TSTP Solution File: LCL941^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL941^5 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 00:24:01 EDT 2024

% Result   : Theorem 33.27s 4.86s
% Output   : Refutation 33.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   44
%            Number of leaves      :  183
% Syntax   : Number of formulae    : 3277 (  38 unt;  66 typ;   0 def)
%            Number of atoms       : 90631 (14453 equ;   0 cnn)
%            Maximal formula atoms :  194 (  28 avg)
%            Number of connectives : 111842 ( 891   ~;13489   |;1769   &;85986   @)
%                                         ( 110 <=>;5677  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  171 ( 171   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  182 ( 178 usr; 166 con; 0-3 aty)
%                                         (3920  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 11040 (4658   ^6381   !;   0   ?;11040   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    mworld: $tType ).

thf(func_def_0,type,
    mworld: $tType ).

thf(func_def_1,type,
    mrel: mworld > mworld > $o ).

thf(func_def_2,type,
    mactual: mworld ).

thf(func_def_3,type,
    mlocal: ( mworld > $o ) > $o ).

thf(func_def_5,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(func_def_6,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_7,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_8,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_9,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_10,type,
    mbox: ( mworld > $o ) > mworld > $o ).

thf(func_def_11,type,
    mdia: ( mworld > $o ) > mworld > $o ).

thf(func_def_12,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(func_def_13,type,
    mexists_di: ( $i > mworld > $o ) > mworld > $o ).

thf(func_def_19,type,
    qmltpeq: $i > $i > mworld > $o ).

thf(func_def_20,type,
    inv: $i > $i ).

thf(func_def_21,type,
    op: $i > $i > $i ).

thf(func_def_41,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_42,type,
    sK2: mworld ).

thf(func_def_43,type,
    sK3: mworld ).

thf(func_def_44,type,
    sK4: mworld ).

thf(func_def_45,type,
    sK5: mworld ).

thf(func_def_46,type,
    sK6: mworld ).

thf(func_def_47,type,
    sK7: mworld ).

thf(func_def_48,type,
    sK8: mworld ).

thf(func_def_49,type,
    sK9: mworld ).

thf(func_def_50,type,
    sK10: mworld ).

thf(func_def_51,type,
    sK11: mworld ).

thf(func_def_52,type,
    sK12: mworld ).

thf(func_def_53,type,
    sK13: mworld ).

thf(func_def_54,type,
    sK14: mworld ).

thf(func_def_55,type,
    sK15: mworld ).

thf(func_def_56,type,
    sK16: mworld ).

thf(func_def_57,type,
    sK17: mworld ).

thf(func_def_58,type,
    sK18: mworld ).

thf(func_def_59,type,
    sK19: mworld ).

thf(func_def_60,type,
    sK20: mworld ).

thf(func_def_61,type,
    sK21: mworld ).

thf(func_def_62,type,
    sK22: mworld ).

thf(func_def_63,type,
    sK23: mworld ).

thf(func_def_64,type,
    sK24: mworld ).

thf(func_def_65,type,
    sK25: mworld ).

thf(func_def_66,type,
    sK26: mworld ).

thf(func_def_67,type,
    sK27: mworld ).

thf(func_def_68,type,
    sK28: mworld ).

thf(func_def_69,type,
    sK29: mworld ).

thf(func_def_70,type,
    sK30: mworld ).

thf(func_def_71,type,
    sK31: mworld ).

thf(func_def_72,type,
    sK32: mworld ).

thf(func_def_73,type,
    sK33: mworld ).

thf(func_def_74,type,
    sK34: mworld ).

thf(func_def_75,type,
    sK35: mworld ).

thf(func_def_76,type,
    sK36: mworld ).

thf(func_def_77,type,
    sK37: mworld ).

thf(func_def_78,type,
    sK38: mworld ).

thf(func_def_79,type,
    sK39: mworld ).

thf(func_def_80,type,
    sK40: mworld ).

thf(func_def_81,type,
    sK41: mworld ).

thf(func_def_82,type,
    sK42: mworld ).

thf(func_def_83,type,
    sK43: mworld ).

thf(func_def_84,type,
    sK44: mworld ).

thf(func_def_85,type,
    sK45: mworld ).

thf(func_def_86,type,
    sK46: mworld ).

thf(func_def_87,type,
    sK47: mworld ).

thf(func_def_88,type,
    sK48: mworld ).

thf(func_def_89,type,
    sK49: mworld ).

