TSTP Solution File: ITP020_3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP020_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 07:00:51 EDT 2024

% Result   : Theorem 0.23s 0.49s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  333
% Syntax   : Number of formulae    :  913 ( 180 unt;  74 typ;   0 def)
%            Number of atoms       : 2835 ( 153 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives : 3134 (1138   ~;1267   |; 401   &)
%                                         ( 276 <=>;  52  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    9 (   1 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  108 (  56   >;  52   *;   0   +;   0  <<)
%            Number of predicates  :  191 ( 189 usr; 173 prp; 0-3 aty)
%            Number of functors    :   55 (  55 usr;   7 con; 0-5 aty)
%            Number of variables   : 1935 (1748   !; 130   ?;1935   :)
%                                         (  57  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    tyop_2Emin_2Ebool: $tType ).

tff(type_def_6,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(type_def_7,type,
    tyop_2Enum_2Enum: $tType ).

tff(type_def_8,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    app_2E2: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_1,type,
    combin_i_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).

tff(func_def_2,type,
    combin_k_2E0: 
      !>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).

tff(func_def_3,type,
    combin_s_2E0: 
      !>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).

tff(func_def_4,type,
    c_2Ebool_2E_21_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(func_def_5,type,
    c_2Ebool_2E_21_2E1: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(func_def_6,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(func_def_7,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(func_def_8,type,
    c_2Emin_2E_3D_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).

tff(func_def_9,type,
    c_2Emin_2E_3D_2E2: 
      !>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).

tff(func_def_10,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(func_def_11,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(func_def_12,type,
    c_2Ebool_2E_3F_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(func_def_13,type,
    c_2Ebool_2E_3F_2E1: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(func_def_14,type,
    c_2Epred__set_2EBIJ_2E0: 
      !>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(func_def_15,type,
    c_2Epred__set_2EBIJ_2E3: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(func_def_16,type,
    c_2Epred__set_2ECROSS_2E0: 
      !>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool))) ).

tff(func_def_17,type,
    c_2Epred__set_2ECROSS_2E2: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool) ) ).

tff(func_def_18,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(func_def_19,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(func_def_20,type,
    c_2Epred__set_2EUNIV_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ).

tff(func_def_21,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(func_def_22,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(func_def_23,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(func_def_24,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(func_def_25,type,
    sK16: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_26,type,
    sK17: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_27,type,
    sK18: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_28,type,
    sK19: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_29,type,
    sK20: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).

tff(func_def_30,type,
    sK21: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_31,type,
    sK22: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).

tff(func_def_32,type,
    sK23: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_33,type,
    sK24: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_34,type,
    sK25: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).

tff(func_def_35,type,
    sK26: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_36,type,
    sK27: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).

tff(func_def_37,type,
    sK28: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_38,type,
    sK29: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).

tff(func_def_39,type,
    sK30: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_40,type,
    sK31: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).

tff(func_def_41,type,
    sK32: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * X0 ) > X1 ) ).

tff(func_def_42,type,
    sK33: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).

tff(func_def_43,type,
    sK34: 
      !>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(X0,X1) ) ).

tff(func_def_44,type,
    sK35: 
      !>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) > X0 ) ).

tff(func_def_45,type,
    sK36: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).

tff(func_def_46,type,
    sK37: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_47,type,
    sK38: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).

tff(func_def_48,type,
    sK39: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_49,type,
    sK40: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).

tff(func_def_50,type,
    sK41: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(X0,X1) ) ).

tff(func_def_51,type,
    sK42: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(X1,X0) ) ).

tff(func_def_52,type,
    sK43: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).

tff(pred_def_1,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(pred_def_2,type,
    sP0: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_3,type,
    sP1: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_4,type,
    sP2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_5,type,
    sP3: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_6,type,
    sP4: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_7,type,
    sP5: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_8,type,
    sP6: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_9,type,
    sP7: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_10,type,
    sP8: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_11,type,
    sP9: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_12,type,
    sP10: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_13,type,
    sP11: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_14,type,
    sP12: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_15,type,
    sP13: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_16,type,
    sP14: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(pred_def_17,type,
    sP15: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).

tff(f2891,plain,
    $false,
    inference(avatar_sat_refutation,[],[f582,f587,f591,f595,f599,f603,f607,f611,f615,f619,f630,f634,f638,f642,f646,f650,f654,f658,f662,f666,f670,f674,f678,f682,f686,f690,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f738,f742,f767,f773,f777,f781,f785,f789,f793,f819,f831,f835,f839,f843,f847,f851,f855,f859,f863,f867,f871,f875,f879,f883,f887,f891,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f935,f939,f943,f951,f955,f959,f963,f967,f971,f975,f979,f983,f987,f991,f1052,f1074,f1080,f1097,f1101,f1114,f1118,f1122,f1126,f1130,f1135,f1139,f1143,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1183,f1187,f1263,f1267,f1271,f1275,f1279,f1283,f1308,f1316,f1326,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1367,f1435,f1440,f1444,f1470,f1474,f1478,f1482,f1486,f1508,f1520,f1521,f1522,f1533,f1534,f1543,f1571,f1842,f1915,f1923,f2146,f2295,f2326,f2347,f2369,f2391,f2416,f2477,f2481,f2485,f2489,f2494,f2499,f2503,f2507,f2511,f2515,f2612,f2677,f2681,f2685,f2702,f2706,f2720,f2742,f2750,f2779,f2841,f2846,f2865,f2869,f2890]) ).

tff(f2890,plain,
    ( spl44_1
    | ~ spl44_4
    | ~ spl44_118
    | ~ spl44_170
    | ~ spl44_171 ),
    inference(avatar_split_clause,[],[f2879,f2863,f2843,f1306,f593,f579]) ).

tff(f579,plain,
    ( spl44_1
  <=> p(c_2Ebool_2EF_2E0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_1])]) ).

tff(f593,plain,
    ( spl44_4
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( ( c_2Ebool_2EF_2E0 = X0 )
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_4])]) ).

tff(f1306,plain,
    ( spl44_118
  <=> ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_118])]) ).

tff(f2843,plain,
    ( spl44_170
  <=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK43),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_170])]) ).

tff(f2863,plain,
    ( spl44_171
  <=> ! [X1: $tType,X0: $tType,X5: tyop_2Emin_2Efun(X1,X0),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),sK41(X0,X1,X2,X3)),X2),X3))
        | ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),X5),X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_171])]) ).

tff(f2879,plain,
    ( p(c_2Ebool_2EF_2E0)
    | ~ spl44_4
    | ~ spl44_118
    | ~ spl44_170
    | ~ spl44_171 ),
    inference(forward_demodulation,[],[f2870,f1321]) ).

tff(f1321,plain,
    ( ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) )
    | ~ spl44_4
    | ~ spl44_118 ),
    inference(resolution,[],[f1307,f594]) ).

tff(f594,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2EF_2E0 = X0 ) )
    | ~ spl44_4 ),
    inference(avatar_component_clause,[],[f593]) ).

tff(f1307,plain,
    ( ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))))
    | ~ spl44_118 ),
    inference(avatar_component_clause,[],[f1306]) ).

tff(f2870,plain,
    ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK41(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))))
    | ~ spl44_170
    | ~ spl44_171 ),
    inference(resolution,[],[f2864,f2845]) ).

tff(f2845,plain,
    ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK43),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))
    | ~ spl44_170 ),
    inference(avatar_component_clause,[],[f2843]) ).

tff(f2864,plain,
    ( ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X5: tyop_2Emin_2Efun(X1,X0)] :
        ( ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),X5),X3),X2))
        | p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),sK41(X0,X1,X2,X3)),X2),X3)) )
    | ~ spl44_171 ),
    inference(avatar_component_clause,[],[f2863]) ).

tff(f2869,plain,
    spl44_172,
    inference(avatar_split_clause,[],[f561,f2867]) ).

tff(f2867,plain,
    ( spl44_172
  <=> ! [X1: $tType,X0: $tType,X7: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),sK42(X0,X1,X2,X3)),X3),X2))
        | ~ p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X7),X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_172])]) ).

tff(f561,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X7: tyop_2Emin_2Efun(X0,X1)] :
      ( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),sK42(X0,X1,X2,X3)),X3),X2))
      | ~ p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X7),X2),X3)) ),
    inference(definition_unfolding,[],[f549,f551,f551]) ).

tff(f551,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X2),X3),X4) ),
    inference(cnf_transformation,[],[f113]) ).

tff(f113,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X2),X3),X4) ),
    inference(rectify,[],[f21]) ).

tff(f21,axiom,
    ! [X0: $tType,X1: $tType,X12: tyop_2Emin_2Efun(X0,X1),X13: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X14: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(X0,X1,X12,X13,X14) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X12),X13),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).

tff(f549,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X7: tyop_2Emin_2Efun(X0,X1)] :
      ( p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK42(X0,X1,X2,X3),X3,X2))
      | ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f309,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EBIJ_2E3(X0,X1,sK41(X0,X1,X2,X3),X2,X3))
        | ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
      & ( p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK42(X0,X1,X2,X3),X3,X2))
        | ! [X7: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f306,f308,f307]) ).

tff(f307,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
      ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
     => p(c_2Epred__set_2EBIJ_2E3(X0,X1,sK41(X0,X1,X2,X3),X2,X3)) ),
    introduced(choice_axiom,[]) ).

tff(f308,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
      ( ? [X6: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X6,X3,X2))
     => p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK42(X0,X1,X2,X3),X3,X2)) ),
    introduced(choice_axiom,[]) ).

tff(f306,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
      ( ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
        | ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
      & ( ? [X6: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X6,X3,X2))
        | ! [X7: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ) ),
    inference(rectify,[],[f305]) ).

tff(f305,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
      ( ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
        | ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
      & ( ? [X5: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2))
        | ! [X4: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3)) ) ),
    inference(nnf_transformation,[],[f112]) ).

tff(f112,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
      ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
    <=> ? [X5: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ! [X0: $tType,X1: $tType,X27: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X28: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
      ( ? [X29: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X29,X27,X28))
    <=> ? [X30: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X30,X28,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM) ).

tff(f2865,plain,
    spl44_171,
    inference(avatar_split_clause,[],[f560,f2863]) ).

tff(f560,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X5: tyop_2Emin_2Efun(X1,X0)] :
      ( p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),sK41(X0,X1,X2,X3)),X2),X3))
      | ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),X5),X3),X2)) ),
    inference(definition_unfolding,[],[f550,f551,f551]) ).

tff(f550,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X5: tyop_2Emin_2Efun(X1,X0)] :
      ( p(c_2Epred__set_2EBIJ_2E3(X0,X1,sK41(X0,X1,X2,X3),X2,X3))
      | ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f2846,plain,
    spl44_170,
    inference(avatar_split_clause,[],[f563,f2843]) ).

tff(f563,plain,
    p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK43),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
    inference(definition_unfolding,[],[f554,f551]) ).

tff(f554,plain,
    p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK43,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
    inference(cnf_transformation,[],[f311]) ).

tff(f311,plain,
    p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK43,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f115,f310]) ).

tff(f310,plain,
    ( ? [X0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))
   => p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK43,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ),
    introduced(choice_axiom,[]) ).

tff(f115,plain,
    ? [X0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ? [X3: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X3,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ) ).

tff(f2841,plain,
    ( spl44_169
    | ~ spl44_3
    | ~ spl44_15 ),
    inference(avatar_split_clause,[],[f755,f644,f589,f2839]) ).

tff(f2839,plain,
    ( spl44_169
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_169])]) ).

tff(f589,plain,
    ( spl44_3
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( ( c_2Ebool_2ET_2E0 = X0 )
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_3])]) ).

tff(f644,plain,
    ( spl44_15
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_15])]) ).

tff(f755,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X1,X0) ) )
    | ~ spl44_3
    | ~ spl44_15 ),
    inference(resolution,[],[f645,f590]) ).

tff(f590,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2ET_2E0 = X0 ) )
    | ~ spl44_3 ),
    inference(avatar_component_clause,[],[f589]) ).

tff(f645,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
        | ~ p(X1) )
    | ~ spl44_15 ),
    inference(avatar_component_clause,[],[f644]) ).

tff(f2779,plain,
    spl44_168,
    inference(avatar_split_clause,[],[f553,f2777]) ).

tff(f2777,plain,
    ( spl44_168
  <=> ! [X1: $tType,X0: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_168])]) ).

tff(f553,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ),
    inference(cnf_transformation,[],[f8]) ).

tff(f8,axiom,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).

tff(f2750,plain,
    spl44_167,
    inference(avatar_split_clause,[],[f538,f2748]) ).

tff(f2748,plain,
    ( spl44_167
  <=> ! [X1: $tType,X0: $tType,X5: tyop_2Emin_2Efun(X0,X1),X3: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
        ( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3)))
        | ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_167])]) ).

tff(f538,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: X0,X5: tyop_2Emin_2Efun(X0,X1)] :
      ( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3)))
      | ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) ),
    inference(cnf_transformation,[],[f290]) ).

tff(f290,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
      ( ( ! [X3: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3)))
        | ! [X5: tyop_2Emin_2Efun(X0,X1)] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) )
      & ( ! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8)))
        | ! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35])],[f285,f289,f288,f287,f286]) ).

tff(f286,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: X0] :
      ( ? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
     => p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3))) ),
    introduced(choice_axiom,[]) ).

tff(f287,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X5: tyop_2Emin_2Efun(X0,X1)] :
      ( ? [X6: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6)))
     => ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) ),
    introduced(choice_axiom,[]) ).

tff(f288,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
      ( ? [X7: tyop_2Emin_2Efun(X0,X1)] :
        ! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,X7,X8)))
     => ! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8))) ),
    introduced(choice_axiom,[]) ).

tff(f289,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
      ( ? [X9: X0] :
        ! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X9),X10))
     => ! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ),
    introduced(choice_axiom,[]) ).

tff(f285,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
      ( ( ! [X3: X0] :
          ? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
        | ! [X5: tyop_2Emin_2Efun(X0,X1)] :
          ? [X6: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6))) )
      & ( ? [X7: tyop_2Emin_2Efun(X0,X1)] :
          ! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,X7,X8)))
        | ? [X9: X0] :
          ! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X9),X10)) ) ),
    inference(rectify,[],[f284]) ).

tff(f284,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
      ( ( ! [X3: X0] :
          ? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
        | ! [X5: tyop_2Emin_2Efun(X0,X1)] :
          ? [X6: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6))) )
      & ( ? [X5: tyop_2Emin_2Efun(X0,X1)] :
          ! [X6: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6)))
        | ? [X3: X0] :
          ! [X4: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4)) ) ),
    inference(nnf_transformation,[],[f107]) ).

tff(f107,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
      ( ! [X3: X0] :
        ? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
    <=> ? [X5: tyop_2Emin_2Efun(X0,X1)] :
        ! [X6: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6))) ),
    inference(rectify,[],[f46]) ).

tff(f46,axiom,
    ! [X0: $tType,X1: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
      ( ! [X11: X0] :
        ? [X24: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17,X11),X24))
    <=> ? [X25: tyop_2Emin_2Efun(X0,X1)] :
        ! [X26: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17,X26),app_2E2(X0,X1,X25,X26))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ESKOLEM__THM) ).

tff(f2742,plain,
    spl44_166,
    inference(avatar_split_clause,[],[f363,f2740]) ).

tff(f2740,plain,
    ( spl44_166
  <=> ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0,X1) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_166])]) ).

tff(f363,plain,
    ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0,X1) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0),X1) ),
    inference(cnf_transformation,[],[f76]) ).

tff(f76,plain,
    ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0,X1) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0),X1) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X12: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X13: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X12,X13) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X12),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) ).

