,[],[f950]) ).

tff(f1554,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(sK16,b,a,X0,X1)
    | ~ spl32_116 ),
    inference(avatar_component_clause,[],[f1553]) ).

tff(f2656,plain,
    ( spl32_231
    | ~ spl32_132
    | ~ spl32_230 ),
    inference(avatar_split_clause,[],[f2652,f2649,f1661,f2654]) ).

tff(f2654,plain,
    ( spl32_231
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP5(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_231])]) ).

tff(f2649,plain,
    ( spl32_230
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP5(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_230])]) ).

tff(f2652,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP5(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
    | ~ spl32_132
    | ~ spl32_230 ),
    inference(forward_demodulation,[],[f2650,f1662]) ).

tff(f2650,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP5(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) )
    | ~ spl32_230 ),
    inference(avatar_component_clause,[],[f2649]) ).

tff(f2651,plain,
    spl32_230,
    inference(avatar_split_clause,[],[f537,f2649]) ).

tff(f537,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP5(X0)
      | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f2647,plain,
    ( spl32_229
    | ~ spl32_132
    | ~ spl32_228 ),
    inference(avatar_split_clause,[],[f2643,f2640,f1661,f2645]) ).

tff(f2645,plain,
    ( spl32_229
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP5(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_229])]) ).

tff(f2640,plain,
    ( spl32_228
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP5(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_228])]) ).

tff(f2643,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP5(X0) )
    | ~ spl32_132
    | ~ spl32_228 ),
    inference(forward_demodulation,[],[f2641,f1662]) ).

tff(f2641,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP5(X0) )
    | ~ spl32_228 ),
    inference(avatar_component_clause,[],[f2640]) ).

tff(f2642,plain,
    spl32_228,
    inference(avatar_split_clause,[],[f534,f2640]) ).

tff(f534,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
      | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ sP5(X0) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f2638,plain,
    ( spl32_227
    | ~ spl32_132
    | ~ spl32_226 ),
    inference(avatar_split_clause,[],[f2634,f2631,f1661,f2636]) ).

tff(f2636,plain,
    ( spl32_227
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP2(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_227])]) ).

tff(f2631,plain,
    ( spl32_226
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP2(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_226])]) ).

tff(f2634,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP2(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
    | ~ spl32_132
    | ~ spl32_226 ),
    inference(forward_demodulation,[],[f2632,f1662]) ).

tff(f2632,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP2(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) )
    | ~ spl32_226 ),
    inference(avatar_component_clause,[],[f2631]) ).

tff(f2633,plain,
    spl32_226,
    inference(avatar_split_clause,[],[f517,f2631]) ).

tff(f517,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP2(X0)
      | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f2629,plain,
    ( spl32_225
    | ~ spl32_54
    | ~ spl32_108 ),
    inference(avatar_split_clause,[],[f1701,f1508,f950,f2627]) ).

tff(f2627,plain,
    ( spl32_225
  <=> ! [X0: arrow_411405190le_alt] : sP12(sK15,X0,b,X0,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_225])]) ).

tff(f1508,plain,
    ( spl32_108
  <=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(sK15,a,b,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_108])]) ).

tff(f1701,plain,
    ( ! [X0: arrow_411405190le_alt] : sP12(sK15,X0,b,X0,a)
    | ~ spl32_54
    | ~ spl32_108 ),
    inference(resolution,[],[f1509,f951]) ).

tff(f1509,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(sK15,a,b,X0,X1)
    | ~ spl32_108 ),
    inference(avatar_component_clause,[],[f1508]) ).

tff(f2625,plain,
    ( spl32_224
    | ~ spl32_132
    | ~ spl32_223 ),
    inference(avatar_split_clause,[],[f2621,f2618,f1661,f2623]) ).

tff(f2623,plain,
    ( spl32_224
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_224])]) ).

tff(f2618,plain,
    ( spl32_223
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_223])]) ).

tff(f2621,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP2(X0) )
    | ~ spl32_132
    | ~ spl32_223 ),
    inference(forward_demodulation,[],[f2619,f1662]) ).

tff(f2619,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP2(X0) )
    | ~ spl32_223 ),
    inference(avatar_component_clause,[],[f2618]) ).

tff(f2620,plain,
    spl32_223,
    inference(avatar_split_clause,[],[f514,f2618]) ).

tff(f514,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
      | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f2616,plain,
    ( spl32_222
    | ~ spl32_132
    | ~ spl32_221 ),
    inference(avatar_split_clause,[],[f2612,f2609,f1661,f2614]) ).

tff(f2614,plain,
    ( spl32_222
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP0(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_222])]) ).

tff(f2609,plain,
    ( spl32_221
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP0(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_221])]) ).

tff(f2612,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | sP0(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) )
    | ~ spl32_132
    | ~ spl32_221 ),
    inference(forward_demodulation,[],[f2610,f1662]) ).

tff(f2610,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP0(X0)
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) )
    | ~ spl32_221 ),
    inference(avatar_component_clause,[],[f2609]) ).

tff(f2611,plain,
    spl32_221,
    inference(avatar_split_clause,[],[f497,f2609]) ).

tff(f497,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP0(X0)
      | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ),
    inference(cnf_transformation,[],[f333]) ).

tff(f2607,plain,
    ( spl32_220
    | ~ spl32_132
    | ~ spl32_219 ),
    inference(avatar_split_clause,[],[f2603,f2600,f1661,f2605]) ).

tff(f2605,plain,
    ( spl32_220
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_220])]) ).

tff(f2600,plain,
    ( spl32_219
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_219])]) ).

tff(f2603,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e),c))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP0(X0) )
    | ~ spl32_132
    | ~ spl32_219 ),
    inference(forward_demodulation,[],[f2601,f1662]) ).

tff(f2601,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
        | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP0(X0) )
    | ~ spl32_219 ),
    inference(avatar_component_clause,[],[f2600]) ).

tff(f2602,plain,
    spl32_219,
    inference(avatar_split_clause,[],[f494,f2600]) ).

tff(f494,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
      | ( n != aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f333]) ).

tff(f2593,plain,
    ( spl32_218
    | ~ spl32_132
    | ~ spl32_216 ),
    inference(avatar_split_clause,[],[f2585,f2582,f1661,f2591]) ).

tff(f2591,plain,
    ( spl32_218
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP6(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_218])]) ).

tff(f2582,plain,
    ( spl32_216
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP6(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_216])]) ).

tff(f2585,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP6(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_132
    | ~ spl32_216 ),
    inference(forward_demodulation,[],[f2583,f1662]) ).

tff(f2583,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP6(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_216 ),
    inference(avatar_component_clause,[],[f2582]) ).

tff(f2589,plain,
    ( spl32_217
    | ~ spl32_54
    | ~ spl32_102 ),
    inference(avatar_split_clause,[],[f1643,f1448,f950,f2587]) ).

tff(f2587,plain,
    ( spl32_217
  <=> ! [X0: arrow_411405190le_alt] : sP12(lba,X0,b,X0,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_217])]) ).

tff(f1448,plain,
    ( spl32_102
  <=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(lba,a,b,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_102])]) ).

tff(f1643,plain,
    ( ! [X0: arrow_411405190le_alt] : sP12(lba,X0,b,X0,a)
    | ~ spl32_54
    | ~ spl32_102 ),
    inference(resolution,[],[f1449,f951]) ).

tff(f1449,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(lba,a,b,X0,X1)
    | ~ spl32_102 ),
    inference(avatar_component_clause,[],[f1448]) ).

tff(f2584,plain,
    spl32_216,
    inference(avatar_split_clause,[],[f531,f2582]) ).

tff(f531,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP6(X0)
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ),
    inference(cnf_transformation,[],[f345]) ).

tff(f345,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP6(X0)
        | ( ~ sP5(X0)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( sP5(X0)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP6(X0) ) ),
    inference(flattening,[],[f344]) ).

tff(f344,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP6(X0)
        | ( ~ sP5(X0)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( sP5(X0)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP6(X0) ) ),
    inference(nnf_transformation,[],[f295]) ).

tff(f295,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP6(X0)
    <=> ( ( sP5(X0)
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

tff(f2570,plain,
    ( spl32_215
    | ~ spl32_132
    | ~ spl32_214 ),
    inference(avatar_split_clause,[],[f2566,f2563,f1661,f2568]) ).

tff(f2568,plain,
    ( spl32_215
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ sP6(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_215])]) ).

tff(f2563,plain,
    ( spl32_214
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP6(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_214])]) ).

tff(f2566,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ sP6(X0) )
    | ~ spl32_132
    | ~ spl32_214 ),
    inference(forward_demodulation,[],[f2564,f1662]) ).

tff(f2564,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP6(X0) )
    | ~ spl32_214 ),
    inference(avatar_component_clause,[],[f2563]) ).

tff(f2565,plain,
    spl32_214,
    inference(avatar_split_clause,[],[f528,f2563]) ).

tff(f528,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f345]) ).

tff(f2556,plain,
    ( spl32_213
    | ~ spl32_132
    | ~ spl32_212 ),
    inference(avatar_split_clause,[],[f2552,f2549,f1661,f2554]) ).

tff(f2554,plain,
    ( spl32_213
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP3(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_213])]) ).

tff(f2549,plain,
    ( spl32_212
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP3(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_212])]) ).

tff(f2552,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP3(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_132
    | ~ spl32_212 ),
    inference(forward_demodulation,[],[f2550,f1662]) ).

tff(f2550,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP3(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_212 ),
    inference(avatar_component_clause,[],[f2549]) ).

tff(f2551,plain,
    spl32_212,
    inference(avatar_split_clause,[],[f511,f2549]) ).

tff(f511,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP3(X0)
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f338,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP3(X0)
        | ( ~ sP2(X0)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( sP2(X0)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP3(X0) ) ),
    inference(flattening,[],[f337]) ).

tff(f337,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP3(X0)
        | ( ~ sP2(X0)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( sP2(X0)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP3(X0) ) ),
    inference(nnf_transformation,[],[f291]) ).

tff(f291,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP3(X0)
    <=> ( ( sP2(X0)
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

tff(f2537,plain,
    ( spl32_211
    | ~ spl32_132
    | ~ spl32_210 ),
    inference(avatar_split_clause,[],[f2533,f2530,f1661,f2535]) ).

tff(f2535,plain,
    ( spl32_211
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_211])]) ).

tff(f2530,plain,
    ( spl32_210
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_210])]) ).

tff(f2533,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ sP3(X0) )
    | ~ spl32_132
    | ~ spl32_210 ),
    inference(forward_demodulation,[],[f2531,f1662]) ).

tff(f2531,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP3(X0) )
    | ~ spl32_210 ),
    inference(avatar_component_clause,[],[f2530]) ).

tff(f2532,plain,
    spl32_210,
    inference(avatar_split_clause,[],[f508,f2530]) ).

tff(f508,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f2523,plain,
    ( spl32_209
    | ~ spl32_132
    | ~ spl32_208 ),
    inference(avatar_split_clause,[],[f2519,f2516,f1661,f2521]) ).

tff(f2521,plain,
    ( spl32_209
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP1(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_209])]) ).

tff(f2516,plain,
    ( spl32_208
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP1(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_208])]) ).

tff(f2519,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP1(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_132
    | ~ spl32_208 ),
    inference(forward_demodulation,[],[f2517,f1662]) ).

tff(f2517,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP1(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
    | ~ spl32_208 ),
    inference(avatar_component_clause,[],[f2516]) ).

tff(f2518,plain,
    spl32_208,
    inference(avatar_split_clause,[],[f491,f2516]) ).

tff(f491,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP1(X0)
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ),
    inference(cnf_transformation,[],[f331]) ).

tff(f331,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( sP0(X0)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP1(X0) ) ),
    inference(flattening,[],[f330]) ).

tff(f330,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( sP0(X0)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP1(X0) ) ),
    inference(nnf_transformation,[],[f288]) ).

tff(f288,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP1(X0)
    <=> ( ( sP0(X0)
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f2504,plain,
    ( spl32_207
    | ~ spl32_132
    | ~ spl32_206 ),
    inference(avatar_split_clause,[],[f2500,f2497,f1661,f2502]) ).

tff(f2502,plain,
    ( spl32_207
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_207])]) ).

tff(f2497,plain,
    ( spl32_206
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_206])]) ).

tff(f2500,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ sP1(X0) )
    | ~ spl32_132
    | ~ spl32_206 ),
    inference(forward_demodulation,[],[f2498,f1662]) ).

tff(f2498,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP1(X0) )
    | ~ spl32_206 ),
    inference(avatar_component_clause,[],[f2497]) ).

tff(f2499,plain,
    spl32_206,
    inference(avatar_split_clause,[],[f488,f2497]) ).

tff(f488,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f331]) ).

tff(f2489,plain,
    spl32_205,
    inference(avatar_split_clause,[],[f487,f2487]) ).

tff(f2487,plain,
    ( spl32_205
  <=> ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK19(X1,X2,X3)))
        | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
        | ~ arrow_2069624013nimity(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_205])]) ).

tff(f487,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK19(X1,X2,X3)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ~ arrow_2069624013nimity(X0) ),
    inference(cnf_transformation,[],[f329]) ).

tff(f329,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
              ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
              | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK19(X1,X2,X3))) )
          | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof) )
      | ~ arrow_2069624013nimity(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f242,f328]) ).

tff(f328,plain,
    ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ? [X4: arrow_159774573e_indi] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
     => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK19(X1,X2,X3))) ),
    introduced(choice_axiom,[]) ).

tff(f242,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
              ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
              | ? [X4: arrow_159774573e_indi] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4)) )
          | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof) )
      | ~ arrow_2069624013nimity(X0) ),
    inference(ennf_transformation,[],[f209]) ).

tff(f209,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( arrow_2069624013nimity(X0)
     => ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
         => ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
              ( ! [X4: arrow_159774573e_indi] : member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ) ),
    inference(unused_predicate_definition_removal,[],[f154]) ).

tff(f154,plain,
    ! [X0: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( arrow_2069624013nimity(X0)
    <=> ! [X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
         => ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
              ( ! [X4: arrow_159774573e_indi] : member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ) ),
    inference(rectify,[],[f46]) ).

tff(f46,axiom,
    ! [X27: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( arrow_2069624013nimity(X27)
    <=> ! [X28: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
          ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X28,arrow_610318064e_Prof)
         => ! [X11: arrow_411405190le_alt,X12: arrow_411405190le_alt] :
              ( ! [X30: arrow_159774573e_indi] : member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X11,X12),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X28,X30))
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X11,X12),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X27,X28)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_unanimity__def) ).

tff(f2475,plain,
    ( spl32_204
    | ~ spl32_132
    | ~ spl32_203 ),
    inference(avatar_split_clause,[],[f2471,f2468,f1661,f2473]) ).

tff(f2473,plain,
    ( spl32_204
  <=> ! [X2: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X3),X4))
        | ~ sP13(X4,X3,X2,X1,X0)
        | ~ sP14(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_204])]) ).

tff(f2468,plain,
    ( spl32_203
  <=> ! [X2: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3))
        | ~ sP13(X4,X3,X2,X1,X0)
        | ~ sP14(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_203])]) ).

tff(f2471,plain,
    ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X3),X4))
        | ~ sP13(X4,X3,X2,X1,X0)
        | ~ sP14(X0,X1,X2,X3,X4) )
    | ~ spl32_132
    | ~ spl32_203 ),
    inference(forward_demodulation,[],[f2469,f1662]) ).

tff(f2469,plain,
    ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3))
        | ~ sP13(X4,X3,X2,X1,X0)
        | ~ sP14(X0,X1,X2,X3,X4) )
    | ~ spl32_203 ),
    inference(avatar_component_clause,[],[f2468]) ).

tff(f2470,plain,
    spl32_203,
    inference(avatar_split_clause,[],[f618,f2468]) ).

tff(f618,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3))
      | ~ sP13(X4,X3,X2,X1,X0)
      | ~ sP14(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f384]) ).

tff(f384,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3))
          | ~ sP13(X4,X3,X2,X1,X0) )
        & ( sP13(X4,X3,X2,X1,X0)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3)) ) )
      | ~ sP14(X0,X1,X2,X3,X4) ),
    inference(rectify,[],[f383]) ).

tff(f383,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X2),X4),X3))
          | ~ sP13(X4,X3,X1,X0,X2) )
        & ( sP13(X4,X3,X1,X0,X2)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X2),X4),X3)) ) )
      | ~ sP14(X2,X0,X1,X3,X4) ),
    inference(nnf_transformation,[],[f307]) ).

tff(f307,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X2),X4),X3))
      <=> sP13(X4,X3,X1,X0,X2) )
      | ~ sP14(X2,X0,X1,X3,X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

tff(f2464,plain,
    ( spl32_202
    | ~ spl32_132
    | ~ spl32_201 ),
    inference(avatar_split_clause,[],[f2460,f2457,f1661,f2462]) ).

tff(f2462,plain,
    ( spl32_202
  <=> ! [X2: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X3),X4))
        | sP13(X4,X3,X2,X1,X0)
        | ~ sP14(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_202])]) ).

tff(f2457,plain,
    ( spl32_201
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP13(X4,X3,X2,X1,X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3))
        | ~ sP14(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_201])]) ).

tff(f2460,plain,
    ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X3),X4))
        | sP13(X4,X3,X2,X1,X0)
        | ~ sP14(X0,X1,X2,X3,X4) )
    | ~ spl32_132
    | ~ spl32_201 ),
    inference(forward_demodulation,[],[f2458,f1662]) ).

tff(f2458,plain,
    ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
        ( sP13(X4,X3,X2,X1,X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3))
        | ~ sP14(X0,X1,X2,X3,X4) )
    | ~ spl32_201 ),
    inference(avatar_component_clause,[],[f2457]) ).

tff(f2459,plain,
    spl32_201,
    inference(avatar_split_clause,[],[f617,f2457]) ).

tff(f617,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP13(X4,X3,X2,X1,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X4),X3))
      | ~ sP14(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f384]) ).

tff(f2454,plain,
    ( spl32_200
    | ~ spl32_132
    | ~ spl32_199 ),
    inference(avatar_split_clause,[],[f2450,f2447,f1661,f2452]) ).

tff(f2452,plain,
    ( spl32_200
  <=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X1),X2),arrow_1985332922le_Lin)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_200])]) ).

tff(f2447,plain,
    ( spl32_199
  <=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X2),X1),arrow_1985332922le_Lin)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_199])]) ).

tff(f2450,plain,
    ( ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X1),X2),arrow_1985332922le_Lin)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
        | ( X1 = X2 ) )
    | ~ spl32_132
    | ~ spl32_199 ),
    inference(forward_demodulation,[],[f2448,f1662]) ).

tff(f2448,plain,
    ( ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X2),X1),arrow_1985332922le_Lin)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
        | ( X1 = X2 ) )
    | ~ spl32_199 ),
    inference(avatar_component_clause,[],[f2447]) ).

tff(f2449,plain,
    spl32_199,
    inference(avatar_split_clause,[],[f565,f2447]) ).

tff(f565,plain,
    ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X2),X1),arrow_1985332922le_Lin)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f256,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X2),X1),arrow_1985332922le_Lin)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
      | ( X1 = X2 ) ),
    inference(flattening,[],[f255]) ).