thf(f4590,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2491,f2496,f2501,f2502,f2507,f2508,f2509,f2510,f2527,f2532,f2541,f2546,f2559,f2564,f2569,f2570,f2587,f2592,f2601,f2606,f2615,f2620,f2625,f2630,f2643,f2648,f2657,f2662,f2667,f2668,f2673,f2674,f2691,f2696,f2705,f2710,f2723,f2728,f2737,f2742,f2755,f2760,f2769,f2774,f2783,f2788,f2793,f2794,f2811,f2816,f2825,f2830,f2843,f2848,f2853,f2854,f2871,f2876,f2885,f2890,f2899,f2904,f2909,f2914,f2927,f2931,f2935,f2939,f2943,f2947,f2951,f2952,f2953,f2954,f2955,f2956,f2957,f2958,f2959,f2960,f2964,f2965,f2966,f2967,f2968,f2969,f2970,f2971,f2972,f2973,f2974,f2975,f2976,f2977,f2978,f2979,f2983,f2984,f2985,f2986,f2987,f2988,f2989,f2990,f2991,f2992,f2993,f2994,f2995,f2996,f2997,f2998,f3002,f3003,f3004,f3005,f3006,f3007,f3008,f3009,f3010,f3011,f3012,f3013,f3014,f3015,f3016,f3017,f3021,f3022,f3023,f3024,f3025,f3026,f3027,f3028,f3029,f3030,f3031,f3032,f3033,f3034,f3035,f3036,f3040,f3041,f3042,f3043,f3044,f3045,f3046,f3047,f3048,f3049,f3050,f3051,f3052,f3053,f3054,f3055,f3059,f3060,f3061,f3062,f3063,f3064,f3065,f3066,f3067,f3068,f3069,f3070,f3071,f3072,f3073,f3074,f3075,f3076,f3077,f3078,f3079,f3080,f3081,f3082,f3083,f3084,f3085,f3086,f3087,f3088,f3089,f3090,f3091,f3092,f3093,f3094,f3095,f3096,f3097,f3098,f3099,f3100,f3101,f3102,f3103,f3104,f3105,f3106,f3107,f3108,f3109,f3110,f3111,f3112,f3113,f3114,f3115,f3116,f3117,f3118,f3119,f3120,f3121,f3122,f3123,f3124,f3125,f3126,f3127,f3128,f3129,f3130,f3131,f3132,f3133,f3134,f3135,f3136,f3137,f3138,f3139,f3140,f3141,f3142,f3143,f3144,f3145,f3146,f3147,f3148,f3149,f3150,f3151,f3152,f3153,f3154,f3155,f3156,f3157,f3158,f3159,f3160,f3161,f3162,f3163,f3164,f3165,f3166,f3167,f3168,f3169,f3170,f3171,f3172,f3173,f3174,f3175,f3176,f3177,f3178,f3179,f3180,f3181,f3182,f3183,f3184,f3185,f3186,f3187,f3188,f3189,f3190,f3191,f3192,f3193,f3194,f3195,f3196,f3197,f3198,f3199,f3200,f3201,f3202,f3203,f3204,f3205,f3206,f3207,f3208,f3209,f3210,f3211,f3212,f3213,f3214,f3215,f3216,f3217,f3218,f3295,f3310,f3330,f3345,f3381,f3404,f3428,f3482,f3502,f3513,f3541,f3566,f3588,f3611,f3635,f3658,f3706,f3715,f3750,f3772,f3797,f3808,f3847,f3870,f3902,f3948,f3972,f3987,f4039,f4055,f4078,f4109,f4129,f4160,f4200,f4225,f4260,f4310,f4341,f4392,f4423,f4455,f4518,f4536,f4547,f4566,f4589]) ).

thf(f4589,plain,
    ( ~ spl0_65
    | ~ spl0_67
    | ~ spl0_101 ),
    inference(avatar_contradiction_clause,[],[f4588]) ).

thf(f4588,plain,
    ( $false
    | ~ spl0_65
    | ~ spl0_67
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f4587]) ).

thf(f4587,plain,
    ( ( $false = $true )
    | ~ spl0_65
    | ~ spl0_67
    | ~ spl0_101 ),
    inference(backward_demodulation,[],[f4573,f4586]) ).

thf(f4586,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK19 ) )
    | ~ spl0_65
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f4584]) ).

thf(f4584,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK19 ) )
    | ( $false = $true )
    | ~ spl0_65
    | ~ spl0_101 ),
    inference(superposition,[],[f2938,f2778]) ).

thf(f2778,plain,
    ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK19 )
      = $false )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f2776]) ).

thf(f2776,plain,
    ( spl0_65
  <=> ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK19 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

thf(f2938,plain,
    ( ! [X4: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f2937]) ).

thf(f2937,plain,
    ( spl0_101
  <=> ! [X4: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

thf(f4573,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK19 ) )
    | ~ spl0_67 ),
    inference(trivial_inequality_removal,[],[f4567]) ).

thf(f4567,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK19 ) )
    | ( $true != $true )
    | ~ spl0_67 ),
    inference(superposition,[],[f3222,f2787]) ).

thf(f2787,plain,
    ( ( ( mrel @ mactual @ sK19 )
      = $true )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f2785]) ).

thf(f2785,plain,
    ( spl0_67
  <=> ( ( mrel @ mactual @ sK19 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

thf(f3222,plain,
    ! [X0: mworld] :
      ( ( $true
       != ( mrel @ mactual @ X0 ) )
      | ( ( mrel @ sK2 @ X0 )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f3220]) ).

thf(f3220,plain,
    ! [X0: mworld] :
      ( ( $true != $true )
      | ( ( mrel @ sK2 @ X0 )
        = $true )
      | ( $true
       != ( mrel @ mactual @ X0 ) ) ),
    inference(superposition,[],[f109,f180]) ).

thf(f180,plain,
    ( ( mrel @ mactual @ sK2 )
    = $true ),
    inference(binary_proxy_clausification,[],[f178]) ).

thf(f178,plain,
    ( $false
    = ( ( mrel @ mactual @ sK2 )
     => ~ ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f177]) ).

thf(f177,plain,
    ( $false
    = ( ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ~ ( ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) )
              | ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
              | ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
              | ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) ) ) )
      @ sK2 ) ),
    inference(sigma_clausification,[],[f176]) ).