tff(f2720,plain,
    spl44_165,
    inference(avatar_split_clause,[],[f537,f2718]) ).

tff(f2718,plain,
    ( spl44_165
  <=> ! [X1: $tType,X0: $tType,X8: X0,X10: X1,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
        ( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8)))
        | ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_165])]) ).

tff(f537,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X10: X1,X8: X0] :
      ( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8)))
      | ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ),
    inference(cnf_transformation,[],[f290]) ).

tff(f2706,plain,
    spl44_164,
    inference(avatar_split_clause,[],[f548,f2704]) ).

tff(f2704,plain,
    ( spl44_164
  <=> ! [X1: $tType,X0: $tType,X3: tyop_2Emin_2Efun(X0,X1),X2: tyop_2Emin_2Efun(X0,X1)] :
        ( ( X2 = X3 )
        | ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_164])]) ).

tff(f548,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
      ( ( X2 = X3 )
      | ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ),
    inference(cnf_transformation,[],[f304]) ).

tff(f304,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
      ( ( X2 = X3 )
      | ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f136,f303]) ).

tff(f303,plain,
    ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
      ( ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) )
     => ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

tff(f136,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
      ( ( X2 = X3 )
      | ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) ) ),
    inference(ennf_transformation,[],[f111]) ).

tff(f111,plain,
    ! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
      ( ! [X4: X0] : ( app_2E2(X0,X1,X2,X4) = app_2E2(X0,X1,X3,X4) )
     => ( X2 = X3 ) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $tType,X1: $tType,X3: tyop_2Emin_2Efun(X0,X1),X4: tyop_2Emin_2Efun(X0,X1)] :
      ( ! [X5: X0] : ( app_2E2(X0,X1,X3,X5) = app_2E2(X0,X1,X4,X5) )
     => ( X3 = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).

tff(f2702,plain,
    ( spl44_163
    | ~ spl44_3
    | ~ spl44_14 ),
    inference(avatar_split_clause,[],[f753,f640,f589,f2700]) ).

tff(f2700,plain,
    ( spl44_163
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_163])]) ).

tff(f640,plain,
    ( spl44_14
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_14])]) ).

tff(f753,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X0,X1) ) )
    | ~ spl44_3
    | ~ spl44_14 ),
    inference(resolution,[],[f641,f590]) ).

tff(f641,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
        | ~ p(X0) )
    | ~ spl44_14 ),
    inference(avatar_component_clause,[],[f640]) ).

tff(f2685,plain,
    spl44_162,
    inference(avatar_split_clause,[],[f455,f2683]) ).

tff(f2683,plain,
    ( spl44_162
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP6(X0,X1,X2)
        | p(X0)
        | ~ sP5(X0,X2,X1)
        | ~ sP4(X1,X2,X0)
        | ~ sP3(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_162])]) ).

tff(f455,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP6(X0,X1,X2)
      | p(X0)
      | ~ sP5(X0,X2,X1)
      | ~ sP4(X1,X2,X0)
      | ~ sP3(X2,X1,X0) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f236,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP6(X0,X1,X2)
        | ( p(X0)
          & p(X1)
          & ~ p(X2) )
        | ~ sP5(X0,X2,X1)
        | ~ sP4(X1,X2,X0)
        | ~ sP3(X2,X1,X0) )
      & ( ( ( ~ p(X0)
            | ~ p(X1)
            | p(X2) )
          & sP5(X0,X2,X1)
          & sP4(X1,X2,X0)
          & sP3(X2,X1,X0) )
        | ~ sP6(X0,X1,X2) ) ),
    inference(rectify,[],[f235]) ).

tff(f235,plain,
    ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
      ( ( sP6(X2,X1,X0)
        | ( p(X2)
          & p(X1)
          & ~ p(X0) )
        | ~ sP5(X2,X0,X1)
        | ~ sP4(X1,X0,X2)
        | ~ sP3(X0,X1,X2) )
      & ( ( ( ~ p(X2)
            | ~ p(X1)
            | p(X0) )
          & sP5(X2,X0,X1)
          & sP4(X1,X0,X2)
          & sP3(X0,X1,X2) )
        | ~ sP6(X2,X1,X0) ) ),
    inference(flattening,[],[f234]) ).

tff(f234,plain,
    ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
      ( ( sP6(X2,X1,X0)
        | ( p(X2)
          & p(X1)
          & ~ p(X0) )
        | ~ sP5(X2,X0,X1)
        | ~ sP4(X1,X0,X2)
        | ~ sP3(X0,X1,X2) )
      & ( ( ( ~ p(X2)
            | ~ p(X1)
            | p(X0) )
          & sP5(X2,X0,X1)
          & sP4(X1,X0,X2)
          & sP3(X0,X1,X2) )
        | ~ sP6(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f145]) ).

tff(f145,plain,
    ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
      ( sP6(X2,X1,X0)
    <=> ( ( ~ p(X2)
          | ~ p(X1)
          | p(X0) )
        & sP5(X2,X0,X1)
        & sP4(X1,X0,X2)
        & sP3(X0,X1,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

tff(f2681,plain,
    spl44_161,
    inference(avatar_split_clause,[],[f454,f2679]) ).

tff(f2679,plain,
    ( spl44_161
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP6(X0,X1,X2)
        | p(X1)
        | ~ sP5(X0,X2,X1)
        | ~ sP4(X1,X2,X0)
        | ~ sP3(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_161])]) ).

tff(f454,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP6(X0,X1,X2)
      | p(X1)
      | ~ sP5(X0,X2,X1)
      | ~ sP4(X1,X2,X0)
      | ~ sP3(X2,X1,X0) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f2677,plain,
    spl44_160,
    inference(avatar_split_clause,[],[f453,f2675]) ).

tff(f2675,plain,
    ( spl44_160
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP6(X0,X1,X2)
        | ~ p(X2)
        | ~ sP5(X0,X2,X1)
        | ~ sP4(X1,X2,X0)
        | ~ sP3(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_160])]) ).

tff(f453,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP6(X0,X1,X2)
      | ~ p(X2)
      | ~ sP5(X0,X2,X1)
      | ~ sP4(X1,X2,X0)
      | ~ sP3(X2,X1,X0) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f2612,plain,
    ( spl44_159
    | ~ spl44_4
    | ~ spl44_13 ),
    inference(avatar_split_clause,[],[f751,f636,f593,f2610]) ).

tff(f2610,plain,
    ( spl44_159
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_159])]) ).

tff(f636,plain,
    ( spl44_13
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_13])]) ).

tff(f751,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X1,X0) ) )
    | ~ spl44_4
    | ~ spl44_13 ),
    inference(resolution,[],[f637,f594]) ).

tff(f637,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
        | p(X1) )
    | ~ spl44_13 ),
    inference(avatar_component_clause,[],[f636]) ).

tff(f2515,plain,
    spl44_158,
    inference(avatar_split_clause,[],[f557,f2513]) ).

tff(f2513,plain,
    ( spl44_158
  <=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
        | ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_158])]) ).

tff(f557,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
      | ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ),
    inference(definition_unfolding,[],[f381,f362]) ).

tff(f362,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
    inference(cnf_transformation,[],[f75]) ).

tff(f75,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
    inference(rectify,[],[f20]) ).

tff(f20,axiom,
    ! [X0: $tType,X12: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X12) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).

tff(f381,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
      | ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ),
    inference(cnf_transformation,[],[f182]) ).

tff(f182,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
        | ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
      & ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
        | ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f180,f181]) ).

tff(f181,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
     => p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f180,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
        | ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
      & ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
    inference(rectify,[],[f179]) ).

tff(f179,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
        | ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
      & ( ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
        | ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
    inference(nnf_transformation,[],[f83]) ).

tff(f83,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(X0,X1))
    <=> ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X0: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(X0,X3))
    <=> ? [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).

tff(f2511,plain,
    spl44_157,
    inference(avatar_split_clause,[],[f545,f2509]) ).

tff(f2509,plain,
    ( spl44_157
  <=> ! [X0: $tType,X4: X0,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2)))
        | ~ p(X2)
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_157])]) ).

tff(f545,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2)))
      | ~ p(X2)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ),
    inference(cnf_transformation,[],[f302]) ).

tff(f302,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ( p(X2)
          & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2))) )
        | ~ p(X2)
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
      & ( ( p(X2)
          & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1))) )
        | ! [X6: X0] :
            ( ~ p(X2)
            | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f299,f301,f300]) ).

tff(f300,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ? [X3: X0] :
          ( p(X2)
          & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
     => ( p(X2)
        & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

tff(f301,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
     => p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f299,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ? [X3: X0] :
            ( p(X2)
            & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
        | ~ p(X2)
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
      & ( ( p(X2)
          & ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
        | ! [X6: X0] :
            ( ~ p(X2)
            | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
    inference(rectify,[],[f298]) ).

tff(f298,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ? [X3: X0] :
            ( p(X2)
            & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
        | ~ p(X2)
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
      & ( ( p(X2)
          & ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
        | ! [X3: X0] :
            ( ~ p(X2)
            | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
    inference(flattening,[],[f297]) ).

tff(f297,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ? [X3: X0] :
            ( p(X2)
            & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
        | ~ p(X2)
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
      & ( ( p(X2)
          & ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
        | ! [X3: X0] :
            ( ~ p(X2)
            | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
    inference(nnf_transformation,[],[f109]) ).

tff(f109,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ? [X3: X0] :
          ( p(X2)
          & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
    <=> ( p(X2)
        & ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
    inference(rectify,[],[f41]) ).

tff(f41,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X18: tyop_2Emin_2Ebool] :
      ( ? [X5: X0] :
          ( p(X18)
          & p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) )
    <=> ( p(X18)
        & ? [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X19)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__EXISTS__AND__THM) ).

tff(f2507,plain,
    spl44_156,
    inference(avatar_split_clause,[],[f542,f2505]) ).

tff(f2505,plain,
    ( spl44_156
  <=> ! [X0: $tType,X4: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_156])]) ).

tff(f542,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X4: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f296,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
          & p(X1) )
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | ~ p(X1) )
      & ( ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2)))
          & p(X1) )
        | ! [X6: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
            | ~ p(X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f293,f295,f294]) ).

tff(f294,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X3: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & p(X1) )
     => ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
        & p(X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f295,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
     => p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f293,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X3: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            & p(X1) )
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | ~ p(X1) )
      & ( ( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
          & p(X1) )
        | ! [X6: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
            | ~ p(X1) ) ) ),
    inference(rectify,[],[f292]) ).

tff(f292,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X3: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            & p(X1) )
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | ~ p(X1) )
      & ( ( ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          & p(X1) )
        | ! [X3: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            | ~ p(X1) ) ) ),
    inference(flattening,[],[f291]) ).

tff(f291,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X3: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            & p(X1) )
        | ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | ~ p(X1) )
      & ( ( ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          & p(X1) )
        | ! [X3: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            | ~ p(X1) ) ) ),
    inference(nnf_transformation,[],[f108]) ).

tff(f108,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X3: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & p(X1) )
    <=> ( ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        & p(X1) ) ),
    inference(rectify,[],[f42]) ).

tff(f42,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X5: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
          & p(X17) )
    <=> ( ? [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
        & p(X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__EXISTS__AND__THM) ).

tff(f2503,plain,
    spl44_155,
    inference(avatar_split_clause,[],[f533,f2501]) ).

tff(f2501,plain,
    ( spl44_155
  <=> ! [X0: $tType,X5: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_155])]) ).

tff(f533,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X5: X0] :
      ( p(X1)
      | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f283,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(X1)
            | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
        | ( ~ p(X1)
          & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ) )
      & ( p(X1)
        | ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
        | ( ~ p(X1)
          & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f280,f282,f281]) ).

tff(f281,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
     => ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f282,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X6: X0] :
          ( ~ p(X1)
          & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) )
     => ( ~ p(X1)
        & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

tff(f280,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(X1)
            | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
        | ( ~ p(X1)
          & ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) )
      & ( p(X1)
        | ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
        | ? [X6: X0] :
            ( ~ p(X1)
            & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ) ) ),
    inference(rectify,[],[f279]) ).

tff(f279,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(X1)
            | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
        | ( ~ p(X1)
          & ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) )
      & ( p(X1)
        | ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | ? [X3: X0] :
            ( ~ p(X1)
            & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) ) ) ),
    inference(flattening,[],[f278]) ).

tff(f278,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(X1)
            | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
        | ( ~ p(X1)
          & ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) )
      & ( p(X1)
        | ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | ? [X3: X0] :
            ( ~ p(X1)
            & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) ) ) ),
    inference(nnf_transformation,[],[f106]) ).

tff(f106,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ! [X3: X0] :
          ( p(X1)
          | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
    <=> ( p(X1)
        | ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) ),
    inference(rectify,[],[f43]) ).

tff(f43,axiom,
    ! [X0: $tType,X20: tyop_2Emin_2Ebool,X21: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ! [X5: X0] :
          ( p(X20)
          | p(app_2E2(X0,tyop_2Emin_2Ebool,X21,X5)) )
    <=> ( p(X20)
        | ! [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X21,X19)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__FORALL__OR__THM) ).

tff(f2499,plain,
    spl44_154,
    inference(avatar_split_clause,[],[f530,f2497]) ).

tff(f2497,plain,
    ( spl44_154
  <=> ! [X0: $tType,X5: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
        | p(X1)
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_154])]) ).

tff(f530,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X5: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
      | p(X1)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f277]) ).

tff(f277,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            | p(X1) )
        | ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2)))
          & ~ p(X1) ) )
      & ( ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
        | p(X1)
        | ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2)))
          & ~ p(X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f274,f276,f275]) ).

tff(f275,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
     => ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f276,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X6: X0] :
          ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
          & ~ p(X1) )
     => ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2)))
        & ~ p(X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f274,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            | p(X1) )
        | ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          & ~ p(X1) ) )
      & ( ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
        | p(X1)
        | ? [X6: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
            & ~ p(X1) ) ) ),
    inference(rectify,[],[f273]) ).

tff(f273,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            | p(X1) )
        | ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          & ~ p(X1) ) )
      & ( ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | p(X1)
        | ? [X3: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            & ~ p(X1) ) ) ),
    inference(flattening,[],[f272]) ).

tff(f272,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            | p(X1) )
        | ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          & ~ p(X1) ) )
      & ( ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | p(X1)
        | ? [X3: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
            & ~ p(X1) ) ) ),
    inference(nnf_transformation,[],[f105]) ).

tff(f105,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ! [X3: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          | p(X1) )
    <=> ( ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
        | p(X1) ) ),
    inference(rectify,[],[f44]) ).

tff(f44,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ! [X5: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
          | p(X17) )
    <=> ( ! [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
        | p(X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__FORALL__OR__THM) ).

tff(f2494,plain,
    ( spl44_153
    | ~ spl44_47
    | ~ spl44_142 ),
    inference(avatar_split_clause,[],[f2186,f2143,f817,f2491]) ).

tff(f2491,plain,
    ( spl44_153
  <=> ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_153])]) ).

tff(f817,plain,
    ( spl44_47
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_47])]) ).

tff(f2143,plain,
    ( spl44_142
  <=> p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_142])]) ).

tff(f2186,plain,
    ( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) )
    | ~ spl44_47
    | ~ spl44_142 ),
    inference(resolution,[],[f2145,f818]) ).

tff(f818,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
    | ~ spl44_47 ),
    inference(avatar_component_clause,[],[f817]) ).

tff(f2145,plain,
    ( p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
    | ~ spl44_142 ),
    inference(avatar_component_clause,[],[f2143]) ).

tff(f2489,plain,
    spl44_152,
    inference(avatar_split_clause,[],[f445,f2487]) ).