tff(f255,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X2),X1),arrow_1985332922le_Lin)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
      | ( X1 = X2 ) ),
    inference(ennf_transformation,[],[f179]) ).

tff(f179,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
      ( ( X1 != X2 )
     => ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
       => member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X0),X2),X1),arrow_1985332922le_Lin) ) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7: arrow_411405190le_alt,X8: arrow_411405190le_alt] :
      ( ( X7 != X8 )
     => ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6,arrow_1985332922le_Lin)
       => member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X6),X8),X7),arrow_1985332922le_Lin) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_above__Lin) ).

tff(f2403,plain,
    spl32_198,
    inference(avatar_split_clause,[],[f538,f2401]) ).

tff(f2401,plain,
    ( spl32_198
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP5(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_198])]) ).

tff(f538,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP5(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f2399,plain,
    spl32_197,
    inference(avatar_split_clause,[],[f535,f2397]) ).

tff(f2397,plain,
    ( spl32_197
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ( n = aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP5(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_197])]) ).

tff(f535,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ( n = aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ sP5(X0) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f2395,plain,
    spl32_196,
    inference(avatar_split_clause,[],[f518,f2393]) ).

tff(f2393,plain,
    ( spl32_196
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP2(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_196])]) ).

tff(f518,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP2(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f2391,plain,
    spl32_195,
    inference(avatar_split_clause,[],[f515,f2389]) ).

tff(f2389,plain,
    ( spl32_195
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ( n = aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_195])]) ).

tff(f515,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ( n = aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f2387,plain,
    spl32_194,
    inference(avatar_split_clause,[],[f498,f2385]) ).

tff(f2385,plain,
    ( spl32_194
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP0(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_194])]) ).

tff(f498,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP0(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) ),
    inference(cnf_transformation,[],[f333]) ).

tff(f2383,plain,
    spl32_193,
    inference(avatar_split_clause,[],[f495,f2381]) ).

tff(f2381,plain,
    ( spl32_193
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
        | ( n = aa(arrow_159774573e_indi,nat,h,X0) )
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_193])]) ).

tff(f495,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
      | ( n = aa(arrow_159774573e_indi,nat,h,X0) )
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f333]) ).

tff(f2358,plain,
    ( spl32_192
    | ~ spl32_132
    | ~ spl32_191 ),
    inference(avatar_split_clause,[],[f2354,f2349,f1661,f2356]) ).

tff(f2356,plain,
    ( spl32_192
  <=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X3),X4))
        | ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X4,X2)))
        | ~ ordere223160158up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_192])]) ).

tff(f2349,plain,
    ( spl32_191
  <=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
        | ~ ordere223160158up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_191])]) ).

tff(f2354,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X3),X4))
        | ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X4,X2)))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_132
    | ~ spl32_191 ),
    inference(forward_demodulation,[],[f2353,f1662]) ).

tff(f2353,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X4,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_132
    | ~ spl32_191 ),
    inference(forward_demodulation,[],[f2352,f1662]) ).

tff(f2352,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
        ( pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X4,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_132
    | ~ spl32_191 ),
    inference(forward_demodulation,[],[f2350,f1662]) ).

tff(f2350,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_191 ),
    inference(avatar_component_clause,[],[f2349]) ).

tff(f2351,plain,
    spl32_191,
    inference(avatar_split_clause,[],[f462,f2349]) ).

tff(f462,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
      | ~ ordere223160158up_add(X0) ),
    inference(cnf_transformation,[],[f226]) ).

tff(f226,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3)) )
      | ~ ordere223160158up_add(X0) ),
    inference(flattening,[],[f225]) ).

tff(f225,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1)))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3)) )
      | ~ ordere223160158up_add(X0) ),
    inference(ennf_transformation,[],[f138]) ).

tff(f138,plain,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0,X4: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X4),X3))
         => ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
           => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X4,X2)),plus_plus(X0,X3,X1))) ) ) ),
    inference(rectify,[],[f95]) ).

tff(f95,axiom,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X48: X0,X37: X0,X25: X0,X26: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X26),X25))
         => ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X37),X48))
           => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X26,X37)),plus_plus(X0,X25,X48))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__strict__mono) ).

tff(f2344,plain,
    spl32_190,
    inference(avatar_split_clause,[],[f431,f2341]) ).

tff(f2341,plain,
    ( spl32_190
  <=> member(fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),f,pi(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_610318064e_Prof,combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_1985332922le_Lin))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_190])]) ).

tff(f431,plain,
    member(fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),f,pi(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_610318064e_Prof,combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_1985332922le_Lin))),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,axiom,
    member(fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),f,pi(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_610318064e_Prof,combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_1985332922le_Lin))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_assms_I1_J) ).

tff(f2330,plain,
    spl32_189,
    inference(avatar_split_clause,[],[f533,f2328]) ).

tff(f2328,plain,
    ( spl32_189
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP6(X0)
        | ~ sP5(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_189])]) ).

tff(f533,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP6(X0)
      | ~ sP5(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ),
    inference(cnf_transformation,[],[f345]) ).

tff(f2326,plain,
    spl32_188,
    inference(avatar_split_clause,[],[f513,f2324]) ).

tff(f2324,plain,
    ( spl32_188
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP3(X0)
        | ~ sP2(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_188])]) ).

tff(f513,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP3(X0)
      | ~ sP2(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f2322,plain,
    spl32_187,
    inference(avatar_split_clause,[],[f493,f2320]) ).

tff(f2320,plain,
    ( spl32_187
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP1(X0)
        | ~ sP0(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_187])]) ).

tff(f493,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP1(X0)
      | ~ sP0(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ),
    inference(cnf_transformation,[],[f331]) ).

tff(f2314,plain,
    spl32_186,
    inference(avatar_split_clause,[],[f552,f2312]) ).

tff(f2312,plain,
    ( spl32_186
  <=> ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0),arrow_1985332922le_Lin)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_186])]) ).

tff(f552,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0),arrow_1985332922le_Lin)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f252,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0),arrow_1985332922le_Lin)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f168]) ).

tff(f168,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin)
     => member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0),arrow_1985332922le_Lin) ),
    inference(rectify,[],[f38]) ).

tff(f38,axiom,
    ! [X8: arrow_411405190le_alt,X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6,arrow_1985332922le_Lin)
     => member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X6),X8),arrow_1985332922le_Lin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_mktop__Lin) ).

tff(f2310,plain,
    spl32_185,
    inference(avatar_split_clause,[],[f551,f2308]) ).

tff(f2308,plain,
    ( spl32_185
  <=> ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0),arrow_1985332922le_Lin)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_185])]) ).

tff(f551,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0),arrow_1985332922le_Lin)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f251]) ).

tff(f251,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0),arrow_1985332922le_Lin)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin)
     => member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0),arrow_1985332922le_Lin) ),
    inference(rectify,[],[f39]) ).

tff(f39,axiom,
    ! [X8: arrow_411405190le_alt,X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6,arrow_1985332922le_Lin)
     => member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X6),X8),arrow_1985332922le_Lin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_mkbot__Lin) ).

tff(f2280,plain,
    spl32_184,
    inference(avatar_split_clause,[],[f612,f2278]) ).

tff(f2278,plain,
    ( spl32_184
  <=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0))
        | ~ sP10(X1,X2,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_184])]) ).

tff(f612,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0))
      | ~ sP10(X1,X2,X3,X0) ),
    inference(cnf_transformation,[],[f379]) ).

tff(f379,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0))
        | ~ sP10(X1,X2,X3,X0) )
      & ( sP10(X1,X2,X3,X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0)) ) ),
    inference(nnf_transformation,[],[f303]) ).

tff(f303,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0))
    <=> sP10(X1,X2,X3,X0) ),
    inference(definition_folding,[],[f268,f302]) ).

tff(f302,plain,
    ! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( sP10(X1,X2,X3,X0)
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          | ( X0 = X2 ) )
        & ( ( X2 != X3 )
          | ( X0 != X2 ) )
        & ( X0 != X3 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

tff(f268,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0))
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          | ( X0 = X2 ) )
        & ( ( X2 != X3 )
          | ( X0 != X2 ) )
        & ( X0 != X3 ) ) ),
    inference(ennf_transformation,[],[f194]) ).

tff(f194,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0))
    <=> ( ( ( X0 != X2 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1) )
        & ( ( X0 = X2 )
         => ( X2 != X3 ) )
        & ( X0 != X3 ) ) ),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X5: arrow_411405190le_alt,X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7: arrow_411405190le_alt,X8: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X7),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X6),X5))
    <=> ( ( ( X5 != X7 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X7),X6) )
        & ( ( X5 = X7 )
         => ( X7 != X8 ) )
        & ( X5 != X8 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_in__mktop) ).

tff(f2276,plain,
    spl32_183,
    inference(avatar_split_clause,[],[f611,f2274]) ).

tff(f2274,plain,
    ( spl32_183
  <=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( sP10(X1,X2,X3,X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_183])]) ).

tff(f611,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP10(X1,X2,X3,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,X1),X0)) ),
    inference(cnf_transformation,[],[f379]) ).

tff(f2272,plain,
    ( spl32_182
    | ~ spl32_110
    | ~ spl32_147 ),
    inference(avatar_split_clause,[],[f1862,f1854,f1517,f2270]) ).

tff(f2270,plain,
    ( spl32_182
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP0(X0)
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_182])]) ).

tff(f1517,plain,
    ( spl32_110
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP0(X0)
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_110])]) ).

tff(f1854,plain,
    ( spl32_147
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | ~ sP7(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_147])]) ).

tff(f1862,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP0(X0)
        | ~ sP1(X0) )
    | ~ spl32_110
    | ~ spl32_147 ),
    inference(resolution,[],[f1855,f1518]) ).

tff(f1518,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP0(X0)
        | ~ sP1(X0) )
    | ~ spl32_110 ),
    inference(avatar_component_clause,[],[f1517]) ).

tff(f1855,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | ~ sP7(X0) )
    | ~ spl32_147 ),
    inference(avatar_component_clause,[],[f1854]) ).

tff(f2268,plain,
    spl32_181,
    inference(avatar_split_clause,[],[f603,f2266]) ).

tff(f2266,plain,
    ( spl32_181
  <=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0))
        | ~ sP9(X1,X2,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_181])]) ).

tff(f603,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0))
      | ~ sP9(X1,X2,X3,X0) ),
    inference(cnf_transformation,[],[f375]) ).

tff(f375,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0))
        | ~ sP9(X1,X2,X3,X0) )
      & ( sP9(X1,X2,X3,X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0)) ) ),
    inference(nnf_transformation,[],[f301]) ).

tff(f301,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0))
    <=> sP9(X1,X2,X3,X0) ),
    inference(definition_folding,[],[f267,f300]) ).

tff(f300,plain,
    ! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( sP9(X1,X2,X3,X0)
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          | ( X0 = X3 ) )
        & ( ( X2 != X3 )
          | ( X0 != X3 ) )
        & ( X0 != X2 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

tff(f267,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0))
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          | ( X0 = X3 ) )
        & ( ( X2 != X3 )
          | ( X0 != X3 ) )
        & ( X0 != X2 ) ) ),
    inference(ennf_transformation,[],[f193]) ).

tff(f193,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0))
    <=> ( ( ( X0 != X3 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1) )
        & ( ( X0 = X3 )
         => ( X2 != X3 ) )
        & ( X0 != X2 ) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X5: arrow_411405190le_alt,X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7: arrow_411405190le_alt,X8: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X7),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X6),X5))
    <=> ( ( ( X5 != X8 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X7),X6) )
        & ( ( X5 = X8 )
         => ( X7 != X8 ) )
        & ( X5 != X7 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_in__mkbot) ).

tff(f2264,plain,
    spl32_180,
    inference(avatar_split_clause,[],[f602,f2262]) ).

tff(f2262,plain,
    ( spl32_180
  <=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( sP9(X1,X2,X3,X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_180])]) ).

tff(f602,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP9(X1,X2,X3,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,X1),X0)) ),
    inference(cnf_transformation,[],[f375]) ).

tff(f2238,plain,
    ( spl32_179
    | ~ spl32_132
    | ~ spl32_178 ),
    inference(avatar_split_clause,[],[f2234,f2230,f1661,f2236]) ).

tff(f2236,plain,
    ( spl32_179
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X3))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X3,X2)))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_179])]) ).

tff(f2230,plain,
    ( spl32_178
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_178])]) ).

tff(f2234,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X3))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X3,X2)))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_178 ),
    inference(forward_demodulation,[],[f2233,f1662]) ).

tff(f2233,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X3,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_178 ),
    inference(forward_demodulation,[],[f2231,f1662]) ).

tff(f2231,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_178 ),
    inference(avatar_component_clause,[],[f2230]) ).

tff(f2232,plain,
    spl32_178,
    inference(avatar_split_clause,[],[f480,f2230]) ).

tff(f480,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f324,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
            | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) )
          & ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
            | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2))) ) )
      | ~ ordere236663937imp_le(X0) ),
    inference(nnf_transformation,[],[f238]) ).

tff(f238,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
        <=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
        <=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) ) ),
    inference(rectify,[],[f62]) ).

tff(f62,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X15: X0,X19: X0,X16: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X16,X19)),plus_plus(X0,X15,X19)))
        <=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X16),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_add__less__cancel__right) ).

tff(f2203,plain,
    ( spl32_177
    | ~ spl32_132
    | ~ spl32_176 ),
    inference(avatar_split_clause,[],[f2199,f2195,f1661,f2201]) ).

tff(f2201,plain,
    ( spl32_177
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X3,X2)))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_177])]) ).

tff(f2195,plain,
    ( spl32_176
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_176])]) ).

tff(f2199,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X3,X2)))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_176 ),
    inference(forward_demodulation,[],[f2198,f1662]) ).

tff(f2198,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X3,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_176 ),
    inference(forward_demodulation,[],[f2196,f1662]) ).

tff(f2196,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_176 ),
    inference(avatar_component_clause,[],[f2195]) ).

tff(f2197,plain,
    spl32_176,
    inference(avatar_split_clause,[],[f478,f2195]) ).

tff(f478,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f323]) ).

tff(f323,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
            | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) )
          & ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
            | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1))) ) )
      | ~ ordere236663937imp_le(X0) ),
    inference(nnf_transformation,[],[f237]) ).

tff(f237,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
        <=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f149]) ).

tff(f149,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
        <=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ),
    inference(rectify,[],[f54]) ).

tff(f54,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X15: X0,X16: X0,X19: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X19,X16)),plus_plus(X0,X19,X15)))
        <=> pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X16),X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__less__cancel__left) ).

tff(f2169,plain,
    ( spl32_175
    | ~ spl32_132
    | ~ spl32_173 ),
    inference(avatar_split_clause,[],[f2161,f2157,f1661,f2167]) ).

tff(f2167,plain,
    ( spl32_175
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X3,X2)))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_175])]) ).

tff(f2157,plain,
    ( spl32_173
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_173])]) ).

tff(f2161,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X3,X2)))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_173 ),
    inference(forward_demodulation,[],[f2160,f1662]) ).

tff(f2160,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X2))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_173 ),
    inference(forward_demodulation,[],[f2158,f1662]) ).

tff(f2158,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_173 ),
    inference(avatar_component_clause,[],[f2157]) ).

tff(f2165,plain,
    ( spl32_174
    | ~ spl32_112
    | ~ spl32_147 ),
    inference(avatar_split_clause,[],[f1861,f1854,f1529,f2163]) ).

tff(f2163,plain,
    ( spl32_174
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP1(X0)
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_174])]) ).

tff(f1529,plain,
    ( spl32_112
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP1(X0)
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_112])]) ).

tff(f1861,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP1(X0)
        | ~ sP0(X0) )
    | ~ spl32_112
    | ~ spl32_147 ),
    inference(resolution,[],[f1855,f1530]) ).

tff(f1530,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP1(X0)
        | ~ sP0(X0) )
    | ~ spl32_112 ),
    inference(avatar_component_clause,[],[f1529]) ).

tff(f2159,plain,
    spl32_173,
    inference(avatar_split_clause,[],[f472,f2157]) ).

tff(f472,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f234]) ).

tff(f234,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1))) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f146]) ).

tff(f146,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X3,X1)))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ),
    inference(rectify,[],[f97]) ).

tff(f97,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X25: X0,X26: X0,X37: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X37,X26)),plus_plus(X0,X37,X25)))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X26),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__less__imp__less__left) ).

tff(f2133,plain,
    ( spl32_172
    | ~ spl32_132
    | ~ spl32_171 ),
    inference(avatar_split_clause,[],[f2129,f2125,f1661,f2131]) ).

tff(f2131,plain,
    ( spl32_172
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X3,X2)))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X3))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_172])]) ).

tff(f2125,plain,
    ( spl32_171
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_171])]) ).

tff(f2129,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X3,X2)))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X3))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_171 ),
    inference(forward_demodulation,[],[f2128,f1662]) ).

tff(f2128,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X1),X3))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_132
    | ~ spl32_171 ),
    inference(forward_demodulation,[],[f2126,f1662]) ).

tff(f2126,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
        | ~ ordere236663937imp_le(X0) )
    | ~ spl32_171 ),
    inference(avatar_component_clause,[],[f2125]) ).

tff(f2127,plain,
    spl32_171,
    inference(avatar_split_clause,[],[f471,f2125]) ).

tff(f471,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f233]) ).

tff(f233,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2))) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f145]) ).

tff(f145,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X2)),plus_plus(X0,X1,X2)))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X1)) ) ),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X25: X0,X37: X0,X26: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X26,X37)),plus_plus(X0,X25,X37)))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X26),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__less__imp__less__right) ).

tff(f2102,plain,
    ( spl32_170
    | ~ spl32_132
    | ~ spl32_169 ),
    inference(avatar_split_clause,[],[f2098,f2094,f1661,f2100]) ).

tff(f2100,plain,
    ( spl32_170
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X2),X3))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X1,X3)))
        | ~ ordere223160158up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_170])]) ).

tff(f2094,plain,
    ( spl32_169
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
        | ~ ordere223160158up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_169])]) ).

tff(f2098,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X2),X3))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X1,X3)))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_132
    | ~ spl32_169 ),
    inference(forward_demodulation,[],[f2097,f1662]) ).

tff(f2097,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X1,X2)),plus_plus(X0,X1,X3)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_132
    | ~ spl32_169 ),
    inference(forward_demodulation,[],[f2095,f1662]) ).

tff(f2095,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_169 ),
    inference(avatar_component_clause,[],[f2094]) ).

tff(f2096,plain,
    spl32_169,
    inference(avatar_split_clause,[],[f460,f2094]) ).

tff(f460,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
      | ~ ordere223160158up_add(X0) ),
    inference(cnf_transformation,[],[f222]) ).

tff(f222,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2)))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2)) )
      | ~ ordere223160158up_add(X0) ),
    inference(ennf_transformation,[],[f136]) ).

tff(f136,plain,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X1,X3)),plus_plus(X0,X1,X2))) ) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X37: X0,X25: X0,X26: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X26),X25))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X37,X26)),plus_plus(X0,X37,X25))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__strict__left__mono) ).

tff(f2074,plain,
    ( spl32_168
    | ~ spl32_132
    | ~ spl32_167 ),
    inference(avatar_split_clause,[],[f2070,f2066,f1661,f2072]) ).