thf(f176,plain,
    ( $false
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ~ ( ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) )
              | ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
              | ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
              | ( ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
                & ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ Y0 @ Y1 )
                     => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f174]) ).

thf(f174,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ~ ( ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f172]) ).

thf(f172,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ~ ( ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f170]) ).

thf(f170,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ~ ( ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f168]) ).

thf(f168,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ~ ( ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) ) )
                | ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
                  & ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) )
   != $true ),
    inference(beta_eta_normalization,[],[f138]) ).

thf(f138,plain,
    ( $true
   != ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
      @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
            ( ( Y1 @ Y2 )
            | ( Y0 @ Y2 ) )
        @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
              ( ( Y1 @ Y2 )
              & ( Y0 @ Y2 ) )
          @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                ( !! @ mworld
                @ ^ [Y2: mworld] :
                    ( ( mrel @ Y1 @ Y2 )
                   => ( Y0 @ Y2 ) ) )
            @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) )
          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                ( ( Y1 @ Y2 )
                & ( Y0 @ Y2 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                  ( ( Y1 @ Y2 )
                  & ( Y0 @ Y2 ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                    ( !! @ mworld
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y1 @ Y2 )
                       => ( Y0 @ Y2 ) ) )
                @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                    ( !! @ mworld
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y1 @ Y2 )
                       => ( Y0 @ Y2 ) ) )
                @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) )
        @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
              ( ( Y1 @ Y2 )
              | ( Y0 @ Y2 ) )
          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                ( ( Y1 @ Y2 )
                & ( Y0 @ Y2 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                  ( ( Y1 @ Y2 )
                  & ( Y0 @ Y2 ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                    ( !! @ mworld
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y1 @ Y2 )
                       => ( Y0 @ Y2 ) ) )
                @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                    ( ( Y1 @ Y2 )
                    & ( Y0 @ Y2 ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                      ( !! @ mworld
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y1 @ Y2 )
                         => ( Y0 @ Y2 ) ) )
                  @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                      ( !! @ mworld
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y1 @ Y2 )
                         => ( Y0 @ Y2 ) ) )
                  @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) )
          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                ( ( Y1 @ Y2 )
                | ( Y0 @ Y2 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                  ( ( Y1 @ Y2 )
                  & ( Y0 @ Y2 ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                    ( !! @ mworld
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y1 @ Y2 )
                       => ( Y0 @ Y2 ) ) )
                @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                    ( ( Y1 @ Y2 )
                    & ( Y0 @ Y2 ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                      ( !! @ mworld
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y1 @ Y2 )
                         => ( Y0 @ Y2 ) ) )
                  @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                      ( ( Y1 @ Y2 )
                      & ( Y0 @ Y2 ) )
                  @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                        ( !! @ mworld
                        @ ^ [Y2: mworld] :
                            ( ( mrel @ Y1 @ Y2 )
                           => ( Y0 @ Y2 ) ) )
                    @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) )
                  @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                        ( !! @ mworld
                        @ ^ [Y2: mworld] :
                            ( ( mrel @ Y1 @ Y2 )
                           => ( Y0 @ Y2 ) ) )
                    @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                  ( ( Y1 @ Y2 )
                  | ( Y0 @ Y2 ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                    ( ( Y1 @ Y2 )
                    & ( Y0 @ Y2 ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                      ( !! @ mworld
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y1 @ Y2 )
                         => ( Y0 @ Y2 ) ) )
                  @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                      ( ( Y1 @ Y2 )
                      & ( Y0 @ Y2 ) )
                  @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                        ( !! @ mworld
                        @ ^ [Y2: mworld] :
                            ( ( mrel @ Y1 @ Y2 )
                           => ( Y0 @ Y2 ) ) )
                    @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) )
                  @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                        ( ( Y1 @ Y2 )
                        & ( Y0 @ Y2 ) )
                    @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                          ( !! @ mworld
                          @ ^ [Y2: mworld] :
                              ( ( mrel @ Y1 @ Y2 )
                             => ( Y0 @ Y2 ) ) )
                      @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) )
                    @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                          ( !! @ mworld
                          @ ^ [Y2: mworld] :
                              ( ( mrel @ Y1 @ Y2 )
                             => ( Y0 @ Y2 ) ) )
                      @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                    ( !! @ mworld
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y1 @ Y2 )
                       => ( Y0 @ Y2 ) ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                      ~ ( Y0 @ Y1 )
                  @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                        ( ( Y1 @ Y2 )
                        | ( Y0 @ Y2 ) )
                    @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                          ( ( Y1 @ Y2 )
                          & ( Y0 @ Y2 ) )
                      @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                            ( !! @ mworld
                            @ ^ [Y2: mworld] :
                                ( ( mrel @ Y1 @ Y2 )
                               => ( Y0 @ Y2 ) ) )