tff(f2487,plain,
    ( spl44_152
  <=> ! [X0: $tType,X6: X0,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(X2)
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2)))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_152])]) ).

tff(f445,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X6: X0] :
      ( p(X2)
      | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2)))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ),
    inference(cnf_transformation,[],[f233]) ).

tff(f233,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1)))
        | ! [X4: X0] :
            ( ~ p(X2)
            & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
      & ( p(X2)
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2)))
        | ( ~ p(X2)
          & ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f230,f232,f231]) ).

tff(f231,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
     => p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f232,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ? [X5: X0] :
          ( p(X2)
          | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
     => ( p(X2)
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

tff(f230,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
        | ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ! [X4: X0] :
            ( ~ p(X2)
            & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
      & ( ? [X5: X0] :
            ( p(X2)
            | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
        | ( ~ p(X2)
          & ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
    inference(rectify,[],[f229]) ).

tff(f229,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
        | ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ! [X4: X0] :
            ( ~ p(X2)
            & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
      & ( ? [X4: X0] :
            ( p(X2)
            | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
        | ( ~ p(X2)
          & ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
    inference(flattening,[],[f228]) ).

tff(f228,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
        | ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ! [X4: X0] :
            ( ~ p(X2)
            & ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
      & ( ? [X4: X0] :
            ( p(X2)
            | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
        | ( ~ p(X2)
          & ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
    inference(nnf_transformation,[],[f100]) ).

tff(f100,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
        | ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
    <=> ? [X4: X0] :
          ( p(X2)
          | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
    inference(rectify,[],[f39]) ).

tff(f39,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X18: tyop_2Emin_2Ebool] :
      ( ( p(X18)
        | ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) )
    <=> ? [X19: X0] :
          ( p(X18)
          | p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X19)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__EXISTS__THM) ).

tff(f2485,plain,
    spl44_151,
    inference(avatar_split_clause,[],[f442,f2483]) ).

tff(f2483,plain,
    ( spl44_151
  <=> ! [X0: $tType,X6: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
        | p(X1)
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_151])]) ).

tff(f442,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X6: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
      | p(X1)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ),
    inference(cnf_transformation,[],[f227]) ).

tff(f227,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2)))
        | p(X1)
        | ! [X4: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            & ~ p(X1) ) )
      & ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
        | p(X1)
        | ( ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
          & ~ p(X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f224,f226,f225]) ).

tff(f225,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
     => p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f226,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X5: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
          | p(X1) )
     => ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
        | p(X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f224,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | p(X1)
        | ! [X4: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            & ~ p(X1) ) )
      & ( ? [X5: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
            | p(X1) )
        | ( ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
          & ~ p(X1) ) ) ),
    inference(rectify,[],[f223]) ).

tff(f223,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | p(X1)
        | ! [X4: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            & ~ p(X1) ) )
      & ( ? [X4: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            | p(X1) )
        | ( ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & ~ p(X1) ) ) ),
    inference(flattening,[],[f222]) ).

tff(f222,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | p(X1)
        | ! [X4: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            & ~ p(X1) ) )
      & ( ? [X4: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            | p(X1) )
        | ( ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & ~ p(X1) ) ) ),
    inference(nnf_transformation,[],[f99]) ).

tff(f99,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | p(X1) )
    <=> ? [X4: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          | p(X1) ) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
        | p(X17) )
    <=> ? [X19: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
          | p(X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__OR__EXISTS__THM) ).

tff(f2481,plain,
    spl44_150,
    inference(avatar_split_clause,[],[f439,f2479]) ).

tff(f2479,plain,
    ( spl44_150
  <=> ! [X0: $tType,X3: X0,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ~ p(X2)
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_150])]) ).

tff(f439,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
      | ~ p(X2)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f221]) ).

tff(f221,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ( p(X2)
          & ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
        | ~ p(X2)
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) )
      & ( ! [X5: X0] :
            ( p(X2)
            & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
        | ~ p(X2)
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f218,f220,f219]) ).

tff(f219,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ? [X4: X0] :
          ( ~ p(X2)
          | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
     => ( ~ p(X2)
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) ) ),
    introduced(choice_axiom,[]) ).

tff(f220,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6))
     => ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f218,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ( p(X2)
          & ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
        | ? [X4: X0] :
            ( ~ p(X2)
            | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
      & ( ! [X5: X0] :
            ( p(X2)
            & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
        | ~ p(X2)
        | ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ),
    inference(rectify,[],[f217]) ).

tff(f217,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ( p(X2)
          & ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
        | ? [X4: X0] :
            ( ~ p(X2)
            | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
      & ( ! [X4: X0] :
            ( p(X2)
            & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
        | ~ p(X2)
        | ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ),
    inference(flattening,[],[f216]) ).

tff(f216,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( ( p(X2)
          & ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
        | ? [X4: X0] :
            ( ~ p(X2)
            | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
      & ( ! [X4: X0] :
            ( p(X2)
            & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
        | ~ p(X2)
        | ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ),
    inference(nnf_transformation,[],[f98]) ).

tff(f98,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
        & ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
    <=> ! [X4: X0] :
          ( p(X2)
          & p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
    inference(rectify,[],[f37]) ).

tff(f37,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X18: tyop_2Emin_2Ebool] :
      ( ( p(X18)
        & ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) )
    <=> ! [X19: X0] :
          ( p(X18)
          & p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X19)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__FORALL__THM) ).

tff(f2477,plain,
    spl44_149,
    inference(avatar_split_clause,[],[f436,f2475]) ).

tff(f2475,plain,
    ( spl44_149
  <=> ! [X0: $tType,X3: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_149])]) ).

tff(f436,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0,X1: tyop_2Emin_2Ebool] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f215]) ).

tff(f215,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & p(X1) )
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
        | ~ p(X1) )
      & ( ! [X5: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
            & p(X1) )
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2)))
        | ~ p(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f212,f214,f213]) ).

tff(f213,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X4: X0] :
          ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          | ~ p(X1) )
     => ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
        | ~ p(X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f214,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
     => ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f212,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & p(X1) )
        | ? [X4: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            | ~ p(X1) ) )
      & ( ! [X5: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
            & p(X1) )
        | ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
        | ~ p(X1) ) ),
    inference(rectify,[],[f211]) ).

tff(f211,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & p(X1) )
        | ? [X4: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            | ~ p(X1) ) )
      & ( ! [X4: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            & p(X1) )
        | ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | ~ p(X1) ) ),
    inference(flattening,[],[f210]) ).

tff(f210,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
          & p(X1) )
        | ? [X4: X0] :
            ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            | ~ p(X1) ) )
      & ( ! [X4: X0] :
            ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
            & p(X1) )
        | ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | ~ p(X1) ) ),
    inference(nnf_transformation,[],[f97]) ).

tff(f97,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        & p(X1) )
    <=> ! [X4: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
          & p(X1) ) ),
    inference(rectify,[],[f38]) ).

tff(f38,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
        & p(X17) )
    <=> ! [X19: X0] :
          ( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
          & p(X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__AND__FORALL__THM) ).

tff(f2416,plain,
    ( spl44_119
    | spl44_148 ),
    inference(avatar_split_clause,[],[f543,f2414,f1310]) ).

tff(f1310,plain,
    ( spl44_119
  <=> ! [X0: tyop_2Emin_2Ebool] : ~ p(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_119])]) ).

tff(f2414,plain,
    ( spl44_148
  <=> ! [X0: $tType,X6: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1)))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_148])]) ).

tff(f543,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X6: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1)))
      | ~ p(X2)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ),
    inference(cnf_transformation,[],[f302]) ).

tff(f2391,plain,
    ( spl44_119
    | spl44_147 ),
    inference(avatar_split_clause,[],[f540,f2389,f1310]) ).

tff(f2389,plain,
    ( spl44_147
  <=> ! [X0: $tType,X6: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2)))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_147])]) ).

tff(f540,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X6: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2)))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f2369,plain,
    ( spl44_146
    | spl44_140 ),
    inference(avatar_split_clause,[],[f535,f1910,f2367]) ).

tff(f2367,plain,
    ( spl44_146
  <=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_146])]) ).

tff(f1910,plain,
    ( spl44_140
  <=> ! [X1: tyop_2Emin_2Ebool] : p(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_140])]) ).

tff(f535,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f2347,plain,
    ( spl44_140
    | spl44_145 ),
    inference(avatar_split_clause,[],[f532,f2345,f1910]) ).

tff(f2345,plain,
    ( spl44_145
  <=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_145])]) ).

tff(f532,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0,X1: tyop_2Emin_2Ebool] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
      | p(X1)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2))) ),
    inference(cnf_transformation,[],[f277]) ).

tff(f2326,plain,
    ( spl44_144
    | spl44_140 ),
    inference(avatar_split_clause,[],[f447,f1910,f2324]) ).

tff(f2324,plain,
    ( spl44_144
  <=> ! [X0: $tType,X4: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1)))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_144])]) ).

tff(f447,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
      ( p(X2)
      | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1)))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ),
    inference(cnf_transformation,[],[f233]) ).

tff(f2295,plain,
    ( spl44_143
    | ~ spl44_3
    | ~ spl44_142 ),
    inference(avatar_split_clause,[],[f2188,f2143,f589,f2292]) ).

tff(f2292,plain,
    ( spl44_143
  <=> ( c_2Ebool_2ET_2E0 = sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_143])]) ).

tff(f2188,plain,
    ( ( c_2Ebool_2ET_2E0 = sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) )
    | ~ spl44_3
    | ~ spl44_142 ),
    inference(resolution,[],[f2145,f590]) ).

tff(f2146,plain,
    ( spl44_142
    | spl44_1
    | ~ spl44_48
    | ~ spl44_114
    | ~ spl44_131 ),
    inference(avatar_split_clause,[],[f1924,f1437,f1269,f829,f579,f2143]) ).

tff(f829,plain,
    ( spl44_48
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_48])]) ).

tff(f1269,plain,
    ( spl44_114
  <=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(c_2Ebool_2E_21_2E1(X0,X1))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_114])]) ).

tff(f1437,plain,
    ( spl44_131
  <=> ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_131])]) ).

tff(f1924,plain,
    ( p(c_2Ebool_2EF_2E0)
    | p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
    | ~ spl44_48
    | ~ spl44_114
    | ~ spl44_131 ),
    inference(forward_demodulation,[],[f1286,f1439]) ).

tff(f1439,plain,
    ( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) )
    | ~ spl44_131 ),
    inference(avatar_component_clause,[],[f1437]) ).

tff(f1286,plain,
    ( p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
    | p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
    | ~ spl44_48
    | ~ spl44_114 ),
    inference(resolution,[],[f1270,f830]) ).

tff(f830,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
        | p(X0) )
    | ~ spl44_48 ),
    inference(avatar_component_clause,[],[f829]) ).

tff(f1270,plain,
    ( ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1)))
        | p(c_2Ebool_2E_21_2E1(X0,X1)) )
    | ~ spl44_114 ),
    inference(avatar_component_clause,[],[f1269]) ).

tff(f1923,plain,
    ( spl44_1
    | ~ spl44_140 ),
    inference(avatar_contradiction_clause,[],[f1921]) ).

tff(f1921,plain,
    ( $false
    | spl44_1
    | ~ spl44_140 ),
    inference(resolution,[],[f1911,f581]) ).

tff(f581,plain,
    ( ~ p(c_2Ebool_2EF_2E0)
    | spl44_1 ),
    inference(avatar_component_clause,[],[f579]) ).

tff(f1911,plain,
    ( ! [X1: tyop_2Emin_2Ebool] : p(X1)
    | ~ spl44_140 ),
    inference(avatar_component_clause,[],[f1910]) ).

tff(f1915,plain,
    ( spl44_140
    | spl44_141 ),
    inference(avatar_split_clause,[],[f444,f1913,f1910]) ).

tff(f1913,plain,
    ( spl44_141
  <=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2)))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_141])]) ).

tff(f444,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X4: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2)))
      | p(X1)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ),
    inference(cnf_transformation,[],[f227]) ).

tff(f1842,plain,
    ( spl44_139
    | ~ spl44_4
    | ~ spl44_12 ),
    inference(avatar_split_clause,[],[f749,f632,f593,f1840]) ).

tff(f1840,plain,
    ( spl44_139
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_139])]) ).

tff(f632,plain,
    ( spl44_12
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_12])]) ).

tff(f749,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X0,X1) ) )
    | ~ spl44_4
    | ~ spl44_12 ),
    inference(resolution,[],[f633,f594]) ).

tff(f633,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
        | p(X0) )
    | ~ spl44_12 ),
    inference(avatar_component_clause,[],[f632]) ).

tff(f1571,plain,
    ( spl44_89
    | ~ spl44_3
    | ~ spl44_47
    | ~ spl44_121 ),
    inference(avatar_split_clause,[],[f1525,f1324,f817,f589,f1049]) ).

tff(f1049,plain,
    ( spl44_89
  <=> ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_89])]) ).

tff(f1324,plain,
    ( spl44_121
  <=> ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_121])]) ).

tff(f1525,plain,
    ( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) )
    | ~ spl44_3
    | ~ spl44_47
    | ~ spl44_121 ),
    inference(forward_demodulation,[],[f1327,f1329]) ).

tff(f1329,plain,
    ( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X1) )
    | ~ spl44_3
    | ~ spl44_121 ),
    inference(resolution,[],[f1325,f590]) ).

tff(f1325,plain,
    ( ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2))
    | ~ spl44_121 ),
    inference(avatar_component_clause,[],[f1324]) ).

tff(f1327,plain,
    ( ! [X0: $tType,X1: X0] : ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X1)) )
    | ~ spl44_47
    | ~ spl44_121 ),
    inference(resolution,[],[f1325,f818]) ).

tff(f1543,plain,
    ( spl44_99
    | ~ spl44_4
    | ~ spl44_55
    | ~ spl44_118 ),
    inference(avatar_split_clause,[],[f1528,f1306,f857,f593,f1132]) ).

tff(f1132,plain,
    ( spl44_99
  <=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_99])]) ).

tff(f857,plain,
    ( spl44_55
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_55])]) ).

tff(f1528,plain,
    ( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) )
    | ~ spl44_4
    | ~ spl44_55
    | ~ spl44_118 ),
    inference(forward_demodulation,[],[f1318,f1321]) ).

tff(f1318,plain,
    ( ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) )
    | ~ spl44_55
    | ~ spl44_118 ),
    inference(resolution,[],[f1307,f858]) ).

tff(f858,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
    | ~ spl44_55 ),
    inference(avatar_component_clause,[],[f857]) ).

tff(f1534,plain,
    ( spl44_2
    | ~ spl44_3
    | ~ spl44_121 ),
    inference(avatar_split_clause,[],[f1523,f1324,f589,f584]) ).

tff(f584,plain,
    ( spl44_2
  <=> p(c_2Ebool_2ET_2E0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_2])]) ).

tff(f1523,plain,
    ( p(c_2Ebool_2ET_2E0)
    | ~ spl44_3
    | ~ spl44_121 ),
    inference(forward_demodulation,[],[f1325,f1329]) ).

tff(f1533,plain,
    ( ~ spl44_1
    | ~ spl44_4
    | ~ spl44_118 ),
    inference(avatar_split_clause,[],[f1531,f1306,f593,f579]) ).

tff(f1531,plain,
    ( ~ p(c_2Ebool_2EF_2E0)
    | ~ spl44_4
    | ~ spl44_118 ),
    inference(forward_demodulation,[],[f1307,f1321]) ).

tff(f1522,plain,
    ( ~ spl44_119
    | ~ spl44_121 ),
    inference(avatar_contradiction_clause,[],[f1515]) ).