tff(f2072,plain,
    ( spl32_168
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X2),X3))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X2,X1)),plus_plus(X0,X3,X1)))
        | ~ ordere223160158up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_168])]) ).

tff(f2066,plain,
    ( spl32_167
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
        | ~ ordere223160158up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_167])]) ).

tff(f2070,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),X2),X3))
        | pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X2,X1)),plus_plus(X0,X3,X1)))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_132
    | ~ spl32_167 ),
    inference(forward_demodulation,[],[f2069,f1662]) ).

tff(f2069,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,combc(X0,X0,bool,ord_less(X0),plus_plus(X0,X2,X1)),plus_plus(X0,X3,X1)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_132
    | ~ spl32_167 ),
    inference(forward_demodulation,[],[f2067,f1662]) ).

tff(f2067,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
        | ~ ordere223160158up_add(X0) )
    | ~ spl32_167 ),
    inference(avatar_component_clause,[],[f2066]) ).

tff(f2068,plain,
    spl32_167,
    inference(avatar_split_clause,[],[f459,f2066]) ).

tff(f459,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
      | ~ ordere223160158up_add(X0) ),
    inference(cnf_transformation,[],[f221]) ).

tff(f221,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1)))
          | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2)) )
      | ~ ordere223160158up_add(X0) ),
    inference(ennf_transformation,[],[f135]) ).

tff(f135,plain,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X3),X2))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X3,X1)),plus_plus(X0,X2,X1))) ) ),
    inference(rectify,[],[f93]) ).

tff(f93,axiom,
    ! [X0: $tType] :
      ( ordere223160158up_add(X0)
     => ! [X37: X0,X25: X0,X26: X0] :
          ( pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),X26),X25))
         => pp(aa(X0,bool,aa(X0,fun(X0,bool),ord_less(X0),plus_plus(X0,X26,X37)),plus_plus(X0,X25,X37))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__strict__right__mono) ).

tff(f2064,plain,
    ( spl32_166
    | ~ spl32_114
    | ~ spl32_147 ),
    inference(avatar_split_clause,[],[f1860,f1854,f1541,f2062]) ).

tff(f2062,plain,
    ( spl32_166
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP2(X0)
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_166])]) ).

tff(f1541,plain,
    ( spl32_114
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP2(X0)
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_114])]) ).

tff(f1860,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP2(X0)
        | ~ sP3(X0) )
    | ~ spl32_114
    | ~ spl32_147 ),
    inference(resolution,[],[f1855,f1542]) ).

tff(f1542,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP2(X0)
        | ~ sP3(X0) )
    | ~ spl32_114 ),
    inference(avatar_component_clause,[],[f1541]) ).

tff(f2052,plain,
    ( spl32_165
    | ~ spl32_132
    | ~ spl32_164 ),
    inference(avatar_split_clause,[],[f2048,f2045,f1661,f2050]) ).

tff(f2050,plain,
    ( spl32_165
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,n,one_one(nat))),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP4(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_165])]) ).

tff(f2045,plain,
    ( spl32_164
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP4(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_164])]) ).

tff(f2048,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,n,one_one(nat))),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP4(X0) )
    | ~ spl32_132
    | ~ spl32_164 ),
    inference(forward_demodulation,[],[f2046,f1662]) ).

tff(f2046,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP4(X0)
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) )
    | ~ spl32_164 ),
    inference(avatar_component_clause,[],[f2045]) ).

tff(f2047,plain,
    ( ~ spl32_41
    | spl32_164 ),
    inference(avatar_split_clause,[],[f505,f2045,f881]) ).

tff(f881,plain,
    ( spl32_41
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_41])]) ).

tff(f505,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP4(X0)
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat))))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab) ),
    inference(cnf_transformation,[],[f336]) ).

tff(f336,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP4(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab)
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab)
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) ) )
        | ~ sP4(X0) ) ),
    inference(flattening,[],[f335]) ).

tff(f335,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP4(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab)
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab)
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) ) )
        | ~ sP4(X0) ) ),
    inference(nnf_transformation,[],[f292]) ).

tff(f292,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP4(X0)
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba)
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab)
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

tff(f2040,plain,
    ( spl32_163
    | ~ spl32_132
    | ~ spl32_162 ),
    inference(avatar_split_clause,[],[f2036,f2033,f1661,f2038]) ).

tff(f2038,plain,
    ( spl32_163
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,n,one_one(nat))),aa(arrow_159774573e_indi,nat,h,X0)))
        | ~ sP4(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_163])]) ).

tff(f2033,plain,
    ( spl32_162
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat))))
        | ~ sP4(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_162])]) ).

tff(f2036,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,n,one_one(nat))),aa(arrow_159774573e_indi,nat,h,X0)))
        | ~ sP4(X0) )
    | ~ spl32_132
    | ~ spl32_162 ),
    inference(forward_demodulation,[],[f2034,f1662]) ).

tff(f2034,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat))))
        | ~ sP4(X0) )
    | ~ spl32_162 ),
    inference(avatar_component_clause,[],[f2033]) ).

tff(f2035,plain,
    ( spl32_162
    | spl32_39 ),
    inference(avatar_split_clause,[],[f503,f871,f2033]) ).

tff(f871,plain,
    ( spl32_39
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_39])]) ).

tff(f503,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat))))
      | ~ sP4(X0) ),
    inference(cnf_transformation,[],[f336]) ).

tff(f2013,plain,
    ( spl32_161
    | ~ spl32_132
    | ~ spl32_160 ),
    inference(avatar_split_clause,[],[f2009,f2005,f1661,f2011]) ).

tff(f2011,plain,
    ( spl32_161
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X1))
        | pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,X2,X0)),plus_plus(nat,X2,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_161])]) ).

tff(f2005,plain,
    ( spl32_160
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_160])]) ).

tff(f2009,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X1))
        | pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,X2,X0)),plus_plus(nat,X2,X1))) )
    | ~ spl32_132
    | ~ spl32_160 ),
    inference(forward_demodulation,[],[f2008,f1662]) ).

tff(f2008,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,X2,X0)),plus_plus(nat,X2,X1)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0)) )
    | ~ spl32_132
    | ~ spl32_160 ),
    inference(forward_demodulation,[],[f2006,f1662]) ).

tff(f2006,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0)) )
    | ~ spl32_160 ),
    inference(avatar_component_clause,[],[f2005]) ).

tff(f2007,plain,
    spl32_160,
    inference(avatar_split_clause,[],[f585,f2005]) ).

tff(f585,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0)))
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0)) ),
    inference(cnf_transformation,[],[f358]) ).

tff(f358,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0)) )
      & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0))) ) ),
    inference(nnf_transformation,[],[f188]) ).

tff(f188,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0)))
    <=> pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0)) ),
    inference(rectify,[],[f53]) ).

tff(f53,axiom,
    ! [X20: nat,X33: nat,X34: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X34,X33)),plus_plus(nat,X34,X20)))
    <=> pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X33),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_nat__add__left__cancel__less) ).

tff(f1984,plain,
    ( spl32_159
    | ~ spl32_117
    | ~ spl32_147 ),
    inference(avatar_split_clause,[],[f1859,f1854,f1557,f1982]) ).

tff(f1982,plain,
    ( spl32_159
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP3(X0)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_159])]) ).

tff(f1557,plain,
    ( spl32_117
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP3(X0)
        | ~ sP2(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_117])]) ).

tff(f1859,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP3(X0)
        | ~ sP2(X0) )
    | ~ spl32_117
    | ~ spl32_147 ),
    inference(resolution,[],[f1855,f1558]) ).

tff(f1558,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP3(X0)
        | ~ sP2(X0) )
    | ~ spl32_117 ),
    inference(avatar_component_clause,[],[f1557]) ).

tff(f1980,plain,
    ( spl32_158
    | ~ spl32_132
    | ~ spl32_157 ),
    inference(avatar_split_clause,[],[f1976,f1972,f1661,f1978]) ).

tff(f1978,plain,
    ( spl32_158
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,X2,X0)),plus_plus(nat,X2,X1)))
        | pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_158])]) ).

tff(f1972,plain,
    ( spl32_157
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_157])]) ).

tff(f1976,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),plus_plus(nat,X2,X0)),plus_plus(nat,X2,X1)))
        | pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X1)) )
    | ~ spl32_132
    | ~ spl32_157 ),
    inference(forward_demodulation,[],[f1975,f1662]) ).

tff(f1975,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X1))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0))) )
    | ~ spl32_132
    | ~ spl32_157 ),
    inference(forward_demodulation,[],[f1973,f1662]) ).

tff(f1973,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0))) )
    | ~ spl32_157 ),
    inference(avatar_component_clause,[],[f1972]) ).

tff(f1974,plain,
    spl32_157,
    inference(avatar_split_clause,[],[f584,f1972]) ).

tff(f584,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X2,X1)),plus_plus(nat,X2,X0))) ),
    inference(cnf_transformation,[],[f358]) ).

tff(f1956,plain,
    ( spl32_156
    | ~ spl32_132
    | ~ spl32_155 ),
    inference(avatar_split_clause,[],[f1952,f1948,f1661,f1954]) ).

tff(f1954,plain,
    ( spl32_156
  <=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X2),X1))
        | pp(aa(nat,bool,combc(nat,nat,bool,X0,X2),X1))
        | ( X1 = X2 )
        | sP8(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_156])]) ).

tff(f1948,plain,
    ( spl32_155
  <=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X2))
        | ( X1 = X2 )
        | sP8(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_155])]) ).

tff(f1952,plain,
    ( ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X2),X1))
        | pp(aa(nat,bool,combc(nat,nat,bool,X0,X2),X1))
        | ( X1 = X2 )
        | sP8(X2,X1,X0) )
    | ~ spl32_132
    | ~ spl32_155 ),
    inference(forward_demodulation,[],[f1951,f1662]) ).

tff(f1951,plain,
    ( ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,X0,X2),X1))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X2))
        | ( X1 = X2 )
        | sP8(X2,X1,X0) )
    | ~ spl32_132
    | ~ spl32_155 ),
    inference(forward_demodulation,[],[f1949,f1662]) ).

tff(f1949,plain,
    ( ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X2))
        | ( X1 = X2 )
        | sP8(X2,X1,X0) )
    | ~ spl32_155 ),
    inference(avatar_component_clause,[],[f1948]) ).

tff(f1950,plain,
    spl32_155,
    inference(avatar_split_clause,[],[f572,f1948]) ).

tff(f572,plain,
    ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X2))
      | ( X1 = X2 )
      | sP8(X2,X1,X0) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f299,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))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ( X1 = X2 ) )
      | sP8(X2,X1,X0) ),
    inference(definition_folding,[],[f264,f298]) ).

tff(f298,plain,
    ! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X2),X1)) )
      | ~ sP8(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

tff(f264,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))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),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))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X2),X1)) ) ),
    inference(flattening,[],[f263]) ).

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))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),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))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X2),X1)) ) ),
    inference(ennf_transformation,[],[f183]) ).

tff(f183,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( ( pp(aa(nat,bool,aa(nat,fun(nat,bool),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)) )
       => ( ( pp(aa(nat,bool,aa(nat,fun(nat,bool),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,[],[f68]) ).

tff(f68,axiom,
    ! [X9: fun(nat,fun(nat,bool)),X20: nat,X33: nat] :
      ( ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X33),X20))
       => pp(aa(nat,bool,aa(nat,fun(nat,bool),X9,X20),X33)) )
     => ( ( ( X20 = X33 )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X9,X20),X33)) )
       => ( ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X20),X33))
           => pp(aa(nat,bool,aa(nat,fun(nat,bool),X9,X20),X33)) )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X9,X20),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nat__less__cases) ).

tff(f1914,plain,
    spl32_154,
    inference(avatar_split_clause,[],[f567,f1912]) ).

tff(f1912,plain,
    ( spl32_154
  <=> ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2)
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
        | ( X0 = X1 )
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_154])]) ).

tff(f567,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2)
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f351]) ).

tff(f351,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2)
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2) ) )
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(nnf_transformation,[],[f260]) ).

tff(f260,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2) )
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(flattening,[],[f259]) ).

tff(f259,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2) )
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f181]) ).

tff(f181,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
     => ( ( X0 != X1 )
       => ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
        <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2) ) ) ),
    inference(rectify,[],[f37]) ).

tff(f37,axiom,
    ! [X7: arrow_411405190le_alt,X8: arrow_411405190le_alt,X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6,arrow_1985332922le_Lin)
     => ( ( X7 != X8 )
       => ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X7),X6)
        <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X7,X8),X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_notin__Lin__iff) ).

tff(f1910,plain,
    spl32_153,
    inference(avatar_split_clause,[],[f430,f1907]) ).

tff(f1907,plain,
    ( spl32_153
  <=> ( arrow_610318064e_Prof = pi(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),top_top(fun(arrow_159774573e_indi,bool)),combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),arrow_159774573e_indi,arrow_1985332922le_Lin)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_153])]) ).

tff(f430,plain,
    arrow_610318064e_Prof = pi(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),top_top(fun(arrow_159774573e_indi,bool)),combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),arrow_159774573e_indi,arrow_1985332922le_Lin)),
    inference(cnf_transformation,[],[f85]) ).

tff(f85,axiom,
    arrow_610318064e_Prof = pi(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),top_top(fun(arrow_159774573e_indi,bool)),combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),arrow_159774573e_indi,arrow_1985332922le_Lin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Prof__def) ).

tff(f1892,plain,
    ( spl32_152
    | ~ spl32_119
    | ~ spl32_147 ),
    inference(avatar_split_clause,[],[f1858,f1854,f1569,f1890]) ).

tff(f1890,plain,
    ( spl32_152
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP5(X0)
        | ~ sP6(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_152])]) ).

tff(f1569,plain,
    ( spl32_119
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP5(X0)
        | ~ sP6(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_119])]) ).

tff(f1858,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ sP7(X0)
        | sP5(X0)
        | ~ sP6(X0) )
    | ~ spl32_119
    | ~ spl32_147 ),
    inference(resolution,[],[f1855,f1570]) ).

tff(f1570,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP5(X0)
        | ~ sP6(X0) )
    | ~ spl32_119 ),
    inference(avatar_component_clause,[],[f1569]) ).

tff(f1888,plain,
    ( spl32_151
    | ~ spl32_132
    | ~ spl32_150 ),
    inference(avatar_split_clause,[],[f1884,f1880,f1661,f1886]) ).

tff(f1886,plain,
    ( spl32_151
  <=> ! [X0: nat,X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X1))
        | pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X1),X0))
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_151])]) ).

tff(f1880,plain,
    ( spl32_150
  <=> ! [X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_150])]) ).

tff(f1884,plain,
    ( ! [X0: nat,X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X1))
        | pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X1),X0))
        | ( X0 = X1 ) )
    | ~ spl32_132
    | ~ spl32_150 ),
    inference(forward_demodulation,[],[f1883,f1662]) ).

tff(f1883,plain,
    ( ! [X0: nat,X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X1),X0))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
        | ( X0 = X1 ) )
    | ~ spl32_132
    | ~ spl32_150 ),
    inference(forward_demodulation,[],[f1881,f1662]) ).

tff(f1881,plain,
    ( ! [X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
        | ( X0 = X1 ) )
    | ~ spl32_150 ),
    inference(avatar_component_clause,[],[f1880]) ).

tff(f1882,plain,
    spl32_150,
    inference(avatar_split_clause,[],[f548,f1880]) ).

tff(f548,plain,
    ! [X0: nat,X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f247]) ).

tff(f247,plain,
    ! [X0: nat,X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
      | ( X0 = X1 ) ),
    inference(flattening,[],[f246]) ).

tff(f246,plain,
    ! [X0: nat,X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f164]) ).

tff(f164,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X1),X0))
       => pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
    inference(rectify,[],[f72]) ).

tff(f72,axiom,
    ! [X42: nat,X43: nat] :
      ( ( X42 != X43 )
     => ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X43),X42))
       => pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X42),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_linorder__neqE__nat) ).

tff(f1874,plain,
    ( spl32_149
    | ~ spl32_132
    | ~ spl32_148 ),
    inference(avatar_split_clause,[],[f1870,f1867,f1661,f1872]) ).

tff(f1872,plain,
    ( spl32_149
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP7(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_149])]) ).

tff(f1867,plain,
    ( spl32_148
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP7(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_148])]) ).

tff(f1870,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP7(X0) )
    | ~ spl32_132
    | ~ spl32_148 ),
    inference(forward_demodulation,[],[f1868,f1662]) ).

tff(f1868,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP7(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
    | ~ spl32_148 ),
    inference(avatar_component_clause,[],[f1867]) ).

tff(f1869,plain,
    ( ~ spl32_40
    | spl32_148 ),
    inference(avatar_split_clause,[],[f526,f1867,f876]) ).

tff(f876,plain,
    ( spl32_40
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_40])]) ).

tff(f526,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP7(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ),
    inference(cnf_transformation,[],[f343]) ).

tff(f343,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP7(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab)
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab)
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP7(X0) ) ),
    inference(flattening,[],[f342]) ).

tff(f342,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP7(X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
          & ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab)
          & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
            | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab)
            | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
        | ~ sP7(X0) ) ),
    inference(nnf_transformation,[],[f296]) ).

tff(f296,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP7(X0)
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab)
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

tff(f1856,plain,
    ( spl32_147
    | ~ spl32_132
    | ~ spl32_146 ),
    inference(avatar_split_clause,[],[f1852,f1849,f1661,f1854]) ).

tff(f1849,plain,
    ( spl32_146
  <=> ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP7(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_146])]) ).

tff(f1852,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | ~ sP7(X0) )
    | ~ spl32_132
    | ~ spl32_146 ),
    inference(forward_demodulation,[],[f1850,f1662]) ).

tff(f1850,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP7(X0) )
    | ~ spl32_146 ),
    inference(avatar_component_clause,[],[f1849]) ).

tff(f1851,plain,
    ( spl32_146
    | spl32_38 ),
    inference(avatar_split_clause,[],[f522,f866,f1849]) ).

tff(f866,plain,
    ( spl32_38
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_38])]) ).

tff(f522,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab)
      | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ sP7(X0) ),
    inference(cnf_transformation,[],[f343]) ).

tff(f1836,plain,
    ( spl32_145
    | ~ spl32_54
    | ~ spl32_96 ),
    inference(avatar_split_clause,[],[f1596,f1410,f950,f1834]) ).

tff(f1834,plain,
    ( spl32_145
  <=> ! [X0: arrow_411405190le_alt] : sP12(lab,X0,a,X0,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_145])]) ).

tff(f1410,plain,
    ( spl32_96
  <=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(lab,b,a,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_96])]) ).

tff(f1596,plain,
    ( ! [X0: arrow_411405190le_alt] : sP12(lab,X0,a,X0,b)
    | ~ spl32_54
    | ~ spl32_96 ),
    inference(resolution,[],[f1411,f951]) ).

tff(f1411,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(lab,b,a,X0,X1)
    | ~ spl32_96 ),
    inference(avatar_component_clause,[],[f1410]) ).

tff(f1832,plain,
    spl32_144,
    inference(avatar_split_clause,[],[f647,f1830]) ).