                        @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) )
                      @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                            ( ( Y1 @ Y2 )
                            & ( Y0 @ Y2 ) )
                        @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                              ( !! @ mworld
                              @ ^ [Y2: mworld] :
                                  ( ( mrel @ Y1 @ Y2 )
                                 => ( Y0 @ Y2 ) ) )
                          @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) )
                        @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                              ( ( Y1 @ Y2 )
                              & ( Y0 @ Y2 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                ( !! @ mworld
                                @ ^ [Y2: mworld] :
                                    ( ( mrel @ Y1 @ Y2 )
                                   => ( Y0 @ Y2 ) ) )
                            @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                ( !! @ mworld
                                @ ^ [Y2: mworld] :
                                    ( ( mrel @ Y1 @ Y2 )
                                   => ( Y0 @ Y2 ) ) )
                            @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) )
                    @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                          ( ( Y1 @ Y2 )
                          | ( Y0 @ Y2 ) )
                      @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                            ( ( Y1 @ Y2 )
                            & ( Y0 @ Y2 ) )
                        @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                              ( !! @ mworld
                              @ ^ [Y2: mworld] :
                                  ( ( mrel @ Y1 @ Y2 )
                                 => ( Y0 @ Y2 ) ) )
                          @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) )
                        @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                              ( ( Y1 @ Y2 )
                              & ( Y0 @ Y2 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                ( !! @ mworld
                                @ ^ [Y2: mworld] :
                                    ( ( mrel @ Y1 @ Y2 )
                                   => ( Y0 @ Y2 ) ) )
                            @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                                ( ( Y1 @ Y2 )
                                & ( Y0 @ Y2 ) )
                            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                  ( !! @ mworld
                                  @ ^ [Y2: mworld] :
                                      ( ( mrel @ Y1 @ Y2 )
                                     => ( Y0 @ Y2 ) ) )
                              @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) )
                            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                  ( !! @ mworld
                                  @ ^ [Y2: mworld] :
                                      ( ( mrel @ Y1 @ Y2 )
                                     => ( Y0 @ Y2 ) ) )
                              @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) )
                      @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                            ( ( Y1 @ Y2 )
                            | ( Y0 @ Y2 ) )
                        @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                              ( ( Y1 @ Y2 )
                              & ( Y0 @ Y2 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                ( !! @ mworld
                                @ ^ [Y2: mworld] :
                                    ( ( mrel @ Y1 @ Y2 )
                                   => ( Y0 @ Y2 ) ) )
                            @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                                ( ( Y1 @ Y2 )
                                & ( Y0 @ Y2 ) )
                            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                  ( !! @ mworld
                                  @ ^ [Y2: mworld] :
                                      ( ( mrel @ Y1 @ Y2 )
                                     => ( Y0 @ Y2 ) ) )
                              @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) )
                            @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                                  ( ( Y1 @ Y2 )
                                  & ( Y0 @ Y2 ) )
                              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                    ( !! @ mworld
                                    @ ^ [Y2: mworld] :
                                        ( ( mrel @ Y1 @ Y2 )
                                       => ( Y0 @ Y2 ) ) )
                                @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) )
                              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                    ( !! @ mworld
                                    @ ^ [Y2: mworld] :
                                        ( ( mrel @ Y1 @ Y2 )
                                       => ( Y0 @ Y2 ) ) )
                                @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) )
                        @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                              ( ( Y1 @ Y2 )
                              & ( Y0 @ Y2 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                ( !! @ mworld
                                @ ^ [Y2: mworld] :
                                    ( ( mrel @ Y1 @ Y2 )
                                   => ( Y0 @ Y2 ) ) )
                            @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) )
                          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                                ( ( Y1 @ Y2 )
                                & ( Y0 @ Y2 ) )
                            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                  ( !! @ mworld
                                  @ ^ [Y2: mworld] :
                                      ( ( mrel @ Y1 @ Y2 )
                                     => ( Y0 @ Y2 ) ) )
                              @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) )
                            @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                                  ( ( Y1 @ Y2 )
                                  & ( Y0 @ Y2 ) )
                              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                    ( !! @ mworld
                                    @ ^ [Y2: mworld] :
                                        ( ( mrel @ Y1 @ Y2 )
                                       => ( Y0 @ Y2 ) ) )
                                @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) )
                              @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                                    ( !! @ mworld
                                    @ ^ [Y2: mworld] :
                                        ( ( mrel @ Y1 @ Y2 )
                                       => ( Y0 @ Y2 ) ) )
                                @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(definition_unfolding,[],[f117,f119,f98,f104,f122,f104,f122,f104,f122,f122,f98,f104,f122,f104,f122,f104,f122,f122,f98,f104,f122,f104,f122,f104,f122,f122,f98,f104,f122,f104,f122,f104,f122,f122,f122,f114,f98,f104,f122,f104,f122,f104,f122,f122,f98,f104,f122,f104,f122,f104,f122,f122,f98,f104,f122,f104,f122,f104,f122,f122,f104,f122,f104,f122,f104,f122,f122]) ).