tff(f1515,plain,
    ( $false
    | ~ spl44_119
    | ~ spl44_121 ),
    inference(resolution,[],[f1311,f1325]) ).

tff(f1311,plain,
    ( ! [X0: tyop_2Emin_2Ebool] : ~ p(X0)
    | ~ spl44_119 ),
    inference(avatar_component_clause,[],[f1310]) ).

tff(f1521,plain,
    ( ~ spl44_10
    | ~ spl44_119 ),
    inference(avatar_contradiction_clause,[],[f1516]) ).

tff(f1516,plain,
    ( $false
    | ~ spl44_10
    | ~ spl44_119 ),
    inference(resolution,[],[f1311,f618]) ).

tff(f618,plain,
    ( ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2))
    | ~ spl44_10 ),
    inference(avatar_component_clause,[],[f617]) ).

tff(f617,plain,
    ( spl44_10
  <=> ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_10])]) ).

tff(f1520,plain,
    ( ~ spl44_2
    | ~ spl44_119 ),
    inference(avatar_contradiction_clause,[],[f1518]) ).

tff(f1518,plain,
    ( $false
    | ~ spl44_2
    | ~ spl44_119 ),
    inference(resolution,[],[f1311,f586]) ).

tff(f586,plain,
    ( p(c_2Ebool_2ET_2E0)
    | ~ spl44_2 ),
    inference(avatar_component_clause,[],[f584]) ).

tff(f1508,plain,
    ( spl44_119
    | spl44_138 ),
    inference(avatar_split_clause,[],[f437,f1506,f1310]) ).

tff(f1506,plain,
    ( spl44_138
  <=> ! [X0: $tType,X5: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_138])]) ).

tff(f437,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X5: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
      | ~ p(X2)
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ),
    inference(cnf_transformation,[],[f221]) ).

tff(f1486,plain,
    ( spl44_119
    | spl44_137 ),
    inference(avatar_split_clause,[],[f434,f1484,f1310]) ).

tff(f1484,plain,
    ( spl44_137
  <=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X5: X0] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_137])]) ).

tff(f434,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X5: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2)))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f215]) ).

tff(f1482,plain,
    spl44_136,
    inference(avatar_split_clause,[],[f430,f1480]) ).

tff(f1480,plain,
    ( spl44_136
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_136])]) ).

tff(f430,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 = X2 )
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
    inference(cnf_transformation,[],[f208]) ).

tff(f208,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( ( ( X1 = X2 )
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) )
      & ( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
        | ( X1 != X2 ) ) ),
    inference(nnf_transformation,[],[f95]) ).

tff(f95,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( ( X1 = X2 )
    <=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
    inference(rectify,[],[f18]) ).

tff(f18,axiom,
    ! [X0: $tType,X12: X0,X13: X0] :
      ( ( X12 = X13 )
    <=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).

tff(f1478,plain,
    spl44_135,
    inference(avatar_split_clause,[],[f395,f1476]) ).

tff(f1476,plain,
    ( spl44_135
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | ~ p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_135])]) ).

tff(f395,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | ~ p(X0)
      | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
    inference(cnf_transformation,[],[f190]) ).

tff(f190,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X1)
        | ~ p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
      & ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
        | ( ~ p(X1)
          & p(X0) ) ) ),
    inference(flattening,[],[f189]) ).

tff(f189,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X1)
        | ~ p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
      & ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
        | ( ~ p(X1)
          & p(X0) ) ) ),
    inference(nnf_transformation,[],[f129]) ).

tff(f129,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X1)
        | ~ p(X0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
    inference(ennf_transformation,[],[f87]) ).

tff(f87,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X0)
       => p(X1) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
      ( ( p(X12)
       => p(X13) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).

tff(f1474,plain,
    spl44_134,
    inference(avatar_split_clause,[],[f388,f1472]) ).

tff(f1472,plain,
    ( spl44_134
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_134])]) ).

tff(f388,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | p(X0)
      | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
    inference(cnf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X1)
        | p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
      & ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
        | ( ~ p(X1)
          & ~ p(X0) ) ) ),
    inference(flattening,[],[f185]) ).

tff(f185,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X1)
        | p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
      & ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
        | ( ~ p(X1)
          & ~ p(X0) ) ) ),
    inference(nnf_transformation,[],[f85]) ).

tff(f85,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X1)
        | p(X0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
      ( ( p(X13)
        | p(X12) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).

tff(f1470,plain,
    spl44_133,
    inference(avatar_split_clause,[],[f383,f1468]) ).

tff(f1468,plain,
    ( spl44_133
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
        | ~ p(X1)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_133])]) ).

tff(f383,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
      | ~ p(X1)
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( ( p(X1)
          & p(X0) )
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
      & ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
        | ~ p(X1)
        | ~ p(X0) ) ),
    inference(flattening,[],[f183]) ).

tff(f183,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( ( p(X1)
          & p(X0) )
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
      & ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
        | ~ p(X1)
        | ~ p(X0) ) ),
    inference(nnf_transformation,[],[f84]) ).

tff(f84,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X1)
        & p(X0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
    inference(rectify,[],[f17]) ).

tff(f17,axiom,
    ! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
      ( ( p(X13)
        & p(X12) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X12),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).

tff(f1444,plain,
    spl44_132,
    inference(avatar_split_clause,[],[f556,f1442]) ).

tff(f1442,plain,
    ( spl44_132
  <=> ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_132])]) ).

tff(f556,plain,
    ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
    inference(definition_unfolding,[],[f382,f362]) ).

tff(f382,plain,
    ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(X0,X1))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
    inference(cnf_transformation,[],[f182]) ).

tff(f1440,plain,
    ( spl44_131
    | ~ spl44_4
    | spl44_120 ),
    inference(avatar_split_clause,[],[f1362,f1313,f593,f1437]) ).

tff(f1313,plain,
    ( spl44_120
  <=> p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_120])]) ).

tff(f1362,plain,
    ( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) )
    | ~ spl44_4
    | spl44_120 ),
    inference(resolution,[],[f1315,f594]) ).

tff(f1315,plain,
    ( ~ p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
    | spl44_120 ),
    inference(avatar_component_clause,[],[f1313]) ).

tff(f1435,plain,
    spl44_130,
    inference(avatar_split_clause,[],[f547,f1433]) ).

tff(f1433,plain,
    ( spl44_130
  <=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_130])]) ).

tff(f547,plain,
    ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
    inference(cnf_transformation,[],[f110]) ).

tff(f110,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X0: $tType,X1: $tType,X9: X0,X10: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X9),X10) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).

tff(f1367,plain,
    spl44_129,
    inference(avatar_split_clause,[],[f424,f1365]) ).

tff(f1365,plain,
    ( spl44_129
  <=> ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_129])]) ).

tff(f424,plain,
    ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
      | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) ),
    inference(cnf_transformation,[],[f206]) ).

tff(f206,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) )
      & ( ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f203,f205,f204]) ).

tff(f204,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
     => p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f205,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
     => p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f203,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
        | ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
      & ( ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
        | ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) ) ),
    inference(rectify,[],[f202]) ).

tff(f202,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
        | ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
      & ( ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ) ),
    inference(nnf_transformation,[],[f134]) ).

tff(f134,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
    <=> ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ),
    inference(ennf_transformation,[],[f91]) ).

tff(f91,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ~ ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
    <=> ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ),
    inference(rectify,[],[f36]) ).

tff(f36,axiom,
    ! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ~ ? [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X11))
    <=> ! [X5: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__EXISTS__THM) ).

tff(f1358,plain,
    spl44_128,
    inference(avatar_split_clause,[],[f423,f1356]) ).

tff(f1356,plain,
    ( spl44_128
  <=> ! [X0: $tType,X4: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
        | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_128])]) ).

tff(f423,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
      ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
      | p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ),
    inference(cnf_transformation,[],[f206]) ).

tff(f1354,plain,
    spl44_127,
    inference(avatar_split_clause,[],[f394,f1352]) ).

tff(f1352,plain,
    ( spl44_127
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_127])]) ).

tff(f394,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f190]) ).

tff(f1350,plain,
    spl44_126,
    inference(avatar_split_clause,[],[f393,f1348]) ).

tff(f1348,plain,
    ( spl44_126
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_126])]) ).

tff(f393,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
      | p(X0) ),
    inference(cnf_transformation,[],[f190]) ).

tff(f1346,plain,
    spl44_125,
    inference(avatar_split_clause,[],[f387,f1344]) ).

tff(f1344,plain,
    ( spl44_125
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_125])]) ).

tff(f387,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f186]) ).

tff(f1342,plain,
    spl44_124,
    inference(avatar_split_clause,[],[f386,f1340]) ).

tff(f1340,plain,
    ( spl44_124
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_124])]) ).

tff(f386,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f186]) ).

tff(f1338,plain,
    spl44_123,
    inference(avatar_split_clause,[],[f385,f1336]) ).

tff(f1336,plain,
    ( spl44_123
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_123])]) ).

tff(f385,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
    inference(cnf_transformation,[],[f184]) ).

tff(f1334,plain,
    spl44_122,
    inference(avatar_split_clause,[],[f384,f1332]) ).

tff(f1332,plain,
    ( spl44_122
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_122])]) ).

tff(f384,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X0)
      | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
    inference(cnf_transformation,[],[f184]) ).

tff(f1326,plain,
    spl44_121,
    inference(avatar_split_clause,[],[f570,f1324]) ).

tff(f570,plain,
    ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)),
    inference(equality_resolution,[],[f429]) ).

tff(f429,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f208]) ).

tff(f1316,plain,
    ( spl44_119
    | ~ spl44_120
    | ~ spl44_49
    | ~ spl44_94 ),
    inference(avatar_split_clause,[],[f1188,f1112,f833,f1313,f1310]) ).

tff(f833,plain,
    ( spl44_49
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_49])]) ).

tff(f1112,plain,
    ( spl44_94
  <=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_94])]) ).

tff(f1188,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
        | ~ p(X0) )
    | ~ spl44_49
    | ~ spl44_94 ),
    inference(resolution,[],[f1113,f834]) ).

tff(f834,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
        | ~ p(X0) )
    | ~ spl44_49 ),
    inference(avatar_component_clause,[],[f833]) ).

tff(f1113,plain,
    ( ! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
        ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ~ p(c_2Ebool_2E_21_2E1(X0,X1)) )
    | ~ spl44_94 ),
    inference(avatar_component_clause,[],[f1112]) ).

tff(f1308,plain,
    spl44_118,
    inference(avatar_split_clause,[],[f555,f1306]) ).

tff(f555,plain,
    ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
    inference(definition_unfolding,[],[f312,f551]) ).

tff(f312,plain,
    ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
    inference(cnf_transformation,[],[f116]) ).

tff(f116,plain,
    ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
    inference(ennf_transformation,[],[f61]) ).

tff(f61,plain,
    ~ ? [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
    inference(rectify,[],[f60]) ).

tff(f60,negated_conjecture,
    ~ ? [X3: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
    inference(negated_conjecture,[],[f59]) ).

tff(f59,conjecture,
    ? [X3: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).

tff(f1283,plain,
    spl44_117,
    inference(avatar_split_clause,[],[f516,f1281]) ).

tff(f1281,plain,
    ( spl44_117
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP15(X0,X1,X2)
        | ~ sP13(X2,X1,X0)
        | p(X1)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_117])]) ).

tff(f516,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP15(X0,X1,X2)
      | ~ sP13(X2,X1,X0)
      | p(X1)
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f265,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP15(X0,X1,X2)
        | ~ sP13(X2,X1,X0)
        | ( p(X1)
          & ~ p(X2) )
        | ( ~ p(X0)
          & ~ p(X2) ) )
      & ( ( sP13(X2,X1,X0)
          & ( ~ p(X1)
            | p(X2) )
          & ( p(X0)
            | p(X2) ) )
        | ~ sP15(X0,X1,X2) ) ),
    inference(rectify,[],[f264]) ).

tff(f264,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP15(X1,X0,X2)
        | ~ sP13(X2,X0,X1)
        | ( p(X0)
          & ~ p(X2) )
        | ( ~ p(X1)
          & ~ p(X2) ) )
      & ( ( sP13(X2,X0,X1)
          & ( ~ p(X0)
            | p(X2) )
          & ( p(X1)
            | p(X2) ) )
        | ~ sP15(X1,X0,X2) ) ),
    inference(flattening,[],[f263]) ).

tff(f263,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP15(X1,X0,X2)
        | ~ sP13(X2,X0,X1)
        | ( p(X0)
          & ~ p(X2) )
        | ( ~ p(X1)
          & ~ p(X2) ) )
      & ( ( sP13(X2,X0,X1)
          & ( ~ p(X0)
            | p(X2) )
          & ( p(X1)
            | p(X2) ) )
        | ~ sP15(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP15(X1,X0,X2)
    <=> ( sP13(X2,X0,X1)
        & ( ~ p(X0)
          | p(X2) )
        & ( p(X1)
          | p(X2) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

tff(f1279,plain,
    spl44_116,
    inference(avatar_split_clause,[],[f497,f1277]) ).

tff(f1277,plain,
    ( spl44_116
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP12(X0,X1,X2)
        | ~ sP10(X2,X1,X0)
        | p(X1)
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_116])]) ).

tff(f497,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP12(X0,X1,X2)
      | ~ sP10(X2,X1,X0)
      | p(X1)
      | p(X0) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f256,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP12(X0,X1,X2)
        | ~ sP10(X2,X1,X0)
        | ( p(X1)
          & ~ p(X2) )
        | ( p(X0)
          & ~ p(X2) ) )
      & ( ( sP10(X2,X1,X0)
          & ( ~ p(X1)
            | p(X2) )
          & ( ~ p(X0)
            | p(X2) ) )
        | ~ sP12(X0,X1,X2) ) ),
    inference(rectify,[],[f255]) ).

tff(f255,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP12(X1,X0,X2)
        | ~ sP10(X2,X0,X1)
        | ( p(X0)
          & ~ p(X2) )
        | ( p(X1)
          & ~ p(X2) ) )
      & ( ( sP10(X2,X0,X1)
          & ( ~ p(X0)
            | p(X2) )
          & ( ~ p(X1)
            | p(X2) ) )
        | ~ sP12(X1,X0,X2) ) ),
    inference(flattening,[],[f254]) ).

tff(f254,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP12(X1,X0,X2)
        | ~ sP10(X2,X0,X1)
        | ( p(X0)
          & ~ p(X2) )
        | ( p(X1)
          & ~ p(X2) ) )
      & ( ( sP10(X2,X0,X1)
          & ( ~ p(X0)
            | p(X2) )
          & ( ~ p(X1)
            | p(X2) ) )
        | ~ sP12(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP12(X1,X0,X2)
    <=> ( sP10(X2,X0,X1)
        & ( ~ p(X0)
          | p(X2) )
        & ( ~ p(X1)
          | p(X2) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

tff(f1275,plain,
    spl44_115,
    inference(avatar_split_clause,[],[f475,f1273]) ).

tff(f1273,plain,
    ( spl44_115
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP9(X0,X1,X2)
        | ~ p(X1)
        | ~ p(X2)
        | ~ sP7(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_115])]) ).

tff(f475,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP9(X0,X1,X2)
      | ~ p(X1)
      | ~ p(X2)
      | ~ sP7(X1,X2,X0) ),
    inference(cnf_transformation,[],[f248]) ).

tff(f248,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP9(X0,X1,X2)
        | ( p(X0)
          & ~ p(X1) )
        | ( p(X0)
          & ~ p(X2) )
        | ~ sP7(X1,X2,X0) )
      & ( ( ( ~ p(X0)
            | p(X1) )
          & ( ~ p(X0)
            | p(X2) )
          & sP7(X1,X2,X0) )
        | ~ sP9(X0,X1,X2) ) ),
    inference(rectify,[],[f247]) ).