tff(f1830,plain,
    ( spl32_144
  <=> ! [X1: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X1,bool),X3: fun(X1,fun(X0,bool)),X2: X1] :
        ( member(X0,aa(X1,X0,X5,X2),aa(X1,fun(X0,bool),X3,X2))
        | ~ member(X1,X2,X4)
        | ~ member(fun(X1,X0),X5,pi(X1,X0,X4,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_144])]) ).

tff(f647,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,fun(X0,bool)),X4: fun(X1,bool),X5: fun(X1,X0)] :
      ( member(X0,aa(X1,X0,X5,X2),aa(X1,fun(X0,bool),X3,X2))
      | ~ member(X1,X2,X4)
      | ~ member(fun(X1,X0),X5,pi(X1,X0,X4,X3)) ),
    inference(cnf_transformation,[],[f280]) ).

tff(f280,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: fun(X1,fun(X0,bool)),X4: fun(X1,bool),X5: fun(X1,X0)] :
      ( member(X0,aa(X1,X0,X5,X2),aa(X1,fun(X0,bool),X3,X2))
      | ~ member(X1,X2,X4)
      | ~ member(fun(X1,X0),X5,pi(X1,X0,X4,X3)) ),
    inference(flattening,[],[f279]) ).

tff(f279,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: fun(X1,fun(X0,bool)),X4: fun(X1,bool),X5: fun(X1,X0)] :
      ( member(X0,aa(X1,X0,X5,X2),aa(X1,fun(X0,bool),X3,X2))
      | ~ member(X1,X2,X4)
      | ~ member(fun(X1,X0),X5,pi(X1,X0,X4,X3)) ),
    inference(ennf_transformation,[],[f203]) ).

tff(f203,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: fun(X1,fun(X0,bool)),X4: fun(X1,bool),X5: fun(X1,X0)] :
      ( member(fun(X1,X0),X5,pi(X1,X0,X4,X3))
     => ( member(X1,X2,X4)
       => member(X0,aa(X1,X0,X5,X2),aa(X1,fun(X0,bool),X3,X2)) ) ),
    inference(rectify,[],[f84]) ).

tff(f84,axiom,
    ! [X1: $tType,X0: $tType,X8: X0,X35: fun(X0,fun(X1,bool)),X32: fun(X0,bool),X36: fun(X0,X1)] :
      ( member(fun(X0,X1),X36,pi(X0,X1,X32,X35))
     => ( member(X0,X8,X32)
       => member(X1,aa(X0,X1,X36,X8),aa(X0,fun(X1,bool),X35,X8)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Pi__mem) ).

tff(f1828,plain,
    spl32_143,
    inference(avatar_split_clause,[],[f569,f1826]) ).

tff(f1826,plain,
    ( spl32_143
  <=> ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_143])]) ).

tff(f569,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f262]) ).

tff(f262,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(flattening,[],[f261]) ).

tff(f261,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f182]) ).

tff(f182,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
     => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
       => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X1),X2) ) ),
    inference(rectify,[],[f36]) ).

tff(f36,axiom,
    ! [X15: arrow_411405190le_alt,X16: arrow_411405190le_alt,X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6,arrow_1985332922le_Lin)
     => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X15),X6)
       => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X15,X16),X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Lin__irrefl) ).

tff(f1821,plain,
    spl32_142,
    inference(avatar_split_clause,[],[f651,f1819]) ).

tff(f1819,plain,
    ( spl32_142
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1),X2: X0] :
        ( member(X1,aa(X0,X1,X5,X2),X3)
        | ~ member(X0,X2,X4)
        | ~ member(fun(X0,X1),X5,pi(X0,X1,X4,combk(fun(X1,bool),X0,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_142])]) ).

tff(f651,plain,
    ! [X1: $tType,X0: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
      ( member(X1,aa(X0,X1,X5,X2),X3)
      | ~ member(X0,X2,X4)
      | ~ member(fun(X0,X1),X5,pi(X0,X1,X4,combk(fun(X1,bool),X0,X3))) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
      ( member(X1,aa(X0,X1,X5,X2),X3)
      | ~ member(X0,X2,X4)
      | ~ member(fun(X0,X1),X5,pi(X0,X1,X4,combk(fun(X1,bool),X0,X3))) ),
    inference(flattening,[],[f284]) ).

tff(f284,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
      ( member(X1,aa(X0,X1,X5,X2),X3)
      | ~ member(X0,X2,X4)
      | ~ member(fun(X0,X1),X5,pi(X0,X1,X4,combk(fun(X1,bool),X0,X3))) ),
    inference(ennf_transformation,[],[f206]) ).

tff(f206,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
      ( member(fun(X0,X1),X5,pi(X0,X1,X4,combk(fun(X1,bool),X0,X3)))
     => ( member(X0,X2,X4)
       => member(X1,aa(X0,X1,X5,X2),X3) ) ),
    inference(rectify,[],[f87]) ).

tff(f87,axiom,
    ! [X0: $tType,X1: $tType,X8: X0,X35: fun(X1,bool),X32: fun(X0,bool),X36: fun(X0,X1)] :
      ( member(fun(X0,X1),X36,pi(X0,X1,X32,combk(fun(X1,bool),X0,X35)))
     => ( member(X0,X8,X32)
       => member(X1,aa(X0,X1,X36,X8),X35) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_funcset__mem) ).

tff(f1755,plain,
    spl32_141,
    inference(avatar_split_clause,[],[f636,f1753]) ).

tff(f1753,plain,
    ( spl32_141
  <=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_141])]) ).

tff(f636,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
    inference(cnf_transformation,[],[f199]) ).

tff(f199,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
    inference(rectify,[],[f116]) ).

tff(f116,axiom,
    ! [X2: $tType,X1: $tType,X0: $tType,X50: X0,X51: fun(X0,X1),X49: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combs(X0,X1,X2,X49,X51),X50) = aa(X1,X2,aa(X0,fun(X1,X2),X49,X50),aa(X0,X1,X51,X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

tff(f1751,plain,
    spl32_140,
    inference(avatar_split_clause,[],[f588,f1749]) ).

tff(f1749,plain,
    ( spl32_140
  <=> ! [X1: $tType,X0: $tType,X8: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
        ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2))))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_140])]) ).

tff(f588,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X8: product_prod(X0,X1)] :
      ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2))))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ),
    inference(cnf_transformation,[],[f368]) ).

tff(f368,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( pp(aa(product_prod(X0,X1),bool,X2,sK23(X0,X1,X2)))
        | ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2))))
        | ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25])],[f365,f367,f366]) ).

tff(f366,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
     => pp(aa(product_prod(X0,X1),bool,X2,sK23(X0,X1,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f367,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
     => pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2)))) ),
    introduced(choice_axiom,[]) ).

tff(f365,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    inference(rectify,[],[f364]) ).

tff(f364,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5)))
        | ! [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
    inference(nnf_transformation,[],[f190]) ).

tff(f190,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
    <=> ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ),
    inference(rectify,[],[f48]) ).

tff(f48,axiom,
    ! [X0: $tType,X1: $tType,X9: fun(product_prod(X0,X1),bool)] :
      ( ? [X10: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X9,X10))
    <=> ? [X11: X0,X12: X1] : pp(aa(product_prod(X0,X1),bool,X9,product_Pair(X0,X1,X11,X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_split__paired__Ex) ).

tff(f1745,plain,
    spl32_139,
    inference(avatar_split_clause,[],[f587,f1743]) ).

tff(f1743,plain,
    ( spl32_139
  <=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
        ( pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK20(X0,X1,X2),sK21(X0,X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_139])]) ).

tff(f587,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
      ( pp(aa(product_prod(X0,X1),bool,X2,X3))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK20(X0,X1,X2),sK21(X0,X1,X2)))) ),
    inference(cnf_transformation,[],[f363]) ).

tff(f363,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK20(X0,X1,X2),sK21(X0,X1,X2)))) )
      & ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f360,f362,f361]) ).

tff(f361,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5)))
     => ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK20(X0,X1,X2),sK21(X0,X1,X2)))) ),
    introduced(choice_axiom,[]) ).

tff(f362,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8))
     => ~ pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f360,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    inference(rectify,[],[f359]) ).

tff(f359,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5)))
        | ? [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
    inference(nnf_transformation,[],[f189]) ).

tff(f189,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
    <=> ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ),
    inference(rectify,[],[f21]) ).

tff(f21,axiom,
    ! [X0: $tType,X1: $tType,X9: fun(product_prod(X0,X1),bool)] :
      ( ! [X10: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X9,X10))
    <=> ! [X11: X0,X12: X1] : pp(aa(product_prod(X0,X1),bool,X9,product_Pair(X0,X1,X11,X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_split__paired__All) ).

tff(f1741,plain,
    spl32_138,
    inference(avatar_split_clause,[],[f429,f1738]) ).

tff(f1738,plain,
    ( spl32_138
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,hilbert_inv_into(arrow_159774573e_indi,nat,top_top(fun(arrow_159774573e_indi,bool)),h,n))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_138])]) ).

tff(f429,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,hilbert_inv_into(arrow_159774573e_indi,nat,top_top(fun(arrow_159774573e_indi,bool)),h,n))),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,axiom,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,hilbert_inv_into(arrow_159774573e_indi,nat,top_top(fun(arrow_159774573e_indi,bool)),h,n))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096) ).

tff(f1731,plain,
    spl32_137,
    inference(avatar_split_clause,[],[f623,f1729]) ).

tff(f1729,plain,
    ( spl32_137
  <=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP13(X0,X1,X2,X3,X4)
        | ~ sP12(X4,X3,X2,X1,X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X3),X4)
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_137])]) ).

tff(f623,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP13(X0,X1,X2,X3,X4)
      | ~ sP12(X4,X3,X2,X1,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X3),X4)
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f387]) ).

tff(f387,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( sP13(X0,X1,X2,X3,X4)
        | ~ sP12(X4,X3,X2,X1,X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X3),X4)
          & ( X1 = X2 ) )
        | ( X2 = X3 ) )
      & ( ( sP12(X4,X3,X2,X1,X0)
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X3),X4)
            | ( X1 != X2 ) )
          & ( X2 != X3 ) )
        | ~ sP13(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f386]) ).

tff(f386,plain,
    ! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( sP13(X4,X3,X1,X0,X2)
        | ~ sP12(X2,X0,X1,X3,X4)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2)
          & ( X1 = X3 ) )
        | ( X0 = X1 ) )
      & ( ( sP12(X2,X0,X1,X3,X4)
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2)
            | ( X1 != X3 ) )
          & ( X0 != X1 ) )
        | ~ sP13(X4,X3,X1,X0,X2) ) ),
    inference(flattening,[],[f385]) ).

tff(f385,plain,
    ! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( sP13(X4,X3,X1,X0,X2)
        | ~ sP12(X2,X0,X1,X3,X4)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2)
          & ( X1 = X3 ) )
        | ( X0 = X1 ) )
      & ( ( sP12(X2,X0,X1,X3,X4)
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2)
            | ( X1 != X3 ) )
          & ( X0 != X1 ) )
        | ~ sP13(X4,X3,X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f306]) ).

tff(f306,plain,
    ! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP13(X4,X3,X1,X0,X2)
    <=> ( sP12(X2,X0,X1,X3,X4)
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2)
          | ( X1 != X3 ) )
        & ( X0 != X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

tff(f1727,plain,
    spl32_136,
    inference(avatar_split_clause,[],[f482,f1725]) ).

tff(f1725,plain,
    ( spl32_136
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0),arrow_610318064e_Prof)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_136])]) ).

tff(f482,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0),arrow_610318064e_Prof)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f240]) ).

tff(f240,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0),arrow_610318064e_Prof)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
     => member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0),arrow_610318064e_Prof) ),
    inference(rectify,[],[f35]) ).

tff(f35,axiom,
    ! [X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6,arrow_1985332922le_Lin)
     => member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X6),arrow_610318064e_Prof) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_const__Lin__Prof) ).

tff(f1722,plain,
    spl32_135,
    inference(avatar_split_clause,[],[f562,f1720]) ).

tff(f1720,plain,
    ( spl32_135
  <=> ! [X1: $tType,X0: $tType,X2: fun(X1,bool)] : ( pi(X1,X0,X2,combk(fun(X0,bool),X1,top_top(fun(X0,bool)))) = top_top(fun(fun(X1,X0),bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_135])]) ).

tff(f562,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,bool)] : ( pi(X1,X0,X2,combk(fun(X0,bool),X1,top_top(fun(X0,bool)))) = top_top(fun(fun(X1,X0),bool)) ),
    inference(cnf_transformation,[],[f176]) ).

tff(f176,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,bool)] : ( pi(X1,X0,X2,combk(fun(X0,bool),X1,top_top(fun(X0,bool)))) = top_top(fun(fun(X1,X0),bool)) ),
    inference(rectify,[],[f51]) ).

tff(f51,axiom,
    ! [X1: $tType,X0: $tType,X32: fun(X0,bool)] : ( pi(X0,X1,X32,combk(fun(X1,bool),X0,top_top(fun(X1,bool)))) = top_top(fun(fun(X0,X1),bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Pi__UNIV) ).

tff(f1699,plain,
    spl32_134,
    inference(avatar_split_clause,[],[f589,f1697]) ).

tff(f1697,plain,
    ( spl32_134
  <=> ! [X1: $tType,X0: $tType,X4: X0,X5: X1,X2: fun(product_prod(X0,X1),bool)] :
        ( pp(aa(product_prod(X0,X1),bool,X2,sK23(X0,X1,X2)))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_134])]) ).

tff(f589,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
      ( pp(aa(product_prod(X0,X1),bool,X2,sK23(X0,X1,X2)))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ),
    inference(cnf_transformation,[],[f368]) ).

tff(f1695,plain,
    spl32_133,
    inference(avatar_split_clause,[],[f586,f1693]) ).

tff(f1693,plain,
    ( spl32_133
  <=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
        ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_133])]) ).

tff(f586,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
      ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f363]) ).

tff(f1663,plain,
    spl32_132,
    inference(avatar_split_clause,[],[f635,f1661]) ).

tff(f635,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(cnf_transformation,[],[f198]) ).

tff(f198,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(rectify,[],[f113]) ).

tff(f113,axiom,
    ! [X0: $tType,X2: $tType,X1: $tType,X50: X0,X51: X1,X49: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X49,X51),X50) = aa(X1,X2,aa(X0,fun(X1,X2),X49,X50),X51) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

tff(f1659,plain,
    spl32_131,
    inference(avatar_split_clause,[],[f628,f1657]) ).

tff(f1657,plain,
    ( spl32_131
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP12(X0,X1,X2,X3,X4)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ~ sP11(X0,X4,X2,X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_131])]) ).

tff(f628,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP12(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ~ sP11(X0,X4,X2,X3,X1) ),
    inference(cnf_transformation,[],[f390]) ).

tff(f390,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP12(X0,X1,X2,X3,X4)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
              & ( X1 != X3 ) )
            | ~ sP11(X0,X4,X2,X3,X1) )
          & ( X2 != X3 ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
            | ( X1 = X3 ) )
          & sP11(X0,X4,X2,X3,X1) )
        | ( X2 = X3 )
        | ~ sP12(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f389]) ).

tff(f389,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP12(X2,X0,X1,X3,X4)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
              & ( X0 != X3 ) )
            | ~ sP11(X2,X4,X1,X3,X0) )
          & ( X1 != X3 ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
            | ( X0 = X3 ) )
          & sP11(X2,X4,X1,X3,X0) )
        | ( X1 = X3 )
        | ~ sP12(X2,X0,X1,X3,X4) ) ),
    inference(flattening,[],[f388]) ).

tff(f388,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP12(X2,X0,X1,X3,X4)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
              & ( X0 != X3 ) )
            | ~ sP11(X2,X4,X1,X3,X0) )
          & ( X1 != X3 ) ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
            | ( X0 = X3 ) )
          & sP11(X2,X4,X1,X3,X0) )
        | ( X1 = X3 )
        | ~ sP12(X2,X0,X1,X3,X4) ) ),
    inference(nnf_transformation,[],[f305]) ).

tff(f305,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP12(X2,X0,X1,X3,X4)
    <=> ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
            | ( X0 = X3 ) )
          & sP11(X2,X4,X1,X3,X0) )
        | ( X1 = X3 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

tff(f1655,plain,
    spl32_130,
    inference(avatar_split_clause,[],[f625,f1653]) ).

tff(f1653,plain,
    ( spl32_130
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X1 = X3 )
        | ( X2 = X3 )
        | ~ sP12(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_130])]) ).

tff(f625,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X1 = X3 )
      | ( X2 = X3 )
      | ~ sP12(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f390]) ).

tff(f1647,plain,
    ( spl32_129
    | ~ spl32_128 ),
    inference(avatar_split_clause,[],[f1641,f1638,f1645]) ).

tff(f1645,plain,
    ( spl32_129
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(bool,fun(X0,X0),combc(bool,X0,fun(X0,X0),if(X0),X2),fTrue),X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_129])]) ).

tff(f1638,plain,
    ( spl32_128
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fTrue),X2),X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_128])]) ).

tff(f1641,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(bool,fun(X0,X0),combc(bool,X0,fun(X0,X0),if(X0),X2),fTrue),X1) = X2 )
    | ~ spl32_128 ),
    inference(forward_demodulation,[],[f1639,f635]) ).

tff(f1639,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fTrue),X2),X1) = X2 )
    | ~ spl32_128 ),
    inference(avatar_component_clause,[],[f1638]) ).

tff(f1640,plain,
    spl32_128,
    inference(avatar_split_clause,[],[f561,f1638]) ).

tff(f561,plain,
    ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fTrue),X2),X1) = X2 ),
    inference(cnf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: $tType,X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fTrue),X2),X1) = X2 ),
    inference(rectify,[],[f107]) ).

tff(f107,axiom,
    ! [X0: $tType,X42: X0,X43: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fTrue),X43),X42) = X43 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).

tff(f1633,plain,
    ( spl32_127
    | ~ spl32_126 ),
    inference(avatar_split_clause,[],[f1629,f1626,f1631]) ).

tff(f1631,plain,
    ( spl32_127
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(bool,fun(X0,X0),combc(bool,X0,fun(X0,X0),if(X0),X2),fFalse),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_127])]) ).

tff(f1626,plain,
    ( spl32_126
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fFalse),X2),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_126])]) ).

tff(f1629,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(bool,fun(X0,X0),combc(bool,X0,fun(X0,X0),if(X0),X2),fFalse),X1) = X1 )
    | ~ spl32_126 ),
    inference(forward_demodulation,[],[f1627,f635]) ).

tff(f1627,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fFalse),X2),X1) = X1 )
    | ~ spl32_126 ),
    inference(avatar_component_clause,[],[f1626]) ).

tff(f1628,plain,
    spl32_126,
    inference(avatar_split_clause,[],[f560,f1626]) ).

tff(f560,plain,
    ! [X0: $tType,X2: X0,X1: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fFalse),X2),X1) = X1 ),
    inference(cnf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: $tType,X1: X0,X2: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fFalse),X2),X1) = X1 ),
    inference(rectify,[],[f108]) ).

tff(f108,axiom,
    ! [X0: $tType,X42: X0,X43: X0] : ( aa(X0,X0,aa(X0,fun(X0,X0),aa(bool,fun(X0,fun(X0,X0)),if(X0),fFalse),X43),X42) = X42 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).