thf(f114,plain,
    ( mnot
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ~ ( Y0 @ Y1 ) ) ),
    inference(cnf_transformation,[],[f81]) ).

thf(f81,plain,
    ( mnot
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ~ ( Y0 @ Y1 ) ) ),
    inference(fool_elimination,[],[f80]) ).

thf(f80,plain,
    ( ( ^ [X0: mworld > $o,X1: mworld] :
          ~ ( X0 @ X1 ) )
    = mnot ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ( ( ^ [X1: mworld > $o,X2: mworld] :
          ~ ( X1 @ X2 ) )
    = mnot ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).

thf(f122,plain,
    ( mbox
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ( !! @ mworld
          @ ^ [Y2: mworld] :
              ( ( mrel @ Y1 @ Y2 )
             => ( Y0 @ Y2 ) ) ) ) ),
    inference(cnf_transformation,[],[f67]) ).

thf(f67,plain,
    ( mbox
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ( !! @ mworld
          @ ^ [Y2: mworld] :
              ( ( mrel @ Y1 @ Y2 )
             => ( Y0 @ Y2 ) ) ) ) ),
    inference(fool_elimination,[],[f66]) ).

thf(f66,plain,
    ( ( ^ [X0: mworld > $o,X1: mworld] :
        ! [X2: mworld] :
          ( ( mrel @ X1 @ X2 )
         => ( X0 @ X2 ) ) )
    = mbox ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ( ( ^ [X0: mworld > $o,X2: mworld] :
        ! [X4: mworld] :
          ( ( mrel @ X2 @ X4 )
         => ( X0 @ X4 ) ) )
    = mbox ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).

thf(f104,plain,
    ( mand
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f36]) ).

thf(f36,plain,
    ( mand
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y1 @ Y2 )
          & ( Y0 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f35]) ).

thf(f35,plain,
    ( mand
    = ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X0 @ X2 )
          & ( X1 @ X2 ) ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ( mand
    = ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
          ( ( X1 @ X2 )
          & ( X3 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).

thf(f98,plain,
    ( mor
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y1 @ Y2 )
          | ( Y0 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f69]) ).

thf(f69,plain,
    ( mor
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y1 @ Y2 )
          | ( Y0 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f68]) ).

thf(f68,plain,
    ( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X0 @ X2 )
          | ( X1 @ X2 ) ) )
    = mor ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
          ( ( X1 @ X2 )
          | ( X3 @ X2 ) ) )
    = mor ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).

thf(f119,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(cnf_transformation,[],[f51]) ).

thf(f51,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(fool_elimination,[],[f1]) ).

thf(f1,axiom,
    ( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
    = mlocal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).

thf(f117,plain,
    ( ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
   != $true ),
    inference(cnf_transformation,[],[f92]) ).

thf(f92,plain,
    ( ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
   != $true ),
    inference(flattening,[],[f83]) ).

thf(f83,plain,
    ( ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
   != $true ),
    inference(fool_elimination,[],[f82]) ).

thf(f82,plain,
    ~ ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f31]) ).

thf(f31,negated_conjecture,
    ~ ( mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f30]) ).

thf(f30,conjecture,
    mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

thf(f109,plain,
    ! [X2: mworld,X0: mworld,X1: mworld] :
      ( ( $true
       != ( mrel @ X0 @ X1 ) )
      | ( $true
        = ( mrel @ X1 @ X2 ) )
      | ( $true
       != ( mrel @ X0 @ X2 ) ) ),
    inference(cnf_transformation,[],[f94]) ).

thf(f94,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( $true
        = ( mrel @ X1 @ X2 ) )
      | ( $true
       != ( mrel @ X0 @ X1 ) )
      | ( $true
       != ( mrel @ X0 @ X2 ) ) ),
    inference(flattening,[],[f93]) ).

thf(f93,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( $true
        = ( mrel @ X1 @ X2 ) )
      | ( $true
       != ( mrel @ X0 @ X2 ) )
      | ( $true
       != ( mrel @ X0 @ X1 ) ) ),
    inference(ennf_transformation,[],[f85]) ).

thf(f85,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( $true
          = ( mrel @ X0 @ X2 ) )
        & ( $true
          = ( mrel @ X0 @ X1 ) ) )
     => ( $true
        = ( mrel @ X1 @ X2 ) ) ),
    inference(fool_elimination,[],[f84]) ).

thf(f84,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( mrel @ X0 @ X2 )
        & ( mrel @ X0 @ X1 ) )
     => ( mrel @ X1 @ X2 ) ),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    ! [X2: mworld,X5: mworld,X4: mworld] :
      ( ( ( mrel @ X2 @ X4 )
        & ( mrel @ X2 @ X5 ) )
     => ( mrel @ X5 @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).

thf(f4566,plain,
    ( ~ spl0_66
    | ~ spl0_68
    | ~ spl0_100 ),
    inference(avatar_contradiction_clause,[],[f4565]) ).

thf(f4565,plain,
    ( $false
    | ~ spl0_66
    | ~ spl0_68
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f4564]) ).

thf(f4564,plain,
    ( ( $false = $true )
    | ~ spl0_66
    | ~ spl0_68
    | ~ spl0_100 ),
    inference(backward_demodulation,[],[f4555,f4563]) ).

thf(f4563,plain,
    ( ( ( mrel @ sK2 @ sK18 )
      = $false )
    | ~ spl0_66
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f4561]) ).

thf(f4561,plain,
    ( ( $false = $true )
    | ( ( mrel @ sK2 @ sK18 )
      = $false )
    | ~ spl0_66
    | ~ spl0_100 ),
    inference(superposition,[],[f2934,f2782]) ).

thf(f2782,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f2780]) ).

thf(f2780,plain,
    ( spl0_66
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

thf(f2934,plain,
    ( ! [X4: mworld] :
        ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f2933]) ).

thf(f2933,plain,
    ( spl0_100
  <=> ! [X4: mworld] :
        ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

thf(f4555,plain,
    ( ( ( mrel @ sK2 @ sK18 )
      = $true )
    | ~ spl0_68 ),
    inference(trivial_inequality_removal,[],[f4550]) ).