tff(f247,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP9(X2,X0,X1)
        | ( p(X2)
          & ~ p(X0) )
        | ( p(X2)
          & ~ p(X1) )
        | ~ sP7(X0,X1,X2) )
      & ( ( ( ~ p(X2)
            | p(X0) )
          & ( ~ p(X2)
            | p(X1) )
          & sP7(X0,X1,X2) )
        | ~ sP9(X2,X0,X1) ) ),
    inference(flattening,[],[f246]) ).

tff(f246,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP9(X2,X0,X1)
        | ( p(X2)
          & ~ p(X0) )
        | ( p(X2)
          & ~ p(X1) )
        | ~ sP7(X0,X1,X2) )
      & ( ( ( ~ p(X2)
            | p(X0) )
          & ( ~ p(X2)
            | p(X1) )
          & sP7(X0,X1,X2) )
        | ~ sP9(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f149]) ).

tff(f149,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP9(X2,X0,X1)
    <=> ( ( ~ p(X2)
          | p(X0) )
        & ( ~ p(X2)
          | p(X1) )
        & sP7(X0,X1,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

tff(f1271,plain,
    spl44_114,
    inference(avatar_split_clause,[],[f380,f1269]) ).

tff(f380,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(X0,X1))
      | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) ),
    inference(cnf_transformation,[],[f178]) ).

tff(f178,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2E_21_2E1(X0,X1))
        | ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) )
      & ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f176,f177]) ).

tff(f177,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
     => ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f176,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2E_21_2E1(X0,X1))
        | ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
      & ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
        | ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
    inference(rectify,[],[f175]) ).

tff(f175,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ebool_2E_21_2E1(X0,X1))
        | ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
      & ( ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
        | ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
    inference(nnf_transformation,[],[f82]) ).

tff(f82,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(X0,X1))
    <=> ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X0: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(X0,X3))
    <=> ! [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).

tff(f1267,plain,
    ( spl44_113
    | ~ spl44_39
    | ~ spl44_58 ),
    inference(avatar_split_clause,[],[f1026,f869,f740,f1265]) ).

tff(f1265,plain,
    ( spl44_113
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP5(X0,X1,X1)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_113])]) ).

tff(f740,plain,
    ( spl44_39
  <=> ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP6(X2,X1,X1)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_39])]) ).

tff(f869,plain,
    ( spl44_58
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP5(X0,X2,X1)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_58])]) ).

tff(f1026,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP5(X0,X1,X1)
        | ~ p(X0) )
    | ~ spl44_39
    | ~ spl44_58 ),
    inference(resolution,[],[f870,f741]) ).

tff(f741,plain,
    ( ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP6(X2,X1,X1)
        | ~ p(X2) )
    | ~ spl44_39 ),
    inference(avatar_component_clause,[],[f740]) ).

tff(f870,plain,
    ( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ sP6(X0,X1,X2)
        | sP5(X0,X2,X1) )
    | ~ spl44_58 ),
    inference(avatar_component_clause,[],[f869]) ).

tff(f1263,plain,
    spl44_112,
    inference(avatar_split_clause,[],[f361,f1261]) ).

tff(f1261,plain,
    ( spl44_112
  <=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_112])]) ).

tff(f361,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
    inference(cnf_transformation,[],[f74]) ).

tff(f74,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ! [X0: $tType,X12: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X12) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).

tff(f1187,plain,
    spl44_111,
    inference(avatar_split_clause,[],[f576,f1185]) ).

tff(f1185,plain,
    ( spl44_111
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP9(X0,X1,X2)
        | p(X0)
        | ~ sP7(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_111])]) ).

tff(f576,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP9(X0,X1,X2)
      | p(X0)
      | ~ sP7(X1,X2,X0) ),
    inference(duplicate_literal_removal,[],[f478]) ).

tff(f478,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP9(X0,X1,X2)
      | p(X0)
      | p(X0)
      | ~ sP7(X1,X2,X0) ),
    inference(cnf_transformation,[],[f248]) ).

tff(f1183,plain,
    spl44_110,
    inference(avatar_split_clause,[],[f575,f1181]) ).

tff(f1181,plain,
    ( spl44_110
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP12(X0,X1,X2)
        | ~ sP10(X2,X1,X0)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_110])]) ).

tff(f575,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP12(X0,X1,X2)
      | ~ sP10(X2,X1,X0)
      | ~ p(X2) ),
    inference(duplicate_literal_removal,[],[f494]) ).

tff(f494,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP12(X0,X1,X2)
      | ~ sP10(X2,X1,X0)
      | ~ p(X2)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f1175,plain,
    spl44_109,
    inference(avatar_split_clause,[],[f574,f1173]) ).

tff(f1173,plain,
    ( spl44_109
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP15(X0,X1,X2)
        | ~ sP13(X2,X1,X0)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_109])]) ).

tff(f574,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP15(X0,X1,X2)
      | ~ sP13(X2,X1,X0)
      | ~ p(X2) ),
    inference(duplicate_literal_removal,[],[f513]) ).

tff(f513,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP15(X0,X1,X2)
      | ~ sP13(X2,X1,X0)
      | ~ p(X2)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f1171,plain,
    spl44_108,
    inference(avatar_split_clause,[],[f523,f1169]) ).

tff(f1169,plain,
    ( spl44_108
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | p(X1)
        | ~ p(X2)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_108])]) ).

tff(f523,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | p(X1)
      | ~ p(X2)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f270,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP13(X0,X1,X2)
        | ( p(X0)
          & ~ p(X1)
          & p(X2) ) )
      & ( ~ p(X0)
        | p(X1)
        | ~ p(X2)
        | ~ sP13(X0,X1,X2) ) ),
    inference(rectify,[],[f269]) ).

tff(f269,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP13(X2,X0,X1)
        | ( p(X2)
          & ~ p(X0)
          & p(X1) ) )
      & ( ~ p(X2)
        | p(X0)
        | ~ p(X1)
        | ~ sP13(X2,X0,X1) ) ),
    inference(flattening,[],[f268]) ).

tff(f268,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP13(X2,X0,X1)
        | ( p(X2)
          & ~ p(X0)
          & p(X1) ) )
      & ( ~ p(X2)
        | p(X0)
        | ~ p(X1)
        | ~ sP13(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f155]) ).

tff(f155,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP13(X2,X0,X1)
    <=> ( ~ p(X2)
        | p(X0)
        | ~ p(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

tff(f1167,plain,
    spl44_107,
    inference(avatar_split_clause,[],[f520,f1165]) ).

tff(f1165,plain,
    ( spl44_107
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP14(X0,X1,X2)
        | p(X0)
        | ~ p(X1)
        | p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_107])]) ).

tff(f520,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP14(X0,X1,X2)
      | p(X0)
      | ~ p(X1)
      | p(X2) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f267,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP14(X0,X1,X2)
        | ( ( ( ~ p(X0)
              & p(X1) )
            | ~ p(X2) )
          & ( p(X0)
            | ~ p(X1)
            | p(X2) ) ) )
      & ( ( ( p(X2)
            | ( ~ p(X0)
              & p(X1) ) )
          & ( p(X0)
            | ~ p(X1)
            | ~ p(X2) ) )
        | ~ sP14(X0,X1,X2) ) ),
    inference(flattening,[],[f266]) ).

tff(f266,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP14(X0,X1,X2)
        | ( ( ( ~ p(X0)
              & p(X1) )
            | ~ p(X2) )
          & ( p(X0)
            | ~ p(X1)
            | p(X2) ) ) )
      & ( ( ( p(X2)
            | ( ~ p(X0)
              & p(X1) ) )
          & ( p(X0)
            | ~ p(X1)
            | ~ p(X2) ) )
        | ~ sP14(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f156]) ).

tff(f156,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP14(X0,X1,X2)
    <=> ( p(X2)
      <=> ( p(X0)
          | ~ p(X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

tff(f1163,plain,
    spl44_106,
    inference(avatar_split_clause,[],[f517,f1161]) ).

tff(f1161,plain,
    ( spl44_106
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ~ p(X1)
        | ~ p(X2)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_106])]) ).

tff(f517,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X0)
      | ~ p(X1)
      | ~ p(X2)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f1159,plain,
    spl44_105,
    inference(avatar_split_clause,[],[f504,f1157]) ).

tff(f1157,plain,
    ( spl44_105
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | p(X1)
        | p(X2)
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_105])]) ).

tff(f504,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | p(X1)
      | p(X2)
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f261,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP10(X0,X1,X2)
        | ( p(X0)
          & ~ p(X1)
          & ~ p(X2) ) )
      & ( ~ p(X0)
        | p(X1)
        | p(X2)
        | ~ sP10(X0,X1,X2) ) ),
    inference(rectify,[],[f260]) ).

tff(f260,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP10(X2,X0,X1)
        | ( p(X2)
          & ~ p(X0)
          & ~ p(X1) ) )
      & ( ~ p(X2)
        | p(X0)
        | p(X1)
        | ~ sP10(X2,X0,X1) ) ),
    inference(flattening,[],[f259]) ).

tff(f259,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP10(X2,X0,X1)
        | ( p(X2)
          & ~ p(X0)
          & ~ p(X1) ) )
      & ( ~ p(X2)
        | p(X0)
        | p(X1)
        | ~ sP10(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP10(X2,X0,X1)
    <=> ( ~ p(X2)
        | p(X0)
        | p(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

tff(f1155,plain,
    spl44_104,
    inference(avatar_split_clause,[],[f501,f1153]) ).

tff(f1153,plain,
    ( spl44_104
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP11(X0,X1,X2)
        | p(X0)
        | p(X1)
        | p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_104])]) ).

tff(f501,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP11(X0,X1,X2)
      | p(X0)
      | p(X1)
      | p(X2) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f258,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP11(X0,X1,X2)
        | ( ( ( ~ p(X0)
              & ~ p(X1) )
            | ~ p(X2) )
          & ( p(X0)
            | p(X1)
            | p(X2) ) ) )
      & ( ( ( p(X2)
            | ( ~ p(X0)
              & ~ p(X1) ) )
          & ( p(X0)
            | p(X1)
            | ~ p(X2) ) )
        | ~ sP11(X0,X1,X2) ) ),
    inference(flattening,[],[f257]) ).

tff(f257,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP11(X0,X1,X2)
        | ( ( ( ~ p(X0)
              & ~ p(X1) )
            | ~ p(X2) )
          & ( p(X0)
            | p(X1)
            | p(X2) ) ) )
      & ( ( ( p(X2)
            | ( ~ p(X0)
              & ~ p(X1) ) )
          & ( p(X0)
            | p(X1)
            | ~ p(X2) ) )
        | ~ sP11(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP11(X0,X1,X2)
    <=> ( p(X2)
      <=> ( p(X0)
          | p(X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

tff(f1151,plain,
    spl44_103,
    inference(avatar_split_clause,[],[f498,f1149]) ).

tff(f1149,plain,
    ( spl44_103
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | p(X1)
        | ~ p(X2)
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_103])]) ).

tff(f498,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X0)
      | p(X1)
      | ~ p(X2)
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f1147,plain,
    spl44_102,
    inference(avatar_split_clause,[],[f485,f1145]) ).

tff(f1145,plain,
    ( spl44_102
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP7(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_102])]) ).

tff(f485,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ~ p(X1)
      | p(X2)
      | ~ sP7(X0,X1,X2) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f252,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP7(X0,X1,X2)
        | ( p(X0)
          & p(X1)
          & ~ p(X2) ) )
      & ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP7(X0,X1,X2) ) ),
    inference(flattening,[],[f251]) ).

tff(f251,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP7(X0,X1,X2)
        | ( p(X0)
          & p(X1)
          & ~ p(X2) ) )
      & ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP7(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP7(X0,X1,X2)
    <=> ( ~ p(X0)
        | ~ p(X1)
        | p(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

tff(f1143,plain,
    spl44_101,
    inference(avatar_split_clause,[],[f484,f1141]) ).

tff(f1141,plain,
    ( spl44_101
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP8(X0,X1,X2)
        | ~ p(X0)
        | ~ p(X1)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_101])]) ).

tff(f484,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP8(X0,X1,X2)
      | ~ p(X0)
      | ~ p(X1)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f250,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP8(X0,X1,X2)
        | ( ( ~ p(X0)
            | ~ p(X1)
            | ~ p(X2) )
          & ( ( p(X0)
              & p(X1) )
            | p(X2) ) ) )
      & ( ( ( p(X2)
            | ~ p(X0)
            | ~ p(X1) )
          & ( ( p(X0)
              & p(X1) )
            | ~ p(X2) ) )
        | ~ sP8(X0,X1,X2) ) ),
    inference(flattening,[],[f249]) ).

tff(f249,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP8(X0,X1,X2)
        | ( ( ~ p(X0)
            | ~ p(X1)
            | ~ p(X2) )
          & ( ( p(X0)
              & p(X1) )
            | p(X2) ) ) )
      & ( ( ( p(X2)
            | ~ p(X0)
            | ~ p(X1) )
          & ( ( p(X0)
              & p(X1) )
            | ~ p(X2) ) )
        | ~ sP8(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f148]) ).

tff(f148,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP8(X0,X1,X2)
    <=> ( p(X2)
      <=> ( p(X0)
          & p(X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

tff(f1139,plain,
    spl44_100,
    inference(avatar_split_clause,[],[f481,f1137]) ).

tff(f1137,plain,
    ( spl44_100
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X2)
        | ~ p(X0)
        | ~ p(X1)
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_100])]) ).

tff(f481,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X2)
      | ~ p(X0)
      | ~ p(X1)
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f1135,plain,
    ( spl44_99
    | spl44_1
    | ~ spl44_55 ),
    inference(avatar_split_clause,[],[f1089,f857,f579,f1132]) ).

tff(f1089,plain,
    ( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) )
    | spl44_1
    | ~ spl44_55 ),
    inference(resolution,[],[f858,f581]) ).

tff(f1130,plain,
    spl44_98,
    inference(avatar_split_clause,[],[f464,f1128]) ).

tff(f1128,plain,
    ( spl44_98
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | p(X1)
        | p(X2)
        | ~ sP3(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_98])]) ).

tff(f464,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X0)
      | p(X1)
      | p(X2)
      | ~ sP3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f244]) ).

tff(f244,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP3(X0,X1,X2)
        | ( ~ p(X0)
          & ~ p(X1)
          & ~ p(X2) ) )
      & ( p(X0)
        | p(X1)
        | p(X2)
        | ~ sP3(X0,X1,X2) ) ),
    inference(flattening,[],[f243]) ).

tff(f243,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP3(X0,X1,X2)
        | ( ~ p(X0)
          & ~ p(X1)
          & ~ p(X2) ) )
      & ( p(X0)
        | p(X1)
        | p(X2)
        | ~ sP3(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f142]) ).

tff(f142,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP3(X0,X1,X2)
    <=> ( p(X0)
        | p(X1)
        | p(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

tff(f1126,plain,
    spl44_97,
    inference(avatar_split_clause,[],[f460,f1124]) ).

tff(f1124,plain,
    ( spl44_97
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP4(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_97])]) ).

tff(f460,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ~ p(X1)
      | p(X2)
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f242]) ).

tff(f242,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP4(X0,X1,X2)
        | ( p(X0)
          & p(X1)
          & ~ p(X2) ) )
      & ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP4(X0,X1,X2) ) ),
    inference(rectify,[],[f241]) ).