tff(f1604,plain,
    spl32_125,
    inference(avatar_split_clause,[],[f610,f1602]) ).

tff(f1602,plain,
    ( spl32_125
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP10(X0,X1,X2,X3)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X1 = X2 )
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_125])]) ).

tff(f610,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP10(X0,X1,X2,X3)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X1 = X2 )
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f378]) ).

tff(f378,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( sP10(X0,X1,X2,X3)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
          & ( X1 != X3 ) )
        | ( ( X1 = X2 )
          & ( X1 = X3 ) )
        | ( X2 = X3 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
            | ( X1 = X3 ) )
          & ( ( X1 != X2 )
            | ( X1 != X3 ) )
          & ( X2 != X3 ) )
        | ~ sP10(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f377]) ).

tff(f377,plain,
    ! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( ( sP10(X1,X2,X3,X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          & ( X0 != X2 ) )
        | ( ( X2 = X3 )
          & ( X0 = X2 ) )
        | ( X0 = X3 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
            | ( X0 = X2 ) )
          & ( ( X2 != X3 )
            | ( X0 != X2 ) )
          & ( X0 != X3 ) )
        | ~ sP10(X1,X2,X3,X0) ) ),
    inference(flattening,[],[f376]) ).

tff(f376,plain,
    ! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( ( sP10(X1,X2,X3,X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          & ( X0 != X2 ) )
        | ( ( X2 = X3 )
          & ( X0 = X2 ) )
        | ( X0 = X3 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
            | ( X0 = X2 ) )
          & ( ( X2 != X3 )
            | ( X0 != X2 ) )
          & ( X0 != X3 ) )
        | ~ sP10(X1,X2,X3,X0) ) ),
    inference(nnf_transformation,[],[f302]) ).

tff(f1600,plain,
    spl32_124,
    inference(avatar_split_clause,[],[f609,f1598]) ).

tff(f1598,plain,
    ( spl32_124
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP10(X0,X1,X2,X3)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X1 = X3 )
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_124])]) ).

tff(f609,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP10(X0,X1,X2,X3)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X1 = X3 )
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f378]) ).

tff(f1594,plain,
    spl32_123,
    inference(avatar_split_clause,[],[f601,f1592]) ).

tff(f1592,plain,
    ( spl32_123
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP9(X0,X1,X2,X3)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X1 = X2 )
        | ( X1 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_123])]) ).

tff(f601,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP9(X0,X1,X2,X3)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X1 = X2 )
      | ( X1 = X3 ) ),
    inference(cnf_transformation,[],[f374]) ).

tff(f374,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( sP9(X0,X1,X2,X3)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
          & ( X2 != X3 ) )
        | ( ( X1 = X2 )
          & ( X2 = X3 ) )
        | ( X1 = X3 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
            | ( X2 = X3 ) )
          & ( ( X1 != X2 )
            | ( X2 != X3 ) )
          & ( X1 != X3 ) )
        | ~ sP9(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f373]) ).

tff(f373,plain,
    ! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( ( sP9(X1,X2,X3,X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          & ( X0 != X3 ) )
        | ( ( X2 = X3 )
          & ( X0 = X3 ) )
        | ( X0 = X2 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
            | ( X0 = X3 ) )
          & ( ( X2 != X3 )
            | ( X0 != X3 ) )
          & ( X0 != X2 ) )
        | ~ sP9(X1,X2,X3,X0) ) ),
    inference(flattening,[],[f372]) ).

tff(f372,plain,
    ! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( ( sP9(X1,X2,X3,X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
          & ( X0 != X3 ) )
        | ( ( X2 = X3 )
          & ( X0 = X3 ) )
        | ( X0 = X2 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),X1)
            | ( X0 = X3 ) )
          & ( ( X2 != X3 )
            | ( X0 != X3 ) )
          & ( X0 != X2 ) )
        | ~ sP9(X1,X2,X3,X0) ) ),
    inference(nnf_transformation,[],[f300]) ).

tff(f1590,plain,
    spl32_122,
    inference(avatar_split_clause,[],[f600,f1588]) ).

tff(f1588,plain,
    ( spl32_122
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP9(X0,X1,X2,X3)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X2 = X3 )
        | ( X1 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_122])]) ).

tff(f600,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP9(X0,X1,X2,X3)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X2 = X3 )
      | ( X1 = X3 ) ),
    inference(cnf_transformation,[],[f374]) ).

tff(f1583,plain,
    ( spl32_121
    | ~ spl32_120 ),
    inference(avatar_split_clause,[],[f1579,f1576,f1581]) ).

tff(f1581,plain,
    ( spl32_121
  <=> ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP6(X0)
        | ~ sP5(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_121])]) ).

tff(f1576,plain,
    ( spl32_120
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP6(X0)
        | ~ sP5(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_120])]) ).

tff(f1579,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP6(X0)
        | ~ sP5(X0) )
    | ~ spl32_120 ),
    inference(forward_demodulation,[],[f1577,f635]) ).

tff(f1577,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP6(X0)
        | ~ sP5(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
    | ~ spl32_120 ),
    inference(avatar_component_clause,[],[f1576]) ).

tff(f1578,plain,
    spl32_120,
    inference(avatar_split_clause,[],[f532,f1576]) ).

tff(f532,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP6(X0)
      | ~ sP5(X0)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ),
    inference(cnf_transformation,[],[f345]) ).

tff(f1571,plain,
    ( spl32_119
    | ~ spl32_118 ),
    inference(avatar_split_clause,[],[f1567,f1564,f1569]) ).

tff(f1564,plain,
    ( spl32_118
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP5(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP6(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_118])]) ).

tff(f1567,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP5(X0)
        | ~ sP6(X0) )
    | ~ spl32_118 ),
    inference(forward_demodulation,[],[f1565,f635]) ).

tff(f1565,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP5(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP6(X0) )
    | ~ spl32_118 ),
    inference(avatar_component_clause,[],[f1564]) ).

tff(f1566,plain,
    spl32_118,
    inference(avatar_split_clause,[],[f529,f1564]) ).

tff(f529,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP5(X0)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f345]) ).

tff(f1559,plain,
    ( spl32_117
    | ~ spl32_115 ),
    inference(avatar_split_clause,[],[f1551,f1548,f1557]) ).

tff(f1548,plain,
    ( spl32_115
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP3(X0)
        | ~ sP2(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_115])]) ).

tff(f1551,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP3(X0)
        | ~ sP2(X0) )
    | ~ spl32_115 ),
    inference(forward_demodulation,[],[f1549,f635]) ).

tff(f1549,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP3(X0)
        | ~ sP2(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
    | ~ spl32_115 ),
    inference(avatar_component_clause,[],[f1548]) ).

tff(f1555,plain,
    ( spl32_116
    | ~ spl32_44
    | ~ spl32_84 ),
    inference(avatar_split_clause,[],[f1365,f1233,f896,f1553]) ).

tff(f896,plain,
    ( spl32_44
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),sK16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_44])]) ).

tff(f1233,plain,
    ( spl32_84
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP11(X0,X1,X2,X3,X4)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_84])]) ).

tff(f1365,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(sK16,b,a,X0,X1)
    | ~ spl32_44
    | ~ spl32_84 ),
    inference(resolution,[],[f1234,f898]) ).

tff(f898,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),sK16)
    | ~ spl32_44 ),
    inference(avatar_component_clause,[],[f896]) ).

tff(f1234,plain,
    ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | sP11(X0,X1,X2,X3,X4) )
    | ~ spl32_84 ),
    inference(avatar_component_clause,[],[f1233]) ).

tff(f1550,plain,
    spl32_115,
    inference(avatar_split_clause,[],[f512,f1548]) ).

tff(f512,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP3(X0)
      | ~ sP2(X0)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f1543,plain,
    ( spl32_114
    | ~ spl32_113 ),
    inference(avatar_split_clause,[],[f1539,f1536,f1541]) ).

tff(f1536,plain,
    ( spl32_113
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP2(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_113])]) ).

tff(f1539,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP2(X0)
        | ~ sP3(X0) )
    | ~ spl32_113 ),
    inference(forward_demodulation,[],[f1537,f635]) ).

tff(f1537,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP2(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP3(X0) )
    | ~ spl32_113 ),
    inference(avatar_component_clause,[],[f1536]) ).

tff(f1538,plain,
    spl32_113,
    inference(avatar_split_clause,[],[f509,f1536]) ).

tff(f509,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP2(X0)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f1531,plain,
    ( spl32_112
    | ~ spl32_111 ),
    inference(avatar_split_clause,[],[f1527,f1524,f1529]) ).

tff(f1524,plain,
    ( spl32_111
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP1(X0)
        | ~ sP0(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_111])]) ).

tff(f1527,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP1(X0)
        | ~ sP0(X0) )
    | ~ spl32_111 ),
    inference(forward_demodulation,[],[f1525,f635]) ).

tff(f1525,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP1(X0)
        | ~ sP0(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
    | ~ spl32_111 ),
    inference(avatar_component_clause,[],[f1524]) ).

tff(f1526,plain,
    spl32_111,
    inference(avatar_split_clause,[],[f492,f1524]) ).

tff(f492,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP1(X0)
      | ~ sP0(X0)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ),
    inference(cnf_transformation,[],[f331]) ).

tff(f1519,plain,
    ( spl32_110
    | ~ spl32_109 ),
    inference(avatar_split_clause,[],[f1515,f1512,f1517]) ).

tff(f1512,plain,
    ( spl32_109
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP0(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_109])]) ).

tff(f1515,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),n),aa(arrow_159774573e_indi,nat,h,X0)))
        | sP0(X0)
        | ~ sP1(X0) )
    | ~ spl32_109 ),
    inference(forward_demodulation,[],[f1513,f635]) ).

tff(f1513,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( sP0(X0)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
        | ~ sP1(X0) )
    | ~ spl32_109 ),
    inference(avatar_component_clause,[],[f1512]) ).

tff(f1514,plain,
    spl32_109,
    inference(avatar_split_clause,[],[f489,f1512]) ).

tff(f489,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP0(X0)
      | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f331]) ).

tff(f1510,plain,
    ( spl32_108
    | ~ spl32_43
    | ~ spl32_84 ),
    inference(avatar_split_clause,[],[f1364,f1233,f891,f1508]) ).

tff(f891,plain,
    ( spl32_43
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),sK15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_43])]) ).

tff(f1364,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(sK15,a,b,X0,X1)
    | ~ spl32_43
    | ~ spl32_84 ),
    inference(resolution,[],[f1234,f893]) ).

tff(f893,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),sK15)
    | ~ spl32_43 ),
    inference(avatar_component_clause,[],[f891]) ).

tff(f1472,plain,
    spl32_107,
    inference(avatar_split_clause,[],[f634,f1470]) ).

tff(f1470,plain,
    ( spl32_107
  <=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_107])]) ).

tff(f634,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    inference(cnf_transformation,[],[f197]) ).

tff(f197,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    inference(rectify,[],[f112]) ).

tff(f112,axiom,
    ! [X2: $tType,X1: $tType,X0: $tType,X50: X0,X51: fun(X0,X1),X49: fun(X1,X2)] : ( aa(X0,X2,combb(X1,X2,X0,X49,X51),X50) = aa(X1,X2,X49,aa(X0,X1,X51,X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

tff(f1468,plain,
    spl32_106,
    inference(avatar_split_clause,[],[f501,f1466]) ).

tff(f1466,plain,
    ( spl32_106
  <=> ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_106])]) ).

tff(f501,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f334]) ).

tff(f334,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        | ~ sP1(X0) )
      & ( sP1(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ) ),
    inference(nnf_transformation,[],[f289]) ).

tff(f289,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
    <=> sP1(X0) ),
    inference(definition_folding,[],[f243,f288,f287]) ).

tff(f243,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
    <=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
              | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
            & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
              | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ) ),
    inference(ennf_transformation,[],[f155]) ).

tff(f155,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
    <=> ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => ( ( ( n != aa(arrow_159774573e_indi,nat,h,X0) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
            & ( ( n = aa(arrow_159774573e_indi,nat,h,X0) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X4: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4))
    <=> ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => ( ( ( n != aa(arrow_159774573e_indi,nat,h,X4) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),e)) )
            & ( ( n = aa(arrow_159774573e_indi,nat,h,X4) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),c),e)) ) ) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),e)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096) ).

tff(f1464,plain,
    spl32_105,
    inference(avatar_split_clause,[],[f500,f1462]) ).

tff(f1462,plain,
    ( spl32_105
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP1(X0)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_105])]) ).

tff(f500,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP1(X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,d),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
    inference(cnf_transformation,[],[f334]) ).

tff(f1460,plain,
    spl32_104,
    inference(avatar_split_clause,[],[f461,f1458]) ).

tff(f1458,plain,
    ( spl32_104
  <=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
        | ~ ord_less_eq(X0,X2,X1)
        | ~ ord_less_eq(X0,X4,X3)
        | ~ ordere779506340up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_104])]) ).

tff(f461,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
      ( ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
      | ~ ord_less_eq(X0,X2,X1)
      | ~ ord_less_eq(X0,X4,X3)
      | ~ ordere779506340up_add(X0) ),
    inference(cnf_transformation,[],[f224]) ).

tff(f224,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
          | ~ ord_less_eq(X0,X2,X1)
          | ~ ord_less_eq(X0,X4,X3) )
      | ~ ordere779506340up_add(X0) ),
    inference(flattening,[],[f223]) ).

tff(f223,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
          | ~ ord_less_eq(X0,X2,X1)
          | ~ ord_less_eq(X0,X4,X3) )
      | ~ ordere779506340up_add(X0) ),
    inference(ennf_transformation,[],[f137]) ).

tff(f137,plain,
    ! [X0: $tType] :
      ( ordere779506340up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0,X4: X0] :
          ( ord_less_eq(X0,X4,X3)
         => ( ord_less_eq(X0,X2,X1)
           => ord_less_eq(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1)) ) ) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X0: $tType] :
      ( ordere779506340up_add(X0)
     => ! [X48: X0,X37: X0,X25: X0,X26: X0] :
          ( ord_less_eq(X0,X26,X25)
         => ( ord_less_eq(X0,X37,X48)
           => ord_less_eq(X0,plus_plus(X0,X26,X37),plus_plus(X0,X25,X48)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_add__mono) ).

tff(f1454,plain,
    spl32_103,
    inference(avatar_split_clause,[],[f685,f1452]) ).

tff(f1452,plain,
    ( spl32_103
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X1 = X2 )
        | ~ sP11(X0,X1,X2,X4,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_103])]) ).

tff(f685,plain,
    ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X1 = X2 )
      | ~ sP11(X0,X1,X2,X4,X4) ),
    inference(equality_resolution,[],[f629]) ).

tff(f629,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X1 = X2 )
      | ( X3 != X4 )
      | ~ sP11(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f393]) ).

tff(f393,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP11(X0,X1,X2,X3,X4)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
          & ( X1 != X2 )
          & ( X3 = X4 ) ) )
      & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X1 = X2 )
        | ( X3 != X4 )
        | ~ sP11(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f392]) ).

tff(f392,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( ( sP11(X2,X4,X1,X3,X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
          & ( X1 != X4 )
          & ( X0 = X3 ) ) )
      & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
        | ( X1 = X4 )
        | ( X0 != X3 )
        | ~ sP11(X2,X4,X1,X3,X0) ) ),
    inference(flattening,[],[f391]) ).

tff(f391,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( ( sP11(X2,X4,X1,X3,X0)
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
          & ( X1 != X4 )
          & ( X0 = X3 ) ) )
      & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
        | ( X1 = X4 )
        | ( X0 != X3 )
        | ~ sP11(X2,X4,X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f304]) ).

tff(f304,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
      ( sP11(X2,X4,X1,X3,X0)
    <=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
        | ( X1 = X4 )
        | ( X0 != X3 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

tff(f1450,plain,
    ( spl32_102
    | ~ spl32_40
    | ~ spl32_84 ),
    inference(avatar_split_clause,[],[f1363,f1233,f876,f1448]) ).

tff(f1363,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(lba,a,b,X0,X1)
    | ~ spl32_40
    | ~ spl32_84 ),
    inference(resolution,[],[f1234,f878]) ).

tff(f878,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
    | ~ spl32_40 ),
    inference(avatar_component_clause,[],[f876]) ).

tff(f1441,plain,
    spl32_101,
    inference(avatar_split_clause,[],[f622,f1439]) ).

tff(f1439,plain,
    ( spl32_101
  <=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP13(X0,X1,X2,X3,X4)
        | ~ sP12(X4,X3,X2,X1,X0)
        | ( X1 = X2 )
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_101])]) ).

tff(f622,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP13(X0,X1,X2,X3,X4)
      | ~ sP12(X4,X3,X2,X1,X0)
      | ( X1 = X2 )
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f387]) ).

tff(f1437,plain,
    spl32_100,
    inference(avatar_split_clause,[],[f606,f1435]) ).

tff(f1435,plain,
    ( spl32_100
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X1 = X3 )
        | ~ sP10(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_100])]) ).

tff(f606,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X1 = X3 )
      | ~ sP10(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f378]) ).

tff(f1433,plain,
    spl32_99,
    inference(avatar_split_clause,[],[f597,f1431]) ).

tff(f1431,plain,
    ( spl32_99
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
        | ( X2 = X3 )
        | ~ sP9(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_99])]) ).

tff(f597,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0)
      | ( X2 = X3 )
      | ~ sP9(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f374]) ).

tff(f1426,plain,
    ( spl32_98
    | ~ spl32_97 ),
    inference(avatar_split_clause,[],[f1421,f1417,f1423]) ).

tff(f1423,plain,
    ( spl32_98
  <=> pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))),sK17)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_98])]) ).

tff(f1417,plain,
    ( spl32_97
  <=> pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK17),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_97])]) ).

tff(f1421,plain,
    ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))),sK17))
    | ~ spl32_97 ),
    inference(forward_demodulation,[],[f1419,f635]) ).

tff(f1419,plain,
    ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK17),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))))
    | ~ spl32_97 ),
    inference(avatar_component_clause,[],[f1417]) ).

tff(f1420,plain,
    spl32_97,
    inference(avatar_split_clause,[],[f445,f1417]) ).

tff(f445,plain,
    pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK17),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))),
    inference(cnf_transformation,[],[f317]) ).

tff(f1412,plain,
    ( spl32_96
    | ~ spl32_41
    | ~ spl32_84 ),
    inference(avatar_split_clause,[],[f1362,f1233,f881,f1410]) ).

tff(f1362,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : sP11(lab,b,a,X0,X1)
    | ~ spl32_41
    | ~ spl32_84 ),
    inference(resolution,[],[f1234,f883]) ).

tff(f883,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab)
    | ~ spl32_41 ),
    inference(avatar_component_clause,[],[f881]) ).

tff(f1408,plain,
    ( spl32_95
    | ~ spl32_94 ),
    inference(avatar_split_clause,[],[f1403,f1399,f1405]) ).

tff(f1405,plain,
    ( spl32_95
  <=> pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))),n)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_95])]) ).

tff(f1399,plain,
    ( spl32_94
  <=> pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),n),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_94])]) ).

tff(f1403,plain,
    ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))),n))
    | ~ spl32_94 ),
    inference(forward_demodulation,[],[f1401,f635]) ).