thf(f4550,plain,
    ( ( ( mrel @ sK2 @ sK18 )
      = $true )
    | ( $true != $true )
    | ~ spl0_68 ),
    inference(superposition,[],[f3222,f2792]) ).

thf(f2792,plain,
    ( ( $true
      = ( mrel @ mactual @ sK18 ) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f2790]) ).

thf(f2790,plain,
    ( spl0_68
  <=> ( $true
      = ( mrel @ mactual @ sK18 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

thf(f4547,plain,
    ( ~ spl0_51
    | ~ spl0_56
    | ~ spl0_101 ),
    inference(avatar_contradiction_clause,[],[f4546]) ).

thf(f4546,plain,
    ( $false
    | ~ spl0_51
    | ~ spl0_56
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f4545]) ).

thf(f4545,plain,
    ( ( $false = $true )
    | ~ spl0_51
    | ~ spl0_56
    | ~ spl0_101 ),
    inference(forward_demodulation,[],[f4544,f4522]) ).

thf(f4522,plain,
    ( ( ( mrel @ sK2 @ sK23 )
      = $false )
    | ~ spl0_51
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f4520]) ).

thf(f4520,plain,
    ( ( ( mrel @ sK2 @ sK23 )
      = $false )
    | ( $false = $true )
    | ~ spl0_51
    | ~ spl0_101 ),
    inference(superposition,[],[f2938,f2714]) ).

thf(f2714,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f2712]) ).

thf(f2712,plain,
    ( spl0_51
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

thf(f4544,plain,
    ( ( ( mrel @ sK2 @ sK23 )
      = $true )
    | ~ spl0_56 ),
    inference(trivial_inequality_removal,[],[f4537]) ).

thf(f4537,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK23 )
      = $true )
    | ~ spl0_56 ),
    inference(superposition,[],[f3222,f2736]) ).

thf(f2736,plain,
    ( ( $true
      = ( mrel @ mactual @ sK23 ) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f2734]) ).

thf(f2734,plain,
    ( spl0_56
  <=> ( $true
      = ( mrel @ mactual @ sK23 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

thf(f4536,plain,
    ( ~ spl0_55
    | ~ spl0_57
    | ~ spl0_100 ),
    inference(avatar_contradiction_clause,[],[f4535]) ).

thf(f4535,plain,
    ( $false
    | ~ spl0_55
    | ~ spl0_57
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f4534]) ).

thf(f4534,plain,
    ( ( $false = $true )
    | ~ spl0_55
    | ~ spl0_57
    | ~ spl0_100 ),
    inference(backward_demodulation,[],[f4492,f4533]) ).

thf(f4533,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK24 ) )
    | ~ spl0_55
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f4531]) ).

thf(f4531,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK24 ) )
    | ~ spl0_55
    | ~ spl0_100 ),
    inference(superposition,[],[f2934,f2732]) ).

thf(f2732,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK24 )
      = $false )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f2730]) ).

thf(f2730,plain,
    ( spl0_55
  <=> ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK24 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

thf(f4492,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK24 ) )
    | ~ spl0_57 ),
    inference(trivial_inequality_removal,[],[f4487]) ).

thf(f4487,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK24 ) )
    | ~ spl0_57 ),
    inference(superposition,[],[f3222,f2741]) ).

thf(f2741,plain,
    ( ( $true
      = ( mrel @ mactual @ sK24 ) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f2739]) ).

thf(f2739,plain,
    ( spl0_57
  <=> ( $true
      = ( mrel @ mactual @ sK24 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

thf(f4518,plain,
    ( ~ spl0_53
    | ~ spl0_54
    | ~ spl0_100 ),
    inference(avatar_contradiction_clause,[],[f4517]) ).

thf(f4517,plain,
    ( $false
    | ~ spl0_53
    | ~ spl0_54
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f4516]) ).

thf(f4516,plain,
    ( ( $false = $true )
    | ~ spl0_53
    | ~ spl0_54
    | ~ spl0_100 ),
    inference(backward_demodulation,[],[f4485,f4515]) ).

thf(f4515,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK25 ) )
    | ~ spl0_53
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f4512]) ).

thf(f4512,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK25 ) )
    | ( $false = $true )
    | ~ spl0_53
    | ~ spl0_100 ),
    inference(superposition,[],[f2722,f2934]) ).

thf(f2722,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK25 ) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f2720]) ).

thf(f2720,plain,
    ( spl0_53
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK25 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

thf(f4485,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK25 ) )
    | ~ spl0_54 ),
    inference(trivial_inequality_removal,[],[f4478]) ).

thf(f4478,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK25 ) )
    | ( $true != $true )
    | ~ spl0_54 ),
    inference(superposition,[],[f3222,f2727]) ).

thf(f2727,plain,
    ( ( ( mrel @ mactual @ sK25 )
      = $true )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f2725]) ).

thf(f2725,plain,
    ( spl0_54
  <=> ( ( mrel @ mactual @ sK25 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

thf(f4455,plain,
    ( ~ spl0_29
    | ~ spl0_31
    | ~ spl0_107 ),
    inference(avatar_contradiction_clause,[],[f4454]) ).

thf(f4454,plain,
    ( $false
    | ~ spl0_29
    | ~ spl0_31
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4453]) ).