tff(f241,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP4(X1,X0,X2)
        | ( p(X1)
          & p(X0)
          & ~ p(X2) ) )
      & ( ~ p(X1)
        | ~ p(X0)
        | p(X2)
        | ~ sP4(X1,X0,X2) ) ),
    inference(flattening,[],[f240]) ).

tff(f240,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP4(X1,X0,X2)
        | ( p(X1)
          & p(X0)
          & ~ p(X2) ) )
      & ( ~ p(X1)
        | ~ p(X0)
        | p(X2)
        | ~ sP4(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f143]) ).

tff(f143,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP4(X1,X0,X2)
    <=> ( ~ p(X1)
        | ~ p(X0)
        | p(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

tff(f1122,plain,
    spl44_96,
    inference(avatar_split_clause,[],[f456,f1120]) ).

tff(f1120,plain,
    ( spl44_96
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP5(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_96])]) ).

tff(f456,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ~ p(X1)
      | p(X2)
      | ~ sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f239,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP5(X0,X1,X2)
        | ( p(X0)
          & p(X1)
          & ~ p(X2) ) )
      & ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP5(X0,X1,X2) ) ),
    inference(rectify,[],[f238]) ).

tff(f238,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP5(X2,X0,X1)
        | ( p(X2)
          & p(X0)
          & ~ p(X1) ) )
      & ( ~ p(X2)
        | ~ p(X0)
        | p(X1)
        | ~ sP5(X2,X0,X1) ) ),
    inference(flattening,[],[f237]) ).

tff(f237,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP5(X2,X0,X1)
        | ( p(X2)
          & p(X0)
          & ~ p(X1) ) )
      & ( ~ p(X2)
        | ~ p(X0)
        | p(X1)
        | ~ sP5(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP5(X2,X0,X1)
    <=> ( ~ p(X2)
        | ~ p(X0)
        | p(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

tff(f1118,plain,
    spl44_95,
    inference(avatar_split_clause,[],[f452,f1116]) ).

tff(f1116,plain,
    ( spl44_95
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ~ p(X1)
        | p(X2)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_95])]) ).

tff(f452,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ~ p(X1)
      | p(X2)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f1114,plain,
    spl44_94,
    inference(avatar_split_clause,[],[f379,f1112]) ).

tff(f379,plain,
    ! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
      | ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ),
    inference(cnf_transformation,[],[f178]) ).

tff(f1101,plain,
    spl44_93,
    inference(avatar_split_clause,[],[f470,f1099]) ).

tff(f1099,plain,
    ( spl44_93
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ( X0 = X1 )
        | ~ p(X2)
        | ~ sP6(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_93])]) ).

tff(f470,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( X0 = X1 )
      | ~ p(X2)
      | ~ sP6(X2,X1,X0) ),
    inference(cnf_transformation,[],[f245]) ).

tff(f245,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( ( ( p(X2)
            | ( X0 != X1 ) )
          & ( ( X0 = X1 )
            | ~ p(X2) ) )
        | ~ sP6(X2,X1,X0) )
      & ( sP6(X2,X1,X0)
        | ( ( ( X0 != X1 )
            | ~ p(X2) )
          & ( ( X0 = X1 )
            | p(X2) ) ) ) ),
    inference(nnf_transformation,[],[f146]) ).

tff(f146,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
      <=> ( X0 = X1 ) )
    <=> sP6(X2,X1,X0) ),
    inference(definition_folding,[],[f101,f145,f144,f143,f142]) ).

tff(f101,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
      <=> ( X0 = X1 ) )
    <=> ( ( ~ p(X2)
          | ~ p(X1)
          | p(X0) )
        & ( ~ p(X2)
          | ~ p(X0)
          | p(X1) )
        & ( ~ p(X1)
          | ~ p(X0)
          | p(X2) )
        & ( p(X0)
          | p(X1)
          | p(X2) ) ) ),
    inference(rectify,[],[f53]) ).

tff(f53,axiom,
    ! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
      ( ( p(X35)
      <=> ( X33 = X34 ) )
    <=> ( ( ~ p(X35)
          | ~ p(X34)
          | p(X33) )
        & ( ~ p(X35)
          | ~ p(X33)
          | p(X34) )
        & ( ~ p(X34)
          | ~ p(X33)
          | p(X35) )
        & ( p(X33)
          | p(X34)
          | p(X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).

tff(f1097,plain,
    spl44_92,
    inference(avatar_split_clause,[],[f468,f1095]) ).

tff(f1095,plain,
    ( spl44_92
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP6(X2,X1,X0)
        | ( X0 = X1 )
        | p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_92])]) ).

tff(f468,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP6(X2,X1,X0)
      | ( X0 = X1 )
      | p(X2) ),
    inference(cnf_transformation,[],[f245]) ).

tff(f1080,plain,
    ( spl44_91
    | spl44_1 ),
    inference(avatar_split_clause,[],[f407,f579,f1078]) ).

tff(f1078,plain,
    ( spl44_91
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ~ sP0(X0,X1)
        | p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_91])]) ).

tff(f407,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2EF_2E0)
      | p(X0)
      | p(X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f196]) ).

tff(f196,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP0(X0,X1)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & ~ p(X0)
          & ~ p(X1) ) )
      & ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | p(X1)
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f195]) ).

tff(f195,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP0(X0,X1)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & ~ p(X0)
          & ~ p(X1) ) )
      & ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | p(X1)
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f137]) ).

tff(f137,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP0(X0,X1)
    <=> ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | p(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f1074,plain,
    ( spl44_90
    | spl44_1 ),
    inference(avatar_split_clause,[],[f402,f579,f1072]) ).

tff(f1072,plain,
    ( spl44_90
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ~ sP1(X0,X1)
        | p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_90])]) ).

tff(f402,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2EF_2E0)
      | p(X0)
      | p(X1)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f194]) ).

tff(f194,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP1(X0,X1)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & ~ p(X0)
          & ( p(c_2Ebool_2EF_2E0)
            | ~ p(X1) ) ) )
      & ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & p(X1) )
        | ~ sP1(X0,X1) ) ),
    inference(flattening,[],[f193]) ).

tff(f193,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP1(X0,X1)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & ~ p(X0)
          & ( p(c_2Ebool_2EF_2E0)
            | ~ p(X1) ) ) )
      & ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & p(X1) )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f138]) ).

tff(f138,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP1(X0,X1)
    <=> ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & p(X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f1052,plain,
    ( spl44_89
    | ~ spl44_10
    | ~ spl44_47
    | ~ spl44_66 ),
    inference(avatar_split_clause,[],[f1039,f901,f817,f617,f1049]) ).

tff(f901,plain,
    ( spl44_66
  <=> ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_66])]) ).

tff(f1039,plain,
    ( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) )
    | ~ spl44_10
    | ~ spl44_47
    | ~ spl44_66 ),
    inference(forward_demodulation,[],[f1032,f902]) ).

tff(f902,plain,
    ( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) )
    | ~ spl44_66 ),
    inference(avatar_component_clause,[],[f901]) ).

tff(f1032,plain,
    ( ! [X0: $tType,X1: X0] : ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Emin_2E_3D_2E2(X0,X1,X1)) )
    | ~ spl44_10
    | ~ spl44_47 ),
    inference(resolution,[],[f818,f618]) ).

tff(f991,plain,
    spl44_88,
    inference(avatar_split_clause,[],[f528,f989]) ).

tff(f989,plain,
    ( spl44_88
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP14(X0,X1,X2)
        | ~ sP15(X1,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_88])]) ).

tff(f528,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP14(X0,X1,X2)
      | ~ sP15(X1,X0,X2) ),
    inference(cnf_transformation,[],[f271]) ).

tff(f271,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP14(X0,X1,X2)
        | ~ sP15(X1,X0,X2) )
      & ( sP15(X1,X0,X2)
        | ~ sP14(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f158]) ).

tff(f158,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP14(X0,X1,X2)
    <=> sP15(X1,X0,X2) ),
    inference(definition_folding,[],[f135,f157,f156,f155]) ).

tff(f135,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
      <=> ( p(X0)
          | ~ p(X1) ) )
    <=> ( ( ~ p(X2)
          | p(X0)
          | ~ p(X1) )
        & ( ~ p(X0)
          | p(X2) )
        & ( p(X1)
          | p(X2) ) ) ),
    inference(ennf_transformation,[],[f104]) ).

tff(f104,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
      <=> ( p(X1)
         => p(X0) ) )
    <=> ( ( ~ p(X2)
          | p(X0)
          | ~ p(X1) )
        & ( ~ p(X0)
          | p(X2) )
        & ( p(X1)
          | p(X2) ) ) ),
    inference(rectify,[],[f56]) ).

tff(f56,axiom,
    ! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
      ( ( p(X35)
      <=> ( p(X34)
         => p(X33) ) )
    <=> ( ( ~ p(X35)
          | p(X33)
          | ~ p(X34) )
        & ( ~ p(X33)
          | p(X35) )
        & ( p(X34)
          | p(X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).

tff(f987,plain,
    spl44_87,
    inference(avatar_split_clause,[],[f527,f985]) ).

tff(f985,plain,
    ( spl44_87
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP15(X1,X0,X2)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_87])]) ).

tff(f527,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP15(X1,X0,X2)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f271]) ).

tff(f983,plain,
    spl44_86,
    inference(avatar_split_clause,[],[f522,f981]) ).

tff(f981,plain,
    ( spl44_86
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP14(X0,X1,X2)
        | ~ p(X0)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_86])]) ).

tff(f522,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP14(X0,X1,X2)
      | ~ p(X0)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f979,plain,
    spl44_85,
    inference(avatar_split_clause,[],[f521,f977]) ).

tff(f977,plain,
    ( spl44_85
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP14(X0,X1,X2)
        | p(X1)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_85])]) ).

tff(f521,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP14(X0,X1,X2)
      | p(X1)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f975,plain,
    spl44_84,
    inference(avatar_split_clause,[],[f519,f973]) ).

tff(f973,plain,
    ( spl44_84
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X2)
        | ~ p(X0)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_84])]) ).

tff(f519,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X2)
      | ~ p(X0)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f971,plain,
    spl44_83,
    inference(avatar_split_clause,[],[f518,f969]) ).

tff(f969,plain,
    ( spl44_83
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X2)
        | p(X1)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_83])]) ).

tff(f518,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X2)
      | p(X1)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f267]) ).

tff(f967,plain,
    spl44_82,
    inference(avatar_split_clause,[],[f512,f965]) ).

tff(f965,plain,
    ( spl44_82
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP13(X2,X1,X0)
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_82])]) ).

tff(f512,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP13(X2,X1,X0)
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f963,plain,
    spl44_81,
    inference(avatar_split_clause,[],[f511,f961]) ).

tff(f961,plain,
    ( spl44_81
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X1)
        | p(X2)
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_81])]) ).

tff(f511,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X1)
      | p(X2)
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f959,plain,
    spl44_80,
    inference(avatar_split_clause,[],[f510,f957]) ).

tff(f957,plain,
    ( spl44_80
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | p(X2)
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_80])]) ).

tff(f510,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X0)
      | p(X2)
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f955,plain,
    spl44_79,
    inference(avatar_split_clause,[],[f509,f953]) ).

tff(f953,plain,
    ( spl44_79
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP11(X0,X1,X2)
        | ~ sP12(X1,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_79])]) ).

tff(f509,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP11(X0,X1,X2)
      | ~ sP12(X1,X0,X2) ),
    inference(cnf_transformation,[],[f262]) ).

tff(f262,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP11(X0,X1,X2)
        | ~ sP12(X1,X0,X2) )
      & ( sP12(X1,X0,X2)
        | ~ sP11(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP11(X0,X1,X2)
    <=> sP12(X1,X0,X2) ),
    inference(definition_folding,[],[f103,f153,f152,f151]) ).

tff(f103,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
      <=> ( p(X0)
          | p(X1) ) )
    <=> ( ( ~ p(X2)
          | p(X0)
          | p(X1) )
        & ( ~ p(X0)
          | p(X2) )
        & ( ~ p(X1)
          | p(X2) ) ) ),
    inference(rectify,[],[f55]) ).

tff(f55,axiom,
    ! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
      ( ( p(X35)
      <=> ( p(X33)
          | p(X34) ) )
    <=> ( ( ~ p(X35)
          | p(X33)
          | p(X34) )
        & ( ~ p(X33)
          | p(X35) )
        & ( ~ p(X34)
          | p(X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).

tff(f951,plain,
    ( spl44_77
    | ~ spl44_78
    | ~ spl44_11 ),
    inference(avatar_split_clause,[],[f748,f628,f948,f945]) ).

tff(f945,plain,
    ( spl44_77
  <=> ! [X0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ET_2E0 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_77])]) ).

tff(f948,plain,
    ( spl44_78
  <=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2EF_2E0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_78])]) ).

tff(f628,plain,
    ( spl44_11
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( ( c_2Ebool_2EF_2E0 = X0 )
        | ( c_2Ebool_2ET_2E0 = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_11])]) ).

tff(f748,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
        | ( c_2Ebool_2ET_2E0 = X0 ) )
    | ~ spl44_11 ),
    inference(equality_factoring,[],[f629]) ).

tff(f629,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ( c_2Ebool_2EF_2E0 = X0 )
        | ( c_2Ebool_2ET_2E0 = X0 ) )
    | ~ spl44_11 ),
    inference(avatar_component_clause,[],[f628]) ).

tff(f943,plain,
    spl44_76,
    inference(avatar_split_clause,[],[f508,f941]) ).

tff(f941,plain,
    ( spl44_76
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP12(X1,X0,X2)
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_76])]) ).

tff(f508,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP12(X1,X0,X2)
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f262]) ).

tff(f939,plain,
    spl44_75,
    inference(avatar_split_clause,[],[f503,f937]) ).

tff(f937,plain,
    ( spl44_75
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP11(X0,X1,X2)
        | ~ p(X0)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_75])]) ).

tff(f503,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP11(X0,X1,X2)
      | ~ p(X0)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f935,plain,
    spl44_74,
    inference(avatar_split_clause,[],[f502,f933]) ).

tff(f933,plain,
    ( spl44_74
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP11(X0,X1,X2)
        | ~ p(X1)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_74])]) ).

tff(f502,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP11(X0,X1,X2)
      | ~ p(X1)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f931,plain,
    spl44_73,
    inference(avatar_split_clause,[],[f500,f929]) ).

tff(f929,plain,
    ( spl44_73
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X2)
        | ~ p(X0)
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_73])]) ).

tff(f500,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X2)
      | ~ p(X0)
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f927,plain,
    spl44_72,
    inference(avatar_split_clause,[],[f499,f925]) ).

tff(f925,plain,
    ( spl44_72
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X2)
        | ~ p(X1)
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_72])]) ).

tff(f499,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X2)
      | ~ p(X1)
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f923,plain,
    spl44_71,
    inference(avatar_split_clause,[],[f493,f921]) ).

tff(f921,plain,
    ( spl44_71
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP10(X2,X1,X0)
        | ~ sP12(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_71])]) ).

tff(f493,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP10(X2,X1,X0)
      | ~ sP12(X0,X1,X2) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f919,plain,
    spl44_70,
    inference(avatar_split_clause,[],[f492,f917]) ).

tff(f917,plain,
    ( spl44_70
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X1)
        | p(X2)
        | ~ sP12(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_70])]) ).

tff(f492,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X1)
      | p(X2)
      | ~ sP12(X0,X1,X2) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f915,plain,
    spl44_69,
    inference(avatar_split_clause,[],[f491,f913]) ).

tff(f913,plain,
    ( spl44_69
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | p(X2)
        | ~ sP12(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_69])]) ).