tff(f1401,plain,
    ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),n),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))))
    | ~ spl32_94 ),
    inference(avatar_component_clause,[],[f1399]) ).

tff(f1402,plain,
    spl32_94,
    inference(avatar_split_clause,[],[f428,f1399]) ).

tff(f428,plain,
    pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),n),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,axiom,
    pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),n),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_n_I1_J) ).

tff(f1389,plain,
    spl32_93,
    inference(avatar_split_clause,[],[f691,f1386]) ).

tff(f1386,plain,
    ( spl32_93
  <=> pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))),sK31)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_93])]) ).

tff(f691,plain,
    pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool)))),sK31)),
    inference(forward_demodulation,[],[f655,f635]) ).

tff(f655,plain,
    pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),sK31),finite_card(arrow_159774573e_indi,top_top(fun(arrow_159774573e_indi,bool))))),
    inference(cnf_transformation,[],[f406]) ).

tff(f1384,plain,
    spl32_92,
    inference(avatar_split_clause,[],[f633,f1382]) ).

tff(f1382,plain,
    ( spl32_92
  <=> ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP14(X2,X0,X1,X3,X4)
        | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
        | ( X3 = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_92])]) ).

tff(f633,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP14(X2,X0,X1,X3,X4)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
      | ( X3 = X4 ) ),
    inference(cnf_transformation,[],[f308]) ).

tff(f308,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP14(X2,X0,X1,X3,X4)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
      | ( X3 = X4 ) ),
    inference(definition_folding,[],[f272,f307,f306,f305,f304]) ).

tff(f272,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X2),X4),X3))
      <=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
                | ( X0 = X3 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
                | ( X1 = X4 )
                | ( X0 != X3 ) ) )
            | ( X1 = X3 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2)
            | ( X1 != X3 ) )
          & ( X0 != X1 ) ) )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
      | ( X3 = X4 ) ),
    inference(flattening,[],[f271]) ).

tff(f271,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X2),X4),X3))
      <=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2)
                | ( X0 = X3 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
                | ( X1 = X4 )
                | ( X0 != X3 ) ) )
            | ( X1 = X3 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2)
            | ( X1 != X3 ) )
          & ( X0 != X1 ) ) )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
      | ( X3 = X4 ) ),
    inference(ennf_transformation,[],[f196]) ).

tff(f196,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( X3 != X4 )
     => ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
       => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X2),X4),X3))
        <=> ( ( ( X1 != X3 )
             => ( ( ( X0 != X3 )
                 => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X0),X2) )
                & ( ( X0 = X3 )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X1,X4),X2)
                    | ( X1 = X4 ) ) ) ) )
            & ( ( X1 = X3 )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X4,X0),X2) )
            & ( X0 != X1 ) ) ) ) ),
    inference(rectify,[],[f42]) ).

tff(f42,axiom,
    ! [X7: arrow_411405190le_alt,X8: arrow_411405190le_alt,X6: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X15: arrow_411405190le_alt,X16: arrow_411405190le_alt] :
      ( ( X15 != X16 )
     => ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6,arrow_1985332922le_Lin)
       => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X7),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,X6),X16),X15))
        <=> ( ( ( X8 != X15 )
             => ( ( ( X7 != X15 )
                 => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X7),X6) )
                & ( ( X7 = X15 )
                 => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X8,X16),X6)
                    | ( X8 = X16 ) ) ) ) )
            & ( ( X8 = X15 )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X16,X7),X6) )
            & ( X7 != X8 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_in__above) ).

tff(f1380,plain,
    ( spl32_91
    | ~ spl32_90 ),
    inference(avatar_split_clause,[],[f1376,f1373,f1378]) ).

tff(f1378,plain,
    ( spl32_91
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X1),X0))
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_91])]) ).

tff(f1373,plain,
    ( spl32_90
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_90])]) ).

tff(f1376,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X1),X0))
        | ~ sP8(X0,X1,X2) )
    | ~ spl32_90 ),
    inference(forward_demodulation,[],[f1374,f635]) ).

tff(f1374,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
        | ~ sP8(X0,X1,X2) )
    | ~ spl32_90 ),
    inference(avatar_component_clause,[],[f1373]) ).

tff(f1375,plain,
    spl32_90,
    inference(avatar_split_clause,[],[f570,f1373]) ).

tff(f570,plain,
    ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1))
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f353]) ).

tff(f353,plain,
    ! [X0: nat,X1: nat,X2: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X1)) )
      | ~ sP8(X0,X1,X2) ),
    inference(rectify,[],[f352]) ).

tff(f352,plain,
    ! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X2),X1)) )
      | ~ sP8(X2,X1,X0) ),
    inference(nnf_transformation,[],[f298]) ).

tff(f1371,plain,
    spl32_89,
    inference(avatar_split_clause,[],[f455,f1369]) ).

tff(f1369,plain,
    ( spl32_89
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
        | ~ ab_semigroup_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_89])]) ).

tff(f455,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
      | ~ ab_semigroup_add(X0) ),
    inference(cnf_transformation,[],[f217]) ).

tff(f217,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
      | ~ ab_semigroup_add(X0) ),
    inference(ennf_transformation,[],[f131]) ).

tff(f131,plain,
    ! [X0: $tType] :
      ( ab_semigroup_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) ) ),
    inference(rectify,[],[f63]) ).

tff(f63,axiom,
    ! [X0: $tType] :
      ( ab_semigroup_add(X0)
     => ! [X37: X0,X25: X0,X26: X0] : ( plus_plus(X0,plus_plus(X0,X26,X25),X37) = plus_plus(X0,X26,plus_plus(X0,X25,X37)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_ab__semigroup__add__class_Oadd__ac_I1_J) ).

tff(f1283,plain,
    ( spl32_88
    | ~ spl32_59
    | ~ spl32_83 ),
    inference(avatar_split_clause,[],[f1228,f1225,f990,f1281]) ).

tff(f1281,plain,
    ( spl32_88
  <=> ! [X0: nat] : ~ sP8(X0,X0,fequal(nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_88])]) ).

tff(f990,plain,
    ( spl32_59
  <=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_59])]) ).

tff(f1225,plain,
    ( spl32_83
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,X2,X0),X1))
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_83])]) ).

tff(f1228,plain,
    ( ! [X0: nat] : ~ sP8(X0,X0,fequal(nat))
    | ~ spl32_59
    | ~ spl32_83 ),
    inference(resolution,[],[f1226,f991]) ).

tff(f991,plain,
    ( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
    | ~ spl32_59 ),
    inference(avatar_component_clause,[],[f990]) ).

tff(f1226,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,X2,X0),X1))
        | ~ sP8(X0,X1,X2) )
    | ~ spl32_83 ),
    inference(avatar_component_clause,[],[f1225]) ).

tff(f1247,plain,
    spl32_87,
    inference(avatar_split_clause,[],[f680,f1245]) ).

tff(f1245,plain,
    ( spl32_87
  <=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X3),X4)
        | ~ sP13(X0,X2,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_87])]) ).

tff(f680,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X3),X4)
      | ~ sP13(X0,X2,X2,X3,X4) ),
    inference(equality_resolution,[],[f620]) ).

tff(f620,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X0,X3),X4)
      | ( X1 != X2 )
      | ~ sP13(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f387]) ).

tff(f1243,plain,
    spl32_86,
    inference(avatar_split_clause,[],[f650,f1241]) ).

tff(f1241,plain,
    ( spl32_86
  <=> ! [X1: $tType,X0: $tType,X5: X0,X4: X1,X3: X0,X2: X1] :
        ( ( X2 = X4 )
        | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_86])]) ).

tff(f650,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( X2 = X4 )
      | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f283,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( ( X2 = X4 )
        & ( X3 = X5 ) )
      | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ),
    inference(ennf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( product_Pair(X0,X1,X5,X4) = product_Pair(X0,X1,X3,X2) )
     => ~ ( ( X3 = X5 )
         => ( X2 != X4 ) ) ),
    inference(rectify,[],[f41]) ).

tff(f41,axiom,
    ! [X0: $tType,X1: $tType,X23: X1,X24: X0,X25: X1,X26: X0] :
      ( ( product_Pair(X0,X1,X26,X25) = product_Pair(X0,X1,X24,X23) )
     => ~ ( ( X24 = X26 )
         => ( X23 != X25 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Pair__inject) ).

tff(f1239,plain,
    spl32_85,
    inference(avatar_split_clause,[],[f649,f1237]) ).

tff(f1237,plain,
    ( spl32_85
  <=> ! [X1: $tType,X0: $tType,X3: X0,X4: X1,X5: X0,X2: X1] :
        ( ( X3 = X5 )
        | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_85])]) ).

tff(f649,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( X3 = X5 )
      | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f1235,plain,
    spl32_84,
    inference(avatar_split_clause,[],[f632,f1233]) ).

tff(f632,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP11(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X1),X0) ),
    inference(cnf_transformation,[],[f393]) ).

tff(f1227,plain,
    ( spl32_83
    | ~ spl32_82 ),
    inference(avatar_split_clause,[],[f1223,f1220,f1225]) ).

tff(f1220,plain,
    ( spl32_82
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_82])]) ).

tff(f1223,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,combc(nat,nat,bool,X2,X0),X1))
        | ~ sP8(X0,X1,X2) )
    | ~ spl32_82 ),
    inference(forward_demodulation,[],[f1221,f635]) ).

tff(f1221,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        | ~ sP8(X0,X1,X2) )
    | ~ spl32_82 ),
    inference(avatar_component_clause,[],[f1220]) ).

tff(f1222,plain,
    spl32_82,
    inference(avatar_split_clause,[],[f571,f1220]) ).

tff(f571,plain,
    ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
      ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f353]) ).

tff(f1214,plain,
    ( spl32_81
    | ~ spl32_80 ),
    inference(avatar_split_clause,[],[f1210,f1207,f1212]) ).

tff(f1212,plain,
    ( spl32_81
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_81])]) ).

tff(f1207,plain,
    ( spl32_80
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_80])]) ).

tff(f1210,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] :
        ( ~ pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X1),X2))
        | ( X1 = X2 ) )
    | ~ spl32_80 ),
    inference(forward_demodulation,[],[f1208,f635]) ).

tff(f1208,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) )
    | ~ spl32_80 ),
    inference(avatar_component_clause,[],[f1207]) ).

tff(f1209,plain,
    spl32_80,
    inference(avatar_split_clause,[],[f564,f1207]) ).

tff(f564,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 = X2 )
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
    inference(cnf_transformation,[],[f178]) ).

tff(f178,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( ( X1 = X2 )
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
    inference(rectify,[],[f117]) ).

tff(f117,axiom,
    ! [X0: $tType,X42: X0,X43: X0] :
      ( ( X42 = X43 )
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X43),X42)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

tff(f1205,plain,
    spl32_79,
    inference(avatar_split_clause,[],[f546,f1203]) ).

tff(f1203,plain,
    ( spl32_79
  <=> ! [X0: $tType,X1: fun(X0,bool)] : member(fun(X0,X0),combi(X0),pi(X0,X0,X1,combk(fun(X0,bool),X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_79])]) ).

tff(f546,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : member(fun(X0,X0),combi(X0),pi(X0,X0,X1,combk(fun(X0,bool),X0,X1))),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : member(fun(X0,X0),combi(X0),pi(X0,X0,X1,combk(fun(X0,bool),X0,X1))),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X0: $tType,X32: fun(X0,bool)] : member(fun(X0,X0),combi(X0),pi(X0,X0,X32,combk(fun(X0,bool),X0,X32))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_funcset__id) ).

tff(f1200,plain,
    spl32_78,
    inference(avatar_split_clause,[],[f545,f1198]) ).

tff(f1198,plain,
    ( spl32_78
  <=> ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X1,X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_78])]) ).

tff(f545,plain,
    ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X1,X0)),X1)),
    inference(cnf_transformation,[],[f161]) ).

tff(f161,plain,
    ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X1,X0)),X1)),
    inference(rectify,[],[f98]) ).

tff(f98,axiom,
    ! [X46: nat,X47: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X47,X46)),X47)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_not__add__less1) ).

tff(f1188,plain,
    ( spl32_77
    | ~ spl32_76 ),
    inference(avatar_split_clause,[],[f1184,f1181,f1186]) ).

tff(f1186,plain,
    ( spl32_77
  <=> ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),plus_plus(nat,X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_77])]) ).

tff(f1181,plain,
    ( spl32_76
  <=> ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X1,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_76])]) ).

tff(f1184,plain,
    ( ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),plus_plus(nat,X1,X0)))
    | ~ spl32_76 ),
    inference(forward_demodulation,[],[f1182,f635]) ).

tff(f1182,plain,
    ( ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X1,X0)),X0))
    | ~ spl32_76 ),
    inference(avatar_component_clause,[],[f1181]) ).

tff(f1183,plain,
    spl32_76,
    inference(avatar_split_clause,[],[f544,f1181]) ).

tff(f544,plain,
    ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X1,X0)),X0)),
    inference(cnf_transformation,[],[f160]) ).

tff(f160,plain,
    ! [X0: nat,X1: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X1,X0)),X0)),
    inference(rectify,[],[f99]) ).

tff(f99,axiom,
    ! [X47: nat,X46: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X46,X47)),X47)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_not__add__less2) ).

tff(f1179,plain,
    spl32_75,
    inference(avatar_split_clause,[],[f476,f1177]) ).

tff(f1177,plain,
    ( spl32_75
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        | ~ ord_less_eq(X0,X2,X1)
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_75])]) ).

tff(f476,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
      | ~ ord_less_eq(X0,X2,X1)
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f322]) ).

tff(f322,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
            | ~ ord_less_eq(X0,X2,X1) )
          & ( ord_less_eq(X0,X2,X1)
            | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1)) ) )
      | ~ ordere236663937imp_le(X0) ),
    inference(nnf_transformation,[],[f236]) ).

tff(f236,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        <=> ord_less_eq(X0,X2,X1) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f148]) ).

tff(f148,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        <=> ord_less_eq(X0,X2,X1) ) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X15: X0,X16: X0,X19: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X19,X16),plus_plus(X0,X19,X15))
        <=> ord_less_eq(X0,X16,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__le__cancel__left) ).

tff(f1175,plain,
    spl32_74,
    inference(avatar_split_clause,[],[f474,f1173]) ).

tff(f1173,plain,
    ( spl32_74
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        | ~ ord_less_eq(X0,X3,X1)
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_74])]) ).

tff(f474,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
      | ~ ord_less_eq(X0,X3,X1)
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f321]) ).

tff(f321,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
            | ~ ord_less_eq(X0,X3,X1) )
          & ( ord_less_eq(X0,X3,X1)
            | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) ) )
      | ~ ordere236663937imp_le(X0) ),
    inference(nnf_transformation,[],[f235]) ).

tff(f235,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        <=> ord_less_eq(X0,X3,X1) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        <=> ord_less_eq(X0,X3,X1) ) ),
    inference(rectify,[],[f61]) ).

tff(f61,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X15: X0,X19: X0,X16: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X16,X19),plus_plus(X0,X15,X19))
        <=> ord_less_eq(X0,X16,X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__le__cancel__right) ).

tff(f1171,plain,
    spl32_73,
    inference(avatar_split_clause,[],[f470,f1169]) ).

tff(f1169,plain,
    ( spl32_73
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,X2,X1)
        | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_73])]) ).

tff(f470,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less_eq(X0,X2,X1)
      | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f232]) ).

tff(f232,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,X2,X1)
          | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1)) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
         => ord_less_eq(X0,X2,X1) ) ),
    inference(rectify,[],[f88]) ).

tff(f88,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X25: X0,X26: X0,X37: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X37,X26),plus_plus(X0,X37,X25))
         => ord_less_eq(X0,X26,X25) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add__le__imp__le__left) ).

tff(f1167,plain,
    ( spl32_72
    | ~ spl32_30
    | ~ spl32_46 ),
    inference(avatar_split_clause,[],[f922,f906,f829,f1165]) ).

tff(f1165,plain,
    ( spl32_72
  <=> ! [X0: bool] :
        ( ~ pp(X0)
        | member(bool,X0,combi(bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_72])]) ).

tff(f829,plain,
    ( spl32_30
  <=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_30])]) ).

tff(f906,plain,
    ( spl32_46
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_46])]) ).

tff(f922,plain,
    ( ! [X0: bool] :
        ( ~ pp(X0)
        | member(bool,X0,combi(bool)) )
    | ~ spl32_30
    | ~ spl32_46 ),
    inference(superposition,[],[f907,f830]) ).

tff(f830,plain,
    ( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
    | ~ spl32_30 ),
    inference(avatar_component_clause,[],[f829]) ).

tff(f907,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ~ pp(aa(X0,bool,X1,X2))
        | member(X0,X2,X1) )
    | ~ spl32_46 ),
    inference(avatar_component_clause,[],[f906]) ).

tff(f1163,plain,
    spl32_71,
    inference(avatar_split_clause,[],[f469,f1161]) ).

tff(f1161,plain,
    ( spl32_71
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,X3,X1)
        | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
        | ~ ordere236663937imp_le(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_71])]) ).

tff(f469,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less_eq(X0,X3,X1)
      | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
      | ~ ordere236663937imp_le(X0) ),
    inference(cnf_transformation,[],[f231]) ).

tff(f231,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,X3,X1)
          | ~ ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) )
      | ~ ordere236663937imp_le(X0) ),
    inference(ennf_transformation,[],[f143]) ).

tff(f143,plain,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
         => ord_less_eq(X0,X3,X1) ) ),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X0: $tType] :
      ( ordere236663937imp_le(X0)
     => ! [X25: X0,X37: X0,X26: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X26,X37),plus_plus(X0,X25,X37))
         => ord_less_eq(X0,X26,X25) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__le__imp__le__right) ).

tff(f1159,plain,
    spl32_70,
    inference(avatar_split_clause,[],[f458,f1157]) ).

tff(f1157,plain,
    ( spl32_70
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
        | ~ ord_less_eq(X0,X3,X2)
        | ~ ordere779506340up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_70])]) ).

tff(f458,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less_eq(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
      | ~ ord_less_eq(X0,X3,X2)
      | ~ ordere779506340up_add(X0) ),
    inference(cnf_transformation,[],[f220]) ).

tff(f220,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
          | ~ ord_less_eq(X0,X3,X2) )
      | ~ ordere779506340up_add(X0) ),
    inference(ennf_transformation,[],[f134]) ).

tff(f134,plain,
    ! [X0: $tType] :
      ( ordere779506340up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,X3,X2)
         => ord_less_eq(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2)) ) ),
    inference(rectify,[],[f91]) ).

tff(f91,axiom,
    ! [X0: $tType] :
      ( ordere779506340up_add(X0)
     => ! [X37: X0,X25: X0,X26: X0] :
          ( ord_less_eq(X0,X26,X25)
         => ord_less_eq(X0,plus_plus(X0,X37,X26),plus_plus(X0,X37,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__left__mono) ).

tff(f1155,plain,
    spl32_69,
    inference(avatar_split_clause,[],[f457,f1153]) ).

tff(f1153,plain,
    ( spl32_69
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1))
        | ~ ord_less_eq(X0,X3,X2)
        | ~ ordere779506340up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_69])]) ).