thf(f4453,plain,
    ( ( $false = $true )
    | ~ spl0_29
    | ~ spl0_31
    | ~ spl0_107 ),
    inference(backward_demodulation,[],[f4436,f4452]) ).

thf(f4452,plain,
    ( ( ( mrel @ sK2 @ sK37 )
      = $false )
    | ~ spl0_29
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4450]) ).

thf(f4450,plain,
    ( ( $false = $true )
    | ( ( mrel @ sK2 @ sK37 )
      = $false )
    | ~ spl0_29
    | ~ spl0_107 ),
    inference(superposition,[],[f3001,f2610]) ).

thf(f2610,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK37 ) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f2608]) ).

thf(f2608,plain,
    ( spl0_29
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK37 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

thf(f3001,plain,
    ( ! [X2: mworld] :
        ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
          = $true )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f3000]) ).

thf(f3000,plain,
    ( spl0_107
  <=> ! [X2: mworld] :
        ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
          = $true )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

thf(f4436,plain,
    ( ( ( mrel @ sK2 @ sK37 )
      = $true )
    | ~ spl0_31 ),
    inference(trivial_inequality_removal,[],[f4432]) ).

thf(f4432,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK37 )
      = $true )
    | ~ spl0_31 ),
    inference(superposition,[],[f3222,f2619]) ).

thf(f2619,plain,
    ( ( $true
      = ( mrel @ mactual @ sK37 ) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f2617]) ).

thf(f2617,plain,
    ( spl0_31
  <=> ( $true
      = ( mrel @ mactual @ sK37 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

thf(f4423,plain,
    ( ~ spl0_32
    | ~ spl0_33
    | ~ spl0_107 ),
    inference(avatar_contradiction_clause,[],[f4422]) ).

thf(f4422,plain,
    ( $false
    | ~ spl0_32
    | ~ spl0_33
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4421]) ).

thf(f4421,plain,
    ( ( $false = $true )
    | ~ spl0_32
    | ~ spl0_33
    | ~ spl0_107 ),
    inference(backward_demodulation,[],[f4397,f4420]) ).

thf(f4420,plain,
    ( ( ( mrel @ sK2 @ sK36 )
      = $false )
    | ~ spl0_32
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4418]) ).

thf(f4418,plain,
    ( ( ( mrel @ sK2 @ sK36 )
      = $false )
    | ( $false = $true )
    | ~ spl0_32
    | ~ spl0_107 ),
    inference(superposition,[],[f3001,f2624]) ).

thf(f2624,plain,
    ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK36 )
      = $false )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f2622]) ).

thf(f2622,plain,
    ( spl0_32
  <=> ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK36 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

thf(f4397,plain,
    ( ( ( mrel @ sK2 @ sK36 )
      = $true )
    | ~ spl0_33 ),
    inference(trivial_inequality_removal,[],[f4393]) ).

thf(f4393,plain,
    ( ( ( mrel @ sK2 @ sK36 )
      = $true )
    | ( $true != $true )
    | ~ spl0_33 ),
    inference(superposition,[],[f3222,f2629]) ).

thf(f2629,plain,
    ( ( $true
      = ( mrel @ mactual @ sK36 ) )
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f2627]) ).

thf(f2627,plain,
    ( spl0_33
  <=> ( $true
      = ( mrel @ mactual @ sK36 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

thf(f4392,plain,
    ( ~ spl0_41
    | ~ spl0_42
    | ~ spl0_105 ),
    inference(avatar_contradiction_clause,[],[f4391]) ).

thf(f4391,plain,
    ( $false
    | ~ spl0_41
    | ~ spl0_42
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f4390]) ).

thf(f4390,plain,
    ( ( $false = $true )
    | ~ spl0_41
    | ~ spl0_42
    | ~ spl0_105 ),
    inference(backward_demodulation,[],[f4350,f4389]) ).

thf(f4389,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK32 ) )
    | ~ spl0_41
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f4382]) ).

thf(f4382,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK32 ) )
    | ~ spl0_41
    | ~ spl0_105 ),
    inference(superposition,[],[f2666,f2963]) ).

thf(f2963,plain,
    ( ! [X2: mworld] :
        ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
          = $true )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) )
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f2962]) ).

thf(f2962,plain,
    ( spl0_105
  <=> ! [X2: mworld] :
        ( ( ( mrel @ sK2 @ X2 )
          = $false )
        | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

thf(f2666,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK32 ) )
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f2664]) ).

thf(f2664,plain,
    ( spl0_41
  <=> ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK32 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

thf(f4350,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK32 ) )
    | ~ spl0_42 ),
    inference(trivial_inequality_removal,[],[f4344]) ).

thf(f4344,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK32 ) )
    | ~ spl0_42 ),
    inference(superposition,[],[f3222,f2672]) ).

thf(f2672,plain,
    ( ( ( mrel @ mactual @ sK32 )
      = $true )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f2670]) ).

thf(f2670,plain,
    ( spl0_42
  <=> ( ( mrel @ mactual @ sK32 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

thf(f4341,plain,
    ( ~ spl0_91
    | ~ spl0_92
    | ~ spl0_103 ),
    inference(avatar_contradiction_clause,[],[f4340]) ).

thf(f4340,plain,
    ( $false
    | ~ spl0_91
    | ~ spl0_92
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f4339]) ).

thf(f4339,plain,
    ( ( $false = $true )
    | ~ spl0_91
    | ~ spl0_92
    | ~ spl0_103 ),
    inference(backward_demodulation,[],[f4323,f4338]) ).