tff(f491,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | p(X2)
      | ~ sP12(X0,X1,X2) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f911,plain,
    spl44_68,
    inference(avatar_split_clause,[],[f490,f909]) ).

tff(f909,plain,
    ( spl44_68
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP8(X0,X1,X2)
        | ~ sP9(X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_68])]) ).

tff(f490,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP8(X0,X1,X2)
      | ~ sP9(X2,X0,X1) ),
    inference(cnf_transformation,[],[f253]) ).

tff(f253,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( sP8(X0,X1,X2)
        | ~ sP9(X2,X0,X1) )
      & ( sP9(X2,X0,X1)
        | ~ sP8(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( sP8(X0,X1,X2)
    <=> sP9(X2,X0,X1) ),
    inference(definition_folding,[],[f102,f149,f148,f147]) ).

tff(f102,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
      ( ( p(X2)
      <=> ( p(X0)
          & p(X1) ) )
    <=> ( ( ~ p(X2)
          | p(X0) )
        & ( ~ p(X2)
          | p(X1) )
        & ( ~ p(X0)
          | ~ p(X1)
          | p(X2) ) ) ),
    inference(rectify,[],[f54]) ).

tff(f54,axiom,
    ! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
      ( ( p(X35)
      <=> ( p(X33)
          & p(X34) ) )
    <=> ( ( ~ p(X35)
          | p(X33) )
        & ( ~ p(X35)
          | p(X34) )
        & ( ~ p(X33)
          | ~ p(X34)
          | p(X35) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__conj) ).

tff(f907,plain,
    spl44_67,
    inference(avatar_split_clause,[],[f489,f905]) ).

tff(f905,plain,
    ( spl44_67
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP9(X2,X0,X1)
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_67])]) ).

tff(f489,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP9(X2,X0,X1)
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f253]) ).

tff(f903,plain,
    ( spl44_66
    | ~ spl44_3
    | ~ spl44_10 ),
    inference(avatar_split_clause,[],[f626,f617,f589,f901]) ).

tff(f626,plain,
    ( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) )
    | ~ spl44_3
    | ~ spl44_10 ),
    inference(resolution,[],[f618,f590]) ).

tff(f899,plain,
    spl44_65,
    inference(avatar_split_clause,[],[f483,f897]) ).

tff(f897,plain,
    ( spl44_65
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP8(X0,X1,X2)
        | p(X0)
        | p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_65])]) ).

tff(f483,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP8(X0,X1,X2)
      | p(X0)
      | p(X2) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f895,plain,
    spl44_64,
    inference(avatar_split_clause,[],[f482,f893]) ).

tff(f893,plain,
    ( spl44_64
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP8(X0,X1,X2)
        | p(X1)
        | p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_64])]) ).

tff(f482,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP8(X0,X1,X2)
      | p(X1)
      | p(X2) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f891,plain,
    spl44_63,
    inference(avatar_split_clause,[],[f480,f889]) ).

tff(f889,plain,
    ( spl44_63
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ~ p(X2)
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_63])]) ).

tff(f480,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X0)
      | ~ p(X2)
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f887,plain,
    spl44_62,
    inference(avatar_split_clause,[],[f479,f885]) ).

tff(f885,plain,
    ( spl44_62
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | ~ p(X2)
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_62])]) ).

tff(f479,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | ~ p(X2)
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f883,plain,
    spl44_61,
    inference(avatar_split_clause,[],[f474,f881]) ).

tff(f881,plain,
    ( spl44_61
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | p(X1)
        | ~ sP9(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_61])]) ).

tff(f474,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | p(X1)
      | ~ sP9(X0,X1,X2) ),
    inference(cnf_transformation,[],[f248]) ).

tff(f879,plain,
    spl44_60,
    inference(avatar_split_clause,[],[f473,f877]) ).

tff(f877,plain,
    ( spl44_60
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | p(X2)
        | ~ sP9(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_60])]) ).

tff(f473,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | p(X2)
      | ~ sP9(X0,X1,X2) ),
    inference(cnf_transformation,[],[f248]) ).

tff(f875,plain,
    spl44_59,
    inference(avatar_split_clause,[],[f472,f873]) ).

tff(f873,plain,
    ( spl44_59
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP7(X1,X2,X0)
        | ~ sP9(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_59])]) ).

tff(f472,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP7(X1,X2,X0)
      | ~ sP9(X0,X1,X2) ),
    inference(cnf_transformation,[],[f248]) ).

tff(f871,plain,
    spl44_58,
    inference(avatar_split_clause,[],[f451,f869]) ).

tff(f451,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP5(X0,X2,X1)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f867,plain,
    spl44_57,
    inference(avatar_split_clause,[],[f450,f865]) ).

tff(f865,plain,
    ( spl44_57
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP4(X1,X2,X0)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_57])]) ).

tff(f450,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP4(X1,X2,X0)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f863,plain,
    spl44_56,
    inference(avatar_split_clause,[],[f449,f861]) ).

tff(f861,plain,
    ( spl44_56
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP3(X2,X1,X0)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_56])]) ).

tff(f449,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP3(X2,X1,X0)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f859,plain,
    ( spl44_55
    | ~ spl44_3
    | ~ spl44_6 ),
    inference(avatar_split_clause,[],[f625,f601,f589,f857]) ).

tff(f601,plain,
    ( spl44_6
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( p(c_2Ebool_2E_7E_2E1(X0))
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_6])]) ).

tff(f625,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( p(X0)
        | ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
    | ~ spl44_3
    | ~ spl44_6 ),
    inference(resolution,[],[f602,f590]) ).

tff(f602,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( p(c_2Ebool_2E_7E_2E1(X0))
        | p(X0) )
    | ~ spl44_6 ),
    inference(avatar_component_clause,[],[f601]) ).

tff(f855,plain,
    spl44_54,
    inference(avatar_split_clause,[],[f431,f853]) ).

tff(f853,plain,
    ( spl44_54
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_54])]) ).

tff(f431,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 = X2 )
      | ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f209,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( ( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
        | ( X1 != X2 ) )
      & ( ( X1 = X2 )
        | ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
    inference(nnf_transformation,[],[f96]) ).

tff(f96,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
    <=> ( X1 = X2 ) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X0: $tType,X6: X0,X7: X0] :
      ( p(c_2Emin_2E_3D_2E2(X0,X6,X7))
    <=> ( X6 = X7 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).

tff(f851,plain,
    spl44_53,
    inference(avatar_split_clause,[],[f376,f849]) ).

tff(f849,plain,
    ( spl44_53
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | ~ p(X0)
        | ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_53])]) ).

tff(f376,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | ~ p(X0)
      | ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ),
    inference(cnf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
        | ( ~ p(X1)
          & p(X0) ) )
      & ( p(X1)
        | ~ p(X0)
        | ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
    inference(flattening,[],[f173]) ).

tff(f173,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
        | ( ~ p(X1)
          & p(X0) ) )
      & ( p(X1)
        | ~ p(X0)
        | ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
    inference(nnf_transformation,[],[f128]) ).

tff(f128,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
    <=> ( p(X1)
        | ~ p(X0) ) ),
    inference(ennf_transformation,[],[f81]) ).

tff(f81,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
    <=> ( p(X0)
       => p(X1) ) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(X6,X7))
    <=> ( p(X6)
       => p(X7) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).

tff(f847,plain,
    spl44_52,
    inference(avatar_split_clause,[],[f373,f845]) ).

tff(f845,plain,
    ( spl44_52
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | p(X0)
        | ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_52])]) ).

tff(f373,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | p(X0)
      | ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ),
    inference(cnf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
        | ( ~ p(X1)
          & ~ p(X0) ) )
      & ( p(X1)
        | p(X0)
        | ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
    inference(flattening,[],[f171]) ).

tff(f171,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
        | ( ~ p(X1)
          & ~ p(X0) ) )
      & ( p(X1)
        | p(X0)
        | ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
    inference(nnf_transformation,[],[f80]) ).

tff(f80,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
    <=> ( p(X1)
        | p(X0) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(X6,X7))
    <=> ( p(X7)
        | p(X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).

tff(f843,plain,
    spl44_51,
    inference(avatar_split_clause,[],[f372,f841]) ).

tff(f841,plain,
    ( spl44_51
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
        | ~ p(X1)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_51])]) ).

tff(f372,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
      | ~ p(X1)
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f170]) ).

tff(f170,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
        | ~ p(X1)
        | ~ p(X0) )
      & ( ( p(X1)
          & p(X0) )
        | ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
    inference(flattening,[],[f169]) ).

tff(f169,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
        | ~ p(X1)
        | ~ p(X0) )
      & ( ( p(X1)
          & p(X0) )
        | ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
    inference(nnf_transformation,[],[f79]) ).

tff(f79,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
    <=> ( p(X1)
        & p(X0) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(X6,X7))
    <=> ( p(X7)
        & p(X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).

tff(f839,plain,
    spl44_50,
    inference(avatar_split_clause,[],[f360,f837]) ).

tff(f837,plain,
    ( spl44_50
  <=> ! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_50])]) ).

tff(f360,plain,
    ! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
    inference(cnf_transformation,[],[f73]) ).

tff(f73,plain,
    ! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0: $tType,X9: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X9) = X9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).

tff(f835,plain,
    spl44_49,
    inference(avatar_split_clause,[],[f355,f833]) ).

tff(f355,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
    inference(cnf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( ~ p(X0)
        | ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) )
      & ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
        | p(X0) ) ),
    inference(nnf_transformation,[],[f70]) ).

tff(f70,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X12: tyop_2Emin_2Ebool] :
      ( ~ p(X12)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).

tff(f831,plain,
    spl44_48,
    inference(avatar_split_clause,[],[f354,f829]) ).

tff(f354,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
      | p(X0) ),
    inference(cnf_transformation,[],[f165]) ).

tff(f819,plain,
    ( spl44_47
    | ~ spl44_4
    | ~ spl44_5 ),
    inference(avatar_split_clause,[],[f623,f597,f593,f817]) ).

tff(f597,plain,
    ( spl44_5
  <=> ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_5])]) ).

tff(f623,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
    | ~ spl44_4
    | ~ spl44_5 ),
    inference(resolution,[],[f598,f594]) ).

tff(f598,plain,
    ( ! [X0: tyop_2Emin_2Ebool] :
        ( ~ p(c_2Ebool_2E_7E_2E1(X0))
        | ~ p(X0) )
    | ~ spl44_5 ),
    inference(avatar_component_clause,[],[f597]) ).

tff(f793,plain,
    spl44_46,
    inference(avatar_split_clause,[],[f418,f791]) ).

tff(f791,plain,
    ( spl44_46
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP2(X0,X1)
        | p(X0)
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_46])]) ).

tff(f418,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP2(X0,X1)
      | p(X0)
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP2(X0,X1)
        | ( p(X0)
          & p(X1) )
        | ( ~ p(X1)
          & ~ p(X0) ) )
      & ( ( ( ~ p(X0)
            | ~ p(X1) )
          & ( p(X1)
            | p(X0) ) )
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f199]) ).

tff(f199,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
      ( ( sP2(X1,X0)
        | ( p(X1)
          & p(X0) )
        | ( ~ p(X0)
          & ~ p(X1) ) )
      & ( ( ( ~ p(X1)
            | ~ p(X0) )
          & ( p(X0)
            | p(X1) ) )
        | ~ sP2(X1,X0) ) ),
    inference(flattening,[],[f198]) ).

tff(f198,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
      ( ( sP2(X1,X0)
        | ( p(X1)
          & p(X0) )
        | ( ~ p(X0)
          & ~ p(X1) ) )
      & ( ( ( ~ p(X1)
            | ~ p(X0) )
          & ( p(X0)
            | p(X1) ) )
        | ~ sP2(X1,X0) ) ),
    inference(nnf_transformation,[],[f140]) ).

tff(f140,plain,
    ! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
      ( sP2(X1,X0)
    <=> ( ( ~ p(X1)
          | ~ p(X0) )
        & ( p(X0)
          | p(X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

tff(f789,plain,
    spl44_45,
    inference(avatar_split_clause,[],[f415,f787]) ).

tff(f787,plain,
    ( spl44_45
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP2(X0,X1)
        | p(X1)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_45])]) ).

tff(f415,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP2(X0,X1)
      | p(X1)
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f785,plain,
    spl44_44,
    inference(avatar_split_clause,[],[f414,f783]) ).

tff(f783,plain,
    ( spl44_44
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ p(X0)
        | ~ p(X1)
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_44])]) ).

tff(f414,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ~ p(X1)
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f781,plain,
    spl44_43,
    inference(avatar_split_clause,[],[f413,f779]) ).

tff(f779,plain,
    ( spl44_43
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X1)
        | p(X0)
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_43])]) ).

tff(f413,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | p(X0)
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f777,plain,
    spl44_42,
    inference(avatar_split_clause,[],[f367,f775]) ).

tff(f775,plain,
    ( spl44_42
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ( X0 = X1 )
        | ~ p(X0)
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_42])]) ).

tff(f367,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( X0 = X1 )
      | ~ p(X0)
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f126]) ).

tff(f126,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( X0 = X1 )
      | ( ~ p(X0)
        & p(X1) )
      | ( ~ p(X1)
        & p(X0) ) ),
    inference(flattening,[],[f125]) ).

tff(f125,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( X0 = X1 )
      | ( ~ p(X0)
        & p(X1) )
      | ( ~ p(X1)
        & p(X0) ) ),
    inference(ennf_transformation,[],[f77]) ).

tff(f77,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X0)
       => p(X1) )
     => ( ( p(X1)
         => p(X0) )
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f29]) ).

tff(f29,axiom,
    ! [X15: tyop_2Emin_2Ebool,X16: tyop_2Emin_2Ebool] :
      ( ( p(X15)
       => p(X16) )
     => ( ( p(X16)
         => p(X15) )
       => ( X15 = X16 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).

tff(f773,plain,
    spl44_41,
    inference(avatar_split_clause,[],[f364,f771]) ).

tff(f771,plain,
    ( spl44_41
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ( X0 = X1 )
        | p(X1)
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_41])]) ).

tff(f364,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( X0 = X1 )
      | p(X1)
      | p(X0) ),
    inference(cnf_transformation,[],[f126]) ).

tff(f767,plain,
    ( spl44_40
    | ~ spl44_8
    | ~ spl44_18 ),
    inference(avatar_split_clause,[],[f762,f656,f609,f765]) ).

tff(f765,plain,
    ( spl44_40
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP1(X0,X1)
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_40])]) ).

tff(f609,plain,
    ( spl44_8
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP0(X0,X1)
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_8])]) ).

tff(f656,plain,
    ( spl44_18
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP1(X0,X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_18])]) ).

tff(f762,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP1(X0,X1)
        | ~ p(X1) )
    | ~ spl44_8
    | ~ spl44_18 ),
    inference(resolution,[],[f657,f610]) ).

tff(f610,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP0(X0,X1)
        | ~ p(X1) )
    | ~ spl44_8 ),
    inference(avatar_component_clause,[],[f609]) ).

tff(f657,plain,
    ( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( ~ sP0(X0,X1)
        | sP1(X0,X1) )
    | ~ spl44_18 ),
    inference(avatar_component_clause,[],[f656]) ).

tff(f742,plain,
    spl44_39,
    inference(avatar_split_clause,[],[f573,f740]) ).

tff(f573,plain,
    ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP6(X2,X1,X1)
      | ~ p(X2) ),
    inference(equality_resolution,[],[f469]) ).

tff(f469,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP6(X2,X1,X0)
      | ( X0 != X1 )
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f245]) ).

tff(f738,plain,
    spl44_38,
    inference(avatar_split_clause,[],[f572,f736]) ).