tff(f457,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less_eq(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1))
      | ~ ord_less_eq(X0,X3,X2)
      | ~ ordere779506340up_add(X0) ),
    inference(cnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1))
          | ~ ord_less_eq(X0,X3,X2) )
      | ~ ordere779506340up_add(X0) ),
    inference(ennf_transformation,[],[f133]) ).

tff(f133,plain,
    ! [X0: $tType] :
      ( ordere779506340up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,X3,X2)
         => ord_less_eq(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1)) ) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X0: $tType] :
      ( ordere779506340up_add(X0)
     => ! [X37: X0,X25: X0,X26: X0] :
          ( ord_less_eq(X0,X26,X25)
         => ord_less_eq(X0,plus_plus(X0,X26,X37),plus_plus(X0,X25,X37)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__right__mono) ).

tff(f1065,plain,
    spl32_68,
    inference(avatar_split_clause,[],[f624,f1063]) ).

tff(f1063,plain,
    ( spl32_68
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP11(X0,X4,X2,X3,X1)
        | ( X2 = X3 )
        | ~ sP12(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_68])]) ).

tff(f624,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP11(X0,X4,X2,X3,X1)
      | ( X2 = X3 )
      | ~ sP12(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f390]) ).

tff(f1061,plain,
    spl32_67,
    inference(avatar_split_clause,[],[f559,f1059]) ).

tff(f1059,plain,
    ( spl32_67
  <=> ! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_67])]) ).

tff(f559,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ),
    inference(cnf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ),
    inference(rectify,[],[f78]) ).

tff(f78,axiom,
    ! [X45: nat,X41: nat,X40: nat] : ( plus_plus(nat,plus_plus(nat,X40,X41),X45) = plus_plus(nat,X40,plus_plus(nat,X41,X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__add__assoc) ).

tff(f1057,plain,
    spl32_66,
    inference(avatar_split_clause,[],[f558,f1055]) ).

tff(f1055,plain,
    ( spl32_66
  <=> ! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,X1,plus_plus(nat,X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_66])]) ).

tff(f558,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,X1,plus_plus(nat,X2,X0)) ),
    inference(cnf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,X1,plus_plus(nat,X2,X0)) ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X44: nat,X42: nat,X43: nat] : ( plus_plus(nat,X43,plus_plus(nat,X42,X44)) = plus_plus(nat,X42,plus_plus(nat,X43,X44)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__commute) ).

tff(f1018,plain,
    spl32_65,
    inference(avatar_split_clause,[],[f583,f1016]) ).

tff(f1016,plain,
    ( spl32_65
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_65])]) ).

tff(f583,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ord_less_eq(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f357]) ).

tff(f357,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ord_less_eq(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
        | ~ ord_less_eq(nat,X1,X0) )
      & ( ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ) ),
    inference(nnf_transformation,[],[f187]) ).

tff(f187,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less_eq(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
    <=> ord_less_eq(nat,X1,X0) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X20: nat,X33: nat,X34: nat] :
      ( ord_less_eq(nat,plus_plus(nat,X34,X33),plus_plus(nat,X34,X20))
    <=> ord_less_eq(nat,X33,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_nat__add__left__cancel__le) ).

tff(f1014,plain,
    spl32_64,
    inference(avatar_split_clause,[],[f582,f1012]) ).

tff(f1012,plain,
    ( spl32_64
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_64])]) ).

tff(f582,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ),
    inference(cnf_transformation,[],[f357]) ).

tff(f1010,plain,
    spl32_63,
    inference(avatar_split_clause,[],[f464,f1008]) ).

tff(f1008,plain,
    ( spl32_63
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
        | ~ cancel_semigroup_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_63])]) ).

tff(f464,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ( X1 = X2 )
      | ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
      | ~ cancel_semigroup_add(X0) ),
    inference(cnf_transformation,[],[f228]) ).

tff(f228,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( X1 = X2 )
          | ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) ) )
      | ~ cancel_semigroup_add(X0) ),
    inference(ennf_transformation,[],[f140]) ).

tff(f140,plain,
    ! [X0: $tType] :
      ( cancel_semigroup_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
         => ( X1 = X2 ) ) ),
    inference(rectify,[],[f64]) ).

tff(f64,axiom,
    ! [X0: $tType] :
      ( cancel_semigroup_add(X0)
     => ! [X37: X0,X25: X0,X26: X0] :
          ( ( plus_plus(X0,X26,X25) = plus_plus(X0,X26,X37) )
         => ( X25 = X37 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_add__left__imp__eq) ).

tff(f1006,plain,
    spl32_62,
    inference(avatar_split_clause,[],[f463,f1004]) ).

tff(f1004,plain,
    ( spl32_62
  <=> ! [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,[spl32_62])]) ).

tff(f463,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,[],[f227]) ).

tff(f227,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( X1 = X3 )
          | ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) ) )
      | ~ cancel_semigroup_add(X0) ),
    inference(ennf_transformation,[],[f139]) ).

tff(f139,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,[],[f66]) ).

tff(f66,axiom,
    ! [X0: $tType] :
      ( cancel_semigroup_add(X0)
     => ! [X37: X0,X26: X0,X25: X0] :
          ( ( plus_plus(X0,X25,X26) = plus_plus(X0,X37,X26) )
         => ( X25 = X37 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_add__right__imp__eq) ).

tff(f1002,plain,
    spl32_61,
    inference(avatar_split_clause,[],[f456,f1000]) ).

tff(f1000,plain,
    ( spl32_61
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
        | ~ cancel146912293up_add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_61])]) ).

tff(f456,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ( X1 = X2 )
      | ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
      | ~ cancel146912293up_add(X0) ),
    inference(cnf_transformation,[],[f218]) ).

tff(f218,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ( X1 = X2 )
          | ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) ) )
      | ~ cancel146912293up_add(X0) ),
    inference(ennf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: $tType] :
      ( cancel146912293up_add(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
         => ( X1 = X2 ) ) ),
    inference(rectify,[],[f65]) ).

tff(f65,axiom,
    ! [X0: $tType] :
      ( cancel146912293up_add(X0)
     => ! [X37: X0,X25: X0,X26: X0] :
          ( ( plus_plus(X0,X26,X25) = plus_plus(X0,X26,X37) )
         => ( X25 = X37 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add__imp__eq) ).

tff(f996,plain,
    ( spl32_60
    | ~ spl32_24
    | ~ spl32_54 ),
    inference(avatar_split_clause,[],[f970,f950,f798,f994]) ).

tff(f994,plain,
    ( spl32_60
  <=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : sP12(X0,X1,X2,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_60])]) ).

tff(f798,plain,
    ( spl32_24
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] : sP11(X0,X2,X2,X3,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_24])]) ).

tff(f970,plain,
    ( ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : sP12(X0,X1,X2,X1,X2)
    | ~ spl32_24
    | ~ spl32_54 ),
    inference(resolution,[],[f951,f799]) ).

tff(f799,plain,
    ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP11(X0,X2,X2,X3,X4)
    | ~ spl32_24 ),
    inference(avatar_component_clause,[],[f798]) ).

tff(f992,plain,
    ( spl32_59
    | ~ spl32_58 ),
    inference(avatar_split_clause,[],[f988,f985,f990]) ).

tff(f985,plain,
    ( spl32_58
  <=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_58])]) ).

tff(f988,plain,
    ( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2))
    | ~ spl32_58 ),
    inference(forward_demodulation,[],[f986,f635]) ).

tff(f986,plain,
    ( ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2))
    | ~ spl32_58 ),
    inference(avatar_component_clause,[],[f985]) ).

tff(f987,plain,
    spl32_58,
    inference(avatar_split_clause,[],[f667,f985]) ).

tff(f667,plain,
    ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
    inference(equality_resolution,[],[f563]) ).

tff(f563,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f177]) ).

tff(f177,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
      | ( X1 != X2 ) ),
    inference(rectify,[],[f118]) ).

tff(f118,axiom,
    ! [X0: $tType,X42: X0,X43: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X43),X42))
      | ( X42 != X43 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

tff(f980,plain,
    ( spl32_57
    | ~ spl32_56 ),
    inference(avatar_split_clause,[],[f976,f973,f978]) ).

tff(f978,plain,
    ( spl32_57
  <=> ! [X0: nat] : ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_57])]) ).

tff(f973,plain,
    ( spl32_56
  <=> ! [X0: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_56])]) ).

tff(f976,plain,
    ( ! [X0: nat] : ~ pp(aa(nat,bool,combc(nat,nat,bool,ord_less(nat),X0),X0))
    | ~ spl32_56 ),
    inference(forward_demodulation,[],[f974,f635]) ).

tff(f974,plain,
    ( ! [X0: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X0))
    | ~ spl32_56 ),
    inference(avatar_component_clause,[],[f973]) ).

tff(f975,plain,
    spl32_56,
    inference(avatar_split_clause,[],[f449,f973]) ).

tff(f449,plain,
    ! [X0: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X0)),
    inference(cnf_transformation,[],[f126]) ).

tff(f126,plain,
    ! [X0: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X0),X0)),
    inference(rectify,[],[f74]) ).

tff(f74,axiom,
    ! [X41: nat] : ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),X41),X41)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__not__refl) ).

tff(f956,plain,
    ( spl32_55
    | ~ spl32_30
    | ~ spl32_45 ),
    inference(avatar_split_clause,[],[f918,f902,f829,f954]) ).

tff(f954,plain,
    ( spl32_55
  <=> ! [X0: bool] :
        ( pp(X0)
        | ~ member(bool,X0,combi(bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_55])]) ).

tff(f902,plain,
    ( spl32_45
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_45])]) ).

tff(f918,plain,
    ( ! [X0: bool] :
        ( pp(X0)
        | ~ member(bool,X0,combi(bool)) )
    | ~ spl32_30
    | ~ spl32_45 ),
    inference(superposition,[],[f903,f830]) ).

tff(f903,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) )
    | ~ spl32_45 ),
    inference(avatar_component_clause,[],[f902]) ).

tff(f952,plain,
    spl32_54,
    inference(avatar_split_clause,[],[f682,f950]) ).

tff(f682,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP12(X0,X3,X2,X3,X4)
      | ~ sP11(X0,X4,X2,X3,X3) ),
    inference(equality_resolution,[],[f627]) ).

tff(f627,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP12(X0,X1,X2,X3,X4)
      | ( X1 != X3 )
      | ~ sP11(X0,X4,X2,X3,X1) ),
    inference(cnf_transformation,[],[f390]) ).

tff(f948,plain,
    spl32_53,
    inference(avatar_split_clause,[],[f621,f946]) ).

tff(f946,plain,
    ( spl32_53
  <=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP12(X4,X3,X2,X1,X0)
        | ~ sP13(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_53])]) ).

tff(f621,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP12(X4,X3,X2,X1,X0)
      | ~ sP13(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f387]) ).

tff(f944,plain,
    spl32_52,
    inference(avatar_split_clause,[],[f580,f942]) ).

tff(f942,plain,
    ( spl32_52
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( plus_plus(nat,X2,X0) != plus_plus(nat,X2,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_52])]) ).

tff(f580,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( plus_plus(nat,X2,X0) != plus_plus(nat,X2,X1) ) ),
    inference(cnf_transformation,[],[f356]) ).

tff(f356,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( plus_plus(nat,X2,X0) = plus_plus(nat,X2,X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( plus_plus(nat,X2,X0) != plus_plus(nat,X2,X1) ) ) ),
    inference(nnf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( plus_plus(nat,X2,X0) = plus_plus(nat,X2,X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X20: nat,X33: nat,X34: nat] :
      ( ( plus_plus(nat,X34,X33) = plus_plus(nat,X34,X20) )
    <=> ( X20 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_nat__add__left__cancel) ).

tff(f940,plain,
    spl32_51,
    inference(avatar_split_clause,[],[f578,f938]) ).

tff(f938,plain,
    ( spl32_51
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( X0 = X2 )
        | ( plus_plus(nat,X0,X1) != plus_plus(nat,X2,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_51])]) ).

tff(f578,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( X0 = X2 )
      | ( plus_plus(nat,X0,X1) != plus_plus(nat,X2,X1) ) ),
    inference(cnf_transformation,[],[f355]) ).

tff(f355,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( plus_plus(nat,X0,X1) = plus_plus(nat,X2,X1) )
        | ( X0 != X2 ) )
      & ( ( X0 = X2 )
        | ( plus_plus(nat,X0,X1) != plus_plus(nat,X2,X1) ) ) ),
    inference(nnf_transformation,[],[f185]) ).

tff(f185,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( plus_plus(nat,X0,X1) = plus_plus(nat,X2,X1) )
    <=> ( X0 = X2 ) ),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X20: nat,X34: nat,X33: nat] :
      ( ( plus_plus(nat,X33,X34) = plus_plus(nat,X20,X34) )
    <=> ( X20 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_nat__add__right__cancel) ).

tff(f936,plain,
    spl32_50,
    inference(avatar_split_clause,[],[f566,f934]) ).

tff(f934,plain,
    ( spl32_50
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X2,X0)
        | ~ ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(nat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_50])]) ).

tff(f566,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ord_less_eq(nat,X2,X0)
      | ~ ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(nat,X2,X1) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f258,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less_eq(nat,X2,X0)
      | ~ ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(nat,X2,X1) ),
    inference(flattening,[],[f257]) ).

tff(f257,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less_eq(nat,X2,X0)
      | ~ ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(nat,X2,X1) ),
    inference(ennf_transformation,[],[f180]) ).

tff(f180,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less_eq(nat,X2,X1)
     => ( ord_less_eq(nat,X1,X0)
       => ord_less_eq(nat,X2,X0) ) ),
    inference(rectify,[],[f82]) ).

tff(f82,axiom,
    ! [X45: nat,X46: nat,X47: nat] :
      ( ord_less_eq(nat,X47,X46)
     => ( ord_less_eq(nat,X46,X45)
       => ord_less_eq(nat,X47,X45) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_le__trans) ).

tff(f929,plain,
    spl32_49,
    inference(avatar_split_clause,[],[f550,f927]) ).

tff(f927,plain,
    ( spl32_49
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ~ ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_49])]) ).

tff(f550,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f250,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(flattening,[],[f249]) ).

tff(f249,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(ennf_transformation,[],[f166]) ).

tff(f166,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
     => ( ord_less_eq(nat,X0,X1)
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f83]) ).

tff(f83,axiom,
    ! [X41: nat,X40: nat] :
      ( ord_less_eq(nat,X40,X41)
     => ( ord_less_eq(nat,X41,X40)
       => ( X40 = X41 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_le__antisym) ).

tff(f916,plain,
    ( spl32_48
    | ~ spl32_21 ),
    inference(avatar_split_clause,[],[f801,f786,f914]) ).

tff(f786,plain,
    ( spl32_21
  <=> ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_21])]) ).

tff(f801,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) )
    | ~ spl32_21 ),
    inference(superposition,[],[f787,f787]) ).

tff(f787,plain,
    ( ! [X0: bool] :
        ( ( fTrue = X0 )
        | ( fFalse = X0 ) )
    | ~ spl32_21 ),
    inference(avatar_component_clause,[],[f786]) ).

tff(f912,plain,
    spl32_47,
    inference(avatar_split_clause,[],[f590,f910]) ).

tff(f910,plain,
    ( spl32_47
  <=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_47])]) ).

tff(f590,plain,
    ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(cnf_transformation,[],[f191]) ).

tff(f191,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(rectify,[],[f115]) ).

tff(f115,axiom,
    ! [X1: $tType,X0: $tType,X51: X1,X49: X0] : ( aa(X1,X0,combk(X0,X1,X49),X51) = X49 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).

tff(f908,plain,
    spl32_46,
    inference(avatar_split_clause,[],[f577,f906]) ).

tff(f577,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( member(X0,X2,X1)
      | ~ pp(aa(X0,bool,X1,X2)) ),
    inference(cnf_transformation,[],[f354]) ).

tff(f354,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) )
      & ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( member(X0,X2,X1)
    <=> pp(aa(X0,bool,X1,X2)) ),
    inference(rectify,[],[f75]) ).

tff(f75,axiom,
    ! [X0: $tType,X32: fun(X0,bool),X8: X0] :
      ( member(X0,X8,X32)
    <=> pp(aa(X0,bool,X32,X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_mem__def) ).

tff(f904,plain,
    spl32_45,
    inference(avatar_split_clause,[],[f576,f902]) ).

tff(f576,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( pp(aa(X0,bool,X1,X2))
      | ~ member(X0,X2,X1) ),
    inference(cnf_transformation,[],[f354]) ).

tff(f899,plain,
    spl32_44,
    inference(avatar_split_clause,[],[f443,f896]) ).

tff(f443,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),sK16),
    inference(cnf_transformation,[],[f315]) ).

tff(f315,plain,
    ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK16,arrow_1985332922le_Lin)
    & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),sK16) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f213,f314]) ).

tff(f314,plain,
    ( ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
        & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),X0) )
   => ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK16,arrow_1985332922le_Lin)
      & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),sK16) ) ),
    introduced(choice_axiom,[]) ).

tff(f213,plain,
    ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
      & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),X0) ),
    inference(ennf_transformation,[],[f123]) ).

tff(f123,plain,
    ~ ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),X0)
       => ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
    inference(rectify,[],[f31]) ).

tff(f31,axiom,
    ~ ! [X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),X22)
       => ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X22,arrow_1985332922le_Lin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

tff(f894,plain,
    spl32_43,
    inference(avatar_split_clause,[],[f441,f891]) ).

tff(f441,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),sK15),
    inference(cnf_transformation,[],[f313]) ).

tff(f313,plain,
    ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK15,arrow_1985332922le_Lin)
    & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),sK15) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f212,f312]) ).

tff(f312,plain,
    ( ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
        & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),X0) )
   => ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK15,arrow_1985332922le_Lin)
      & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),sK15) ) ),
    introduced(choice_axiom,[]) ).

tff(f212,plain,
    ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
      & member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),X0) ),
    inference(ennf_transformation,[],[f122]) ).

tff(f122,plain,
    ~ ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),X0)
       => ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
    inference(rectify,[],[f30]) ).

tff(f30,axiom,
    ~ ! [X21: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),X21)
       => ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X21,arrow_1985332922le_Lin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

tff(f889,plain,
    spl32_42,
    inference(avatar_split_clause,[],[f427,f886]) ).

tff(f886,plain,
    ( spl32_42
  <=> member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_42])]) ).

tff(f427,plain,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof),
    inference(cnf_transformation,[],[f8]) ).

tff(f8,axiom,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096P_A_058_AProf_096) ).

tff(f884,plain,
    spl32_41,
    inference(avatar_split_clause,[],[f426,f881]) ).

tff(f426,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab),
    inference(cnf_transformation,[],[f5]) ).

tff(f5,axiom,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

tff(f879,plain,
    spl32_40,
    inference(avatar_split_clause,[],[f425,f876]) ).

tff(f425,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba),
    inference(cnf_transformation,[],[f6]) ).

tff(f6,axiom,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

tff(f874,plain,
    ~ spl32_39,
    inference(avatar_split_clause,[],[f424,f871]) ).

tff(f424,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,axiom,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

tff(f869,plain,
    ~ spl32_38,
    inference(avatar_split_clause,[],[f423,f866]) ).

tff(f423,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab),
    inference(cnf_transformation,[],[f20]) ).

tff(f20,axiom,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

tff(f864,plain,
    spl32_37,
    inference(avatar_split_clause,[],[f630,f862]) ).

tff(f862,plain,
    ( spl32_37
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
        ( sP11(X0,X1,X2,X3,X4)
        | ( X3 = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_37])]) ).

tff(f630,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP11(X0,X1,X2,X3,X4)
      | ( X3 = X4 ) ),
    inference(cnf_transformation,[],[f393]) ).

tff(f860,plain,
    ( spl32_35
    | ~ spl32_36
    | ~ spl32_21 ),
    inference(avatar_split_clause,[],[f803,f786,f857,f854]) ).

tff(f854,plain,
    ( spl32_35
  <=> ! [X0: bool] : ( fFalse = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_35])]) ).

tff(f857,plain,
    ( spl32_36
  <=> ( fTrue = fFalse ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_36])]) ).

tff(f803,plain,
    ( ! [X0: bool] :
        ( ( fTrue != fFalse )
        | ( fFalse = X0 ) )
    | ~ spl32_21 ),
    inference(equality_factoring,[],[f787]) ).

tff(f852,plain,
    spl32_34,
    inference(avatar_split_clause,[],[f543,f850]) ).

tff(f850,plain,
    ( spl32_34
  <=> ! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_34])]) ).

tff(f543,plain,
    ! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
    inference(cnf_transformation,[],[f159]) ).

tff(f159,plain,
    ! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
    inference(rectify,[],[f76]) ).

tff(f76,axiom,
    ! [X41: nat,X40: nat] : ( plus_plus(nat,X40,X41) = plus_plus(nat,X41,X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_nat__add__commute) ).

tff(f844,plain,
    spl32_33,
    inference(avatar_split_clause,[],[f689,f842]) ).

tff(f842,plain,
    ( spl32_33
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
        ( sP9(X0,X1,X3,X3)
        | ( X1 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_33])]) ).

tff(f689,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP9(X0,X1,X3,X3)
      | ( X1 = X3 ) ),
    inference(duplicate_literal_removal,[],[f670]) ).

tff(f670,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP9(X0,X1,X3,X3)
      | ( X1 = X3 )
      | ( X1 = X3 ) ),
    inference(equality_resolution,[],[f599]) ).

tff(f599,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP9(X0,X1,X2,X3)
      | ( X2 != X3 )
      | ( X1 = X2 )
      | ( X1 = X3 ) ),
    inference(cnf_transformation,[],[f374]) ).

tff(f839,plain,
    spl32_32,
    inference(avatar_split_clause,[],[f688,f837]) ).

tff(f837,plain,
    ( spl32_32
  <=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt] :
        ( sP10(X0,X3,X2,X3)
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_32])]) ).

tff(f688,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP10(X0,X3,X2,X3)
      | ( X2 = X3 ) ),
    inference(duplicate_literal_removal,[],[f675]) ).

tff(f675,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP10(X0,X3,X2,X3)
      | ( X2 = X3 )
      | ( X2 = X3 ) ),
    inference(equality_resolution,[],[f608]) ).

tff(f608,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( sP10(X0,X1,X2,X3)
      | ( X1 != X3 )
      | ( X1 = X2 )
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f378]) ).

tff(f835,plain,
    spl32_31,
    inference(avatar_split_clause,[],[f547,f833]) ).

tff(f833,plain,
    ( spl32_31
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_31])]) ).

tff(f547,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X0,X1)
      | ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X0,X1)
      | ord_less_eq(nat,X1,X0) ),
    inference(rectify,[],[f80]) ).

tff(f80,axiom,
    ! [X41: nat,X40: nat] :
      ( ord_less_eq(nat,X41,X40)
      | ord_less_eq(nat,X40,X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_nat__le__linear) ).

tff(f831,plain,
    spl32_30,
    inference(avatar_split_clause,[],[f542,f829]) ).

tff(f542,plain,
    ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
    inference(cnf_transformation,[],[f158]) ).

tff(f158,plain,
    ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
    inference(rectify,[],[f114]) ).

tff(f114,axiom,
    ! [X0: $tType,X49: X0] : ( aa(X0,X0,combi(X0),X49) = X49 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).

tff(f827,plain,
    spl32_29,
    inference(avatar_split_clause,[],[f444,f824]) ).

tff(f824,plain,
    ( spl32_29
  <=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK16,arrow_1985332922le_Lin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_29])]) ).

tff(f444,plain,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK16,arrow_1985332922le_Lin),
    inference(cnf_transformation,[],[f315]) ).

tff(f822,plain,
    spl32_28,
    inference(avatar_split_clause,[],[f442,f819]) ).

tff(f819,plain,
    ( spl32_28
  <=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK15,arrow_1985332922le_Lin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_28])]) ).

tff(f442,plain,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK15,arrow_1985332922le_Lin),
    inference(cnf_transformation,[],[f313]) ).

tff(f817,plain,
    spl32_27,
    inference(avatar_split_clause,[],[f422,f814]) ).

tff(f814,plain,
    ( spl32_27
  <=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_27])]) ).

tff(f422,plain,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096Lab_A_058_ALin_096) ).

tff(f812,plain,
    spl32_26,
    inference(avatar_split_clause,[],[f421,f809]) ).

tff(f809,plain,
    ( spl32_26
  <=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lba,arrow_1985332922le_Lin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_26])]) ).

tff(f421,plain,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lba,arrow_1985332922le_Lin),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lba,arrow_1985332922le_Lin),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096Lba_A_058_ALin_096) ).

tff(f807,plain,
    ( spl32_25
    | ~ spl32_11
    | ~ spl32_21 ),
    inference(avatar_split_clause,[],[f802,f786,f743,f805]) ).

tff(f805,plain,
    ( spl32_25
  <=> ! [X0: bool] :
        ( pp(X0)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_25])]) ).

tff(f743,plain,
    ( spl32_11
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_11])]) ).

tff(f802,plain,
    ( ! [X0: bool] :
        ( pp(X0)
        | ( fFalse = X0 ) )
    | ~ spl32_11
    | ~ spl32_21 ),
    inference(superposition,[],[f745,f787]) ).

tff(f745,plain,
    ( pp(fTrue)
    | ~ spl32_11 ),
    inference(avatar_component_clause,[],[f743]) ).

tff(f800,plain,
    spl32_24,
    inference(avatar_split_clause,[],[f684,f798]) ).

tff(f684,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP11(X0,X2,X2,X3,X4),
    inference(equality_resolution,[],[f631]) ).

tff(f631,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP11(X0,X1,X2,X3,X4)
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f393]) ).

tff(f796,plain,
    spl32_23,
    inference(avatar_split_clause,[],[f683,f794]) ).

tff(f794,plain,
    ( spl32_23
  <=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : sP12(X0,X1,X3,X3,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_23])]) ).

tff(f683,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] : sP12(X0,X1,X3,X3,X4),
    inference(equality_resolution,[],[f626]) ).

tff(f626,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP12(X0,X1,X2,X3,X4)
      | ( X2 != X3 ) ),
    inference(cnf_transformation,[],[f390]) ).

tff(f792,plain,
    spl32_22,
    inference(avatar_split_clause,[],[f681,f790]) ).

tff(f790,plain,
    ( spl32_22
  <=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : ~ sP13(X0,X1,X3,X3,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_22])]) ).

tff(f681,plain,
    ! [X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ sP13(X0,X1,X3,X3,X4),
    inference(equality_resolution,[],[f619]) ).

tff(f619,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( X2 != X3 )
      | ~ sP13(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f387]) ).

tff(f788,plain,
    spl32_21,
    inference(avatar_split_clause,[],[f452,f786]) ).

tff(f452,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(cnf_transformation,[],[f129]) ).

tff(f129,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(rectify,[],[f109]) ).

tff(f109,axiom,
    ! [X49: bool] :
      ( ( fFalse = X49 )
      | ( fTrue = X49 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).

tff(f784,plain,
    spl32_20,
    inference(avatar_split_clause,[],[f679,f782]) ).

tff(f782,plain,
    ( spl32_20
  <=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : ~ sP10(X0,X1,X3,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_20])]) ).

tff(f679,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : ~ sP10(X0,X1,X3,X3),
    inference(equality_resolution,[],[f604]) ).

tff(f604,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( ( X2 != X3 )
      | ~ sP10(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f378]) ).

tff(f780,plain,
    spl32_19,
    inference(avatar_split_clause,[],[f674,f778]) ).

tff(f778,plain,
    ( spl32_19
  <=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt] : ~ sP9(X0,X3,X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_19])]) ).

tff(f674,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ sP9(X0,X3,X2,X3),
    inference(equality_resolution,[],[f595]) ).

tff(f595,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( ( X1 != X3 )
      | ~ sP9(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f374]) ).

tff(f776,plain,
    spl32_18,
    inference(avatar_split_clause,[],[f541,f774]) ).

tff(f774,plain,
    ( spl32_18
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP6(X0)
        | ~ sP7(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_18])]) ).

tff(f541,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP6(X0)
      | ~ sP7(X0) ),
    inference(cnf_transformation,[],[f348]) ).

tff(f348,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP6(X0)
        | ~ sP7(X0) )
      & ( sP7(X0)
        | ~ sP6(X0) ) ),
    inference(nnf_transformation,[],[f297]) ).

tff(f297,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP6(X0)
    <=> sP7(X0) ),
    inference(definition_folding,[],[f245,f296,f295,f294]) ).

tff(f245,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
              | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
            & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
              | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba)
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab)
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) ) ),
    inference(ennf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => ( ( ( n != aa(arrow_159774573e_indi,nat,h,X0) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
            & ( ( n = aa(arrow_159774573e_indi,nat,h,X0) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) )
    <=> ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab) ) ) ),
    inference(rectify,[],[f17]) ).

tff(f17,axiom,
    ! [X4: arrow_159774573e_indi] :
      ( ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => ( ( ( n != aa(arrow_159774573e_indi,nat,h,X4) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),e)) )
            & ( ( n = aa(arrow_159774573e_indi,nat,h,X4) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),c),e)) ) ) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,e,d),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),e)) ) )
    <=> ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lba) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),lab) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).

tff(f772,plain,
    spl32_17,
    inference(avatar_split_clause,[],[f540,f770]) ).

tff(f770,plain,
    ( spl32_17
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP7(X0)
        | ~ sP6(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_17])]) ).

tff(f540,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP7(X0)
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f348]) ).

tff(f768,plain,
    spl32_16,
    inference(avatar_split_clause,[],[f521,f766]) ).

tff(f766,plain,
    ( spl32_16
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP3(X0)
        | ~ sP4(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_16])]) ).

tff(f521,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP3(X0)
      | ~ sP4(X0) ),
    inference(cnf_transformation,[],[f341]) ).

tff(f341,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( sP3(X0)
        | ~ sP4(X0) )
      & ( sP4(X0)
        | ~ sP3(X0) ) ),
    inference(nnf_transformation,[],[f293]) ).

tff(f293,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP3(X0)
    <=> sP4(X0) ),
    inference(definition_folding,[],[f244,f292,f291,f290]) ).

tff(f244,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
              | ( n = aa(arrow_159774573e_indi,nat,h,X0) ) )
            & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e))
              | ( n != aa(arrow_159774573e_indi,nat,h,X0) ) ) )
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e))
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n)) ) )
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba)
          | pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab)
          | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat)))) ) ) ),
    inference(ennf_transformation,[],[f156]) ).

tff(f156,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => ( ( ( n != aa(arrow_159774573e_indi,nat,h,X0) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) )
            & ( ( n = aa(arrow_159774573e_indi,nat,h,X0) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),e)) ) ) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),e)) ) )
    <=> ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat))))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X0)),plus_plus(nat,n,one_one(nat))))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab) ) ) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ! [X4: arrow_159774573e_indi] :
      ( ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => ( ( ( n != aa(arrow_159774573e_indi,nat,h,X4) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_276188178_mkbot,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),e)) )
            & ( ( n = aa(arrow_159774573e_indi,nat,h,X4) )
             => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1158827142_above,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),c),e)) ) ) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),n))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,c,e),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_424895264_mktop,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X4)),e)) ) )
    <=> ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),plus_plus(nat,n,one_one(nat))))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lba) )
        & ( pp(aa(nat,bool,aa(nat,fun(nat,bool),ord_less(nat),aa(arrow_159774573e_indi,nat,h,X4)),plus_plus(nat,n,one_one(nat))))
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),lab) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096) ).

tff(f764,plain,
    spl32_15,
    inference(avatar_split_clause,[],[f520,f762]) ).

tff(f762,plain,
    ( spl32_15
  <=> ! [X0: arrow_159774573e_indi] :
        ( sP4(X0)
        | ~ sP3(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_15])]) ).

tff(f520,plain,
    ! [X0: arrow_159774573e_indi] :
      ( sP4(X0)
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f341]) ).

tff(f760,plain,
    spl32_14,
    inference(avatar_split_clause,[],[f448,f758]) ).

tff(f448,plain,
    ! [X0: nat] : ord_less_eq(nat,X0,X0),
    inference(cnf_transformation,[],[f125]) ).

tff(f125,plain,
    ! [X0: nat] : ord_less_eq(nat,X0,X0),
    inference(rectify,[],[f79]) ).

tff(f79,axiom,
    ! [X41: nat] : ord_less_eq(nat,X41,X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_le__refl) ).

tff(f756,plain,
    ~ spl32_13,
    inference(avatar_split_clause,[],[f420,f753]) ).

tff(f753,plain,
    ( spl32_13
  <=> ( c = d ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_13])]) ).

tff(f420,plain,
    c != d,
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096c_A_126_061_Ad_096) ).

tff(f751,plain,
    ~ spl32_12,
    inference(avatar_split_clause,[],[f419,f748]) ).

tff(f748,plain,
    ( spl32_12
  <=> ( a = b ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_12])]) ).

tff(f419,plain,
    a != b,
    inference(cnf_transformation,[],[f28]) ).

tff(f28,axiom,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__096a_A_126_061_Ab_096) ).

tff(f746,plain,
    spl32_11,
    inference(avatar_split_clause,[],[f418,f743]) ).

tff(f418,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f741,plain,
    spl32_10,
    inference(avatar_split_clause,[],[f417,f738]) ).

tff(f738,plain,
    ( spl32_10
  <=> ordere236663937imp_le(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_10])]) ).

tff(f417,plain,
    ordere236663937imp_le(nat),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,axiom,
    ordere236663937imp_le(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).

tff(f736,plain,
    spl32_9,
    inference(avatar_split_clause,[],[f416,f733]) ).

tff(f733,plain,
    ( spl32_9
  <=> cancel_semigroup_add(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_9])]) ).

tff(f416,plain,
    cancel_semigroup_add(nat),
    inference(cnf_transformation,[],[f104]) ).

tff(f104,axiom,
    cancel_semigroup_add(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).

tff(f731,plain,
    spl32_8,
    inference(avatar_split_clause,[],[f415,f728]) ).

tff(f728,plain,
    ( spl32_8
  <=> ordere223160158up_add(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_8])]) ).

tff(f415,plain,
    ordere223160158up_add(nat),
    inference(cnf_transformation,[],[f100]) ).

tff(f100,axiom,
    ordere223160158up_add(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).

tff(f726,plain,
    spl32_7,
    inference(avatar_split_clause,[],[f414,f723]) ).

tff(f723,plain,
    ( spl32_7
  <=> ordere779506340up_add(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_7])]) ).

tff(f414,plain,
    ordere779506340up_add(nat),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    ordere779506340up_add(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).

tff(f721,plain,
    spl32_6,
    inference(avatar_split_clause,[],[f413,f718]) ).

tff(f718,plain,
    ( spl32_6
  <=> cancel146912293up_add(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_6])]) ).

tff(f413,plain,
    cancel146912293up_add(nat),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    cancel146912293up_add(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).

tff(f716,plain,
    spl32_5,
    inference(avatar_split_clause,[],[f412,f713]) ).

tff(f713,plain,
    ( spl32_5
  <=> ab_semigroup_add(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_5])]) ).

tff(f412,plain,
    ab_semigroup_add(nat),
    inference(cnf_transformation,[],[f105]) ).

tff(f105,axiom,
    ab_semigroup_add(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).

tff(f711,plain,
    spl32_4,
    inference(avatar_split_clause,[],[f411,f708]) ).

tff(f708,plain,
    ( spl32_4
  <=> one(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_4])]) ).

tff(f411,plain,
    one(nat),
    inference(cnf_transformation,[],[f106]) ).

tff(f106,axiom,
    one(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).

tff(f706,plain,
    spl32_3,
    inference(avatar_split_clause,[],[f410,f703]) ).

tff(f703,plain,
    ( spl32_3
  <=> arrow_2069624013nimity(f) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_3])]) ).

tff(f410,plain,
    arrow_2069624013nimity(f),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    arrow_2069624013nimity(f),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_u) ).

tff(f701,plain,
    spl32_2,
    inference(avatar_split_clause,[],[f409,f698]) ).

tff(f698,plain,
    ( spl32_2
  <=> arrow_1958449194le_IIA(f) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_2])]) ).

tff(f409,plain,
    arrow_1958449194le_IIA(f),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    arrow_1958449194le_IIA(f),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).

tff(f696,plain,
    ~ spl32_1,
    inference(avatar_split_clause,[],[f408,f693]) ).

tff(f408,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f110]) ).

tff(f110,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem    : SCT264_5 : TPTP v8.1.2. Released v6.0.0.
% 0.05/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33  % Computer : n015.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon Apr 29 22:39:32 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  % (31603)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.38  % (31606)WARNING: value z3 for option sas not known
% 0.11/0.38  % (31610)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)
% 0.11/0.38  % (31609)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)
% 0.11/0.38  % (31606)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)
% 0.11/0.38  % (31608)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)
% 0.17/0.39  % (31610)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.39  % (31607)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.40  % (31605)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.41  % (31604)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.51  % Exception at run slice level
% 0.17/0.51  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.52  % Exception at run slice level
% 0.17/0.52  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.52  % Exception at run slice level
% 0.17/0.52  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.74/0.56  % (31611)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.74/0.56  % (31612)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)
% 0.74/0.58  % (31613)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)
% 0.74/0.59  % (31611)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.74/0.59  % Exception at run slice level
% 0.74/0.59  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.74/0.59  % (31612)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.04/0.65  % (31614)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)
% 1.04/0.67  % (31608)First to succeed.
% 1.26/0.72  % (31608)Refutation found. Thanks to Tanya!
% 1.26/0.72  % SZS status Theorem for theBenchmark
% 1.26/0.72  % SZS output start Proof for theBenchmark
% See solution above
% 1.26/0.73  % (31608)------------------------------
% 1.26/0.73  % (31608)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.26/0.73  % (31608)Termination reason: Refutation
% 1.26/0.73  
% 1.26/0.73  % (31608)Memory used [KB]: 3002
% 1.26/0.73  % (31608)Time elapsed: 0.345 s
% 1.26/0.73  % (31608)Instructions burned: 447 (million)
% 1.26/0.73  % (31608)------------------------------
% 1.26/0.73  % (31608)------------------------------
% 1.26/0.73  % (31603)Success in time 0.394 s
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