tff(f736,plain,
    ( spl44_38
  <=> ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(X2)
        | ~ sP6(X2,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_38])]) ).

tff(f572,plain,
    ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X2)
      | ~ sP6(X2,X1,X1) ),
    inference(equality_resolution,[],[f471]) ).

tff(f471,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X2)
      | ( X0 != X1 )
      | ~ sP6(X2,X1,X0) ),
    inference(cnf_transformation,[],[f245]) ).

tff(f734,plain,
    spl44_37,
    inference(avatar_split_clause,[],[f526,f732]) ).

tff(f732,plain,
    ( spl44_37
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP13(X0,X1,X2)
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_37])]) ).

tff(f526,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP13(X0,X1,X2)
      | p(X0) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f730,plain,
    spl44_36,
    inference(avatar_split_clause,[],[f525,f728]) ).

tff(f728,plain,
    ( spl44_36
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP13(X0,X1,X2)
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_36])]) ).

tff(f525,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP13(X0,X1,X2)
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f726,plain,
    spl44_35,
    inference(avatar_split_clause,[],[f524,f724]) ).

tff(f724,plain,
    ( spl44_35
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP13(X0,X1,X2)
        | p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_35])]) ).

tff(f524,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP13(X0,X1,X2)
      | p(X2) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f722,plain,
    spl44_34,
    inference(avatar_split_clause,[],[f507,f720]) ).

tff(f720,plain,
    ( spl44_34
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP10(X0,X1,X2)
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_34])]) ).

tff(f507,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP10(X0,X1,X2)
      | p(X0) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f718,plain,
    spl44_33,
    inference(avatar_split_clause,[],[f506,f716]) ).

tff(f716,plain,
    ( spl44_33
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP10(X0,X1,X2)
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_33])]) ).

tff(f506,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP10(X0,X1,X2)
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f714,plain,
    spl44_32,
    inference(avatar_split_clause,[],[f505,f712]) ).

tff(f712,plain,
    ( spl44_32
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP10(X0,X1,X2)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_32])]) ).

tff(f505,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP10(X0,X1,X2)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f710,plain,
    spl44_31,
    inference(avatar_split_clause,[],[f488,f708]) ).

tff(f708,plain,
    ( spl44_31
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP7(X0,X1,X2)
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_31])]) ).

tff(f488,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP7(X0,X1,X2)
      | p(X0) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f706,plain,
    spl44_30,
    inference(avatar_split_clause,[],[f487,f704]) ).

tff(f704,plain,
    ( spl44_30
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP7(X0,X1,X2)
        | p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_30])]) ).

tff(f487,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP7(X0,X1,X2)
      | p(X1) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f702,plain,
    spl44_29,
    inference(avatar_split_clause,[],[f486,f700]) ).

tff(f700,plain,
    ( spl44_29
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP7(X0,X1,X2)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_29])]) ).

tff(f486,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP7(X0,X1,X2)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f698,plain,
    spl44_28,
    inference(avatar_split_clause,[],[f467,f696]) ).

tff(f696,plain,
    ( spl44_28
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP3(X0,X1,X2)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_28])]) ).

tff(f467,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP3(X0,X1,X2)
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f244]) ).

tff(f694,plain,
    spl44_27,
    inference(avatar_split_clause,[],[f466,f692]) ).

tff(f692,plain,
    ( spl44_27
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP3(X0,X1,X2)
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_27])]) ).

tff(f466,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP3(X0,X1,X2)
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f244]) ).

tff(f690,plain,
    spl44_26,
    inference(avatar_split_clause,[],[f465,f688]) ).

tff(f688,plain,
    ( spl44_26
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP3(X0,X1,X2)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_26])]) ).

tff(f465,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP3(X0,X1,X2)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f244]) ).

tff(f686,plain,
    spl44_25,
    inference(avatar_split_clause,[],[f463,f684]) ).

tff(f684,plain,
    ( spl44_25
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP4(X0,X1,X2)
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_25])]) ).

tff(f463,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP4(X0,X1,X2)
      | p(X0) ),
    inference(cnf_transformation,[],[f242]) ).

tff(f682,plain,
    spl44_24,
    inference(avatar_split_clause,[],[f462,f680]) ).

tff(f680,plain,
    ( spl44_24
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP4(X0,X1,X2)
        | p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_24])]) ).

tff(f462,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP4(X0,X1,X2)
      | p(X1) ),
    inference(cnf_transformation,[],[f242]) ).

tff(f678,plain,
    spl44_23,
    inference(avatar_split_clause,[],[f461,f676]) ).

tff(f676,plain,
    ( spl44_23
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP4(X0,X1,X2)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_23])]) ).

tff(f461,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP4(X0,X1,X2)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f242]) ).

tff(f674,plain,
    spl44_22,
    inference(avatar_split_clause,[],[f459,f672]) ).

tff(f672,plain,
    ( spl44_22
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP5(X0,X1,X2)
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_22])]) ).

tff(f459,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP5(X0,X1,X2)
      | p(X0) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f670,plain,
    spl44_21,
    inference(avatar_split_clause,[],[f458,f668]) ).

tff(f668,plain,
    ( spl44_21
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP5(X0,X1,X2)
        | p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_21])]) ).

tff(f458,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP5(X0,X1,X2)
      | p(X1) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f666,plain,
    spl44_20,
    inference(avatar_split_clause,[],[f457,f664]) ).

tff(f664,plain,
    ( spl44_20
  <=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP5(X0,X1,X2)
        | ~ p(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_20])]) ).

tff(f457,plain,
    ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP5(X0,X1,X2)
      | ~ p(X2) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f662,plain,
    spl44_19,
    inference(avatar_split_clause,[],[f412,f660]) ).

tff(f660,plain,
    ( spl44_19
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP0(X0,X1)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_19])]) ).

tff(f412,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP0(X0,X1)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f197]) ).

tff(f197,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( sP0(X0,X1)
        | ~ sP1(X0,X1) )
      & ( sP1(X0,X1)
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP0(X0,X1)
    <=> sP1(X0,X1) ),
    inference(definition_folding,[],[f133,f138,f137]) ).

tff(f133,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | p(X1) )
    <=> ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & p(X1) ) ) ),
    inference(flattening,[],[f132]) ).

tff(f132,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | p(X1) )
    <=> ( p(c_2Ebool_2EF_2E0)
        | p(X0)
        | ( ~ p(c_2Ebool_2EF_2E0)
          & p(X1) ) ) ),
    inference(ennf_transformation,[],[f89]) ).

tff(f89,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( ~ ( p(X0)
            | p(X1) )
       => p(c_2Ebool_2EF_2E0) )
    <=> ( ( p(X1)
         => p(c_2Ebool_2EF_2E0) )
       => ( ~ p(X0)
         => p(c_2Ebool_2EF_2E0) ) ) ),
    inference(rectify,[],[f50]) ).

tff(f50,axiom,
    ! [X31: tyop_2Emin_2Ebool,X32: tyop_2Emin_2Ebool] :
      ( ( ~ ( p(X31)
            | p(X32) )
       => p(c_2Ebool_2EF_2E0) )
    <=> ( ( p(X32)
         => p(c_2Ebool_2EF_2E0) )
       => ( ~ p(X31)
         => p(c_2Ebool_2EF_2E0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).

tff(f658,plain,
    spl44_18,
    inference(avatar_split_clause,[],[f411,f656]) ).

tff(f411,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP1(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f197]) ).

tff(f654,plain,
    spl44_17,
    inference(avatar_split_clause,[],[f378,f652]) ).

tff(f652,plain,
    ( spl44_17
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
        | ~ p(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_17])]) ).

tff(f378,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f174]) ).

tff(f650,plain,
    spl44_16,
    inference(avatar_split_clause,[],[f377,f648]) ).

tff(f648,plain,
    ( spl44_16
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
        | p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_16])]) ).

tff(f377,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
      | p(X0) ),
    inference(cnf_transformation,[],[f174]) ).

tff(f646,plain,
    spl44_15,
    inference(avatar_split_clause,[],[f375,f644]) ).

tff(f375,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f172]) ).

tff(f642,plain,
    spl44_14,
    inference(avatar_split_clause,[],[f374,f640]) ).

tff(f374,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f172]) ).

tff(f638,plain,
    spl44_13,
    inference(avatar_split_clause,[],[f371,f636]) ).

tff(f371,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
    inference(cnf_transformation,[],[f170]) ).

tff(f634,plain,
    spl44_12,
    inference(avatar_split_clause,[],[f370,f632]) ).

tff(f370,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X0)
      | ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
    inference(cnf_transformation,[],[f170]) ).

tff(f630,plain,
    spl44_11,
    inference(avatar_split_clause,[],[f345,f628]) ).

tff(f345,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2EF_2E0 = X0 )
      | ( c_2Ebool_2ET_2E0 = X0 ) ),
    inference(cnf_transformation,[],[f65]) ).

tff(f65,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2EF_2E0 = X0 )
      | ( c_2Ebool_2ET_2E0 = X0 ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X8: tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2EF_2E0 = X8 )
      | ( c_2Ebool_2ET_2E0 = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).

tff(f619,plain,
    spl44_10,
    inference(avatar_split_clause,[],[f571,f617]) ).

tff(f571,plain,
    ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)),
    inference(equality_resolution,[],[f432]) ).

tff(f432,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f615,plain,
    spl44_9,
    inference(avatar_split_clause,[],[f409,f613]) ).

tff(f613,plain,
    ( spl44_9
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP0(X0,X1)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_9])]) ).

tff(f409,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP0(X0,X1)
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f196]) ).

tff(f611,plain,
    spl44_8,
    inference(avatar_split_clause,[],[f408,f609]) ).

tff(f408,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP0(X0,X1)
      | ~ p(X1) ),
    inference(cnf_transformation,[],[f196]) ).

tff(f607,plain,
    spl44_7,
    inference(avatar_split_clause,[],[f405,f605]) ).

tff(f605,plain,
    ( spl44_7
  <=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
        ( sP1(X0,X1)
        | ~ p(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl44_7])]) ).

tff(f405,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( sP1(X0,X1)
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f194]) ).

tff(f603,plain,
    spl44_6,
    inference(avatar_split_clause,[],[f359,f601]) ).

tff(f359,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(X0))
      | p(X0) ),
    inference(cnf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( p(c_2Ebool_2E_7E_2E1(X0))
        | p(X0) )
      & ( ~ p(X0)
        | ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
    inference(nnf_transformation,[],[f72]) ).

tff(f72,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(X0))
    <=> ~ p(X0) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X6: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(X6))
    <=> ~ p(X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).

tff(f599,plain,
    spl44_5,
    inference(avatar_split_clause,[],[f358,f597]) ).

tff(f358,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ~ p(c_2Ebool_2E_7E_2E1(X0)) ),
    inference(cnf_transformation,[],[f167]) ).

tff(f595,plain,
    spl44_4,
    inference(avatar_split_clause,[],[f329,f593]) ).

tff(f329,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2EF_2E0 = X0 )
      | p(X0) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( ( c_2Ebool_2EF_2E0 = X0 )
        | p(X0) )
      & ( ~ p(X0)
        | ( c_2Ebool_2EF_2E0 != X0 ) )
      & ( ( c_2Ebool_2EF_2E0 = X0 )
        | p(X0) )
      & ( ~ p(X0)
        | ( c_2Ebool_2EF_2E0 != X0 ) )
      & ( ( c_2Ebool_2ET_2E0 = X0 )
        | ~ p(X0) )
      & ( p(X0)
        | ( c_2Ebool_2ET_2E0 != X0 ) )
      & ( ( c_2Ebool_2ET_2E0 = X0 )
        | ~ p(X0) )
      & ( p(X0)
        | ( c_2Ebool_2ET_2E0 != X0 ) ) ),
    inference(flattening,[],[f161]) ).

tff(f161,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( ( c_2Ebool_2EF_2E0 = X0 )
        | p(X0) )
      & ( ~ p(X0)
        | ( c_2Ebool_2EF_2E0 != X0 ) )
      & ( ( c_2Ebool_2EF_2E0 = X0 )
        | p(X0) )
      & ( ~ p(X0)
        | ( c_2Ebool_2EF_2E0 != X0 ) )
      & ( ( c_2Ebool_2ET_2E0 = X0 )
        | ~ p(X0) )
      & ( p(X0)
        | ( c_2Ebool_2ET_2E0 != X0 ) )
      & ( ( c_2Ebool_2ET_2E0 = X0 )
        | ~ p(X0) )
      & ( p(X0)
        | ( c_2Ebool_2ET_2E0 != X0 ) ) ),
    inference(nnf_transformation,[],[f63]) ).

tff(f63,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( ( c_2Ebool_2EF_2E0 = X0 )
      <=> ~ p(X0) )
      & ( ( c_2Ebool_2EF_2E0 = X0 )
      <=> ~ p(X0) )
      & ( ( c_2Ebool_2ET_2E0 = X0 )
      <=> p(X0) )
      & ( ( c_2Ebool_2ET_2E0 = X0 )
      <=> p(X0) ) ),
    inference(rectify,[],[f35]) ).

tff(f35,axiom,
    ! [X8: tyop_2Emin_2Ebool] :
      ( ( ( c_2Ebool_2EF_2E0 = X8 )
      <=> ~ p(X8) )
      & ( ( c_2Ebool_2EF_2E0 = X8 )
      <=> ~ p(X8) )
      & ( ( c_2Ebool_2ET_2E0 = X8 )
      <=> p(X8) )
      & ( ( c_2Ebool_2ET_2E0 = X8 )
      <=> p(X8) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).

tff(f591,plain,
    spl44_3,
    inference(avatar_split_clause,[],[f325,f589]) ).

tff(f325,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2ET_2E0 = X0 )
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f587,plain,
    spl44_2,
    inference(avatar_split_clause,[],[f314,f584]) ).

tff(f314,plain,
    p(c_2Ebool_2ET_2E0),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    p(c_2Ebool_2ET_2E0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).

tff(f582,plain,
    ~ spl44_1,
    inference(avatar_split_clause,[],[f313,f579]) ).

tff(f313,plain,
    ~ p(c_2Ebool_2EF_2E0),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    ~ p(c_2Ebool_2EF_2E0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : ITP020_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.08/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 18:56:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (26339)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (26342)WARNING: value z3 for option sas not known
% 0.15/0.38  % (26340)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (26341)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (26343)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (26342)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)
% 0.15/0.38  % (26344)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)
% 0.15/0.38  % (26345)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)
% 0.15/0.38  % (26346)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)
% 0.15/0.39  % (26346)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39  % Exception at run slice level
% 0.15/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39  % Exception at run slice level
% 0.15/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39  % Exception at run slice level
% 0.15/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41  % (26347)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.41  % (26349)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)
% 0.15/0.41  % (26348)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)
% 0.23/0.41  % (26347)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.41  % Exception at run slice level
% 0.23/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.41  % (26348)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.43  % (26350)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.23/0.48  % (26344)First to succeed.
% 0.23/0.49  % (26344)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26339"
% 0.23/0.49  % (26344)Refutation found. Thanks to Tanya!
% 0.23/0.49  % SZS status Theorem for theBenchmark
% 0.23/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.50  % (26344)------------------------------
% 0.23/0.50  % (26344)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.23/0.50  % (26344)Termination reason: Refutation
% 0.23/0.50  
% 0.23/0.50  % (26344)Memory used [KB]: 2080
% 0.23/0.50  % (26344)Time elapsed: 0.109 s
% 0.23/0.50  % (26344)Instructions burned: 179 (million)
% 0.23/0.50  % (26339)Success in time 0.13 s
%------------------------------------------------------------------------------