thf(f4338,plain,
    ( ( ( mrel @ sK2 @ sK7 )
      = $false )
    | ~ spl0_91
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f4336]) ).

thf(f4336,plain,
    ( ( ( mrel @ sK2 @ sK7 )
      = $false )
    | ( $false = $true )
    | ~ spl0_91
    | ~ spl0_103 ),
    inference(superposition,[],[f2946,f2898]) ).

thf(f2898,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK7 ) )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f2896]) ).

thf(f2896,plain,
    ( spl0_91
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK7 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

thf(f2946,plain,
    ( ! [X4: mworld] :
        ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) )
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f2945]) ).

thf(f2945,plain,
    ( spl0_103
  <=> ! [X4: mworld] :
        ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

thf(f4323,plain,
    ( ( ( mrel @ sK2 @ sK7 )
      = $true )
    | ~ spl0_92 ),
    inference(trivial_inequality_removal,[],[f4319]) ).

thf(f4319,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK7 )
      = $true )
    | ~ spl0_92 ),
    inference(superposition,[],[f3222,f2903]) ).

thf(f2903,plain,
    ( ( ( mrel @ mactual @ sK7 )
      = $true )
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f2901]) ).

thf(f2901,plain,
    ( spl0_92
  <=> ( ( mrel @ mactual @ sK7 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

thf(f4310,plain,
    ( ~ spl0_93
    | ~ spl0_94
    | ~ spl0_103 ),
    inference(avatar_contradiction_clause,[],[f4309]) ).

thf(f4309,plain,
    ( $false
    | ~ spl0_93
    | ~ spl0_94
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f4308]) ).

thf(f4308,plain,
    ( ( $false = $true )
    | ~ spl0_93
    | ~ spl0_94
    | ~ spl0_103 ),
    inference(backward_demodulation,[],[f4275,f4307]) ).

thf(f4307,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK6 ) )
    | ~ spl0_93
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f4305]) ).

thf(f4305,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK6 ) )
    | ( $false = $true )
    | ~ spl0_93
    | ~ spl0_103 ),
    inference(superposition,[],[f2946,f2908]) ).

thf(f2908,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK6 ) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f2906]) ).

thf(f2906,plain,
    ( spl0_93
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

thf(f4275,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK6 ) )
    | ~ spl0_94 ),
    inference(trivial_inequality_removal,[],[f4270]) ).

thf(f4270,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK6 ) )
    | ~ spl0_94 ),
    inference(superposition,[],[f3222,f2913]) ).

thf(f2913,plain,
    ( ( ( mrel @ mactual @ sK6 )
      = $true )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f2911]) ).

thf(f2911,plain,
    ( spl0_94
  <=> ( ( mrel @ mactual @ sK6 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

thf(f4260,plain,
    ( ~ spl0_1
    | ~ spl0_7
    | ~ spl0_109 ),
    inference(avatar_contradiction_clause,[],[f4259]) ).

thf(f4259,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_7
    | ~ spl0_109 ),
    inference(trivial_inequality_removal,[],[f4258]) ).

thf(f4258,plain,
    ( ( $false = $true )
    | ~ spl0_1
    | ~ spl0_7
    | ~ spl0_109 ),
    inference(backward_demodulation,[],[f4233,f4255]) ).

thf(f4255,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK48 ) )
    | ~ spl0_1
    | ~ spl0_109 ),
    inference(trivial_inequality_removal,[],[f4253]) ).

thf(f4253,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK48 ) )
    | ~ spl0_1
    | ~ spl0_109 ),
    inference(superposition,[],[f2478,f3039]) ).

thf(f3039,plain,
    ( ! [X3: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
        | ( $false
          = ( mrel @ sK2 @ X3 ) ) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f3038]) ).

thf(f3038,plain,
    ( spl0_109
  <=> ! [X3: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
        | ( $false
          = ( mrel @ sK2 @ X3 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

thf(f2478,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f2476]) ).

thf(f2476,plain,
    ( spl0_1
  <=> ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f4233,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK48 ) )
    | ~ spl0_7 ),
    inference(trivial_inequality_removal,[],[f4226]) ).

thf(f4226,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK48 ) )
    | ( $true != $true )
    | ~ spl0_7 ),
    inference(superposition,[],[f3222,f2506]) ).

thf(f2506,plain,
    ( ( ( mrel @ mactual @ sK48 )
      = $true )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f2504]) ).

thf(f2504,plain,
    ( spl0_7
  <=> ( ( mrel @ mactual @ sK48 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

thf(f4225,plain,
    ( ~ spl0_2
    | ~ spl0_6
    | ~ spl0_110 ),
    inference(avatar_contradiction_clause,[],[f4224]) ).

thf(f4224,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_6
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f4223]) ).

thf(f4223,plain,
    ( ( $false = $true )
    | ~ spl0_2
    | ~ spl0_6
    | ~ spl0_110 ),
    inference(backward_demodulation,[],[f4208,f4222]) ).

thf(f4222,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK49 ) )
    | ~ spl0_2
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f4220]) ).

thf(f4220,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK49 ) )
    | ( $false = $true )
    | ~ spl0_2
    | ~ spl0_110 ),
    inference(superposition,[],[f3058,f2482]) ).

thf(f2482,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f2480]) ).

thf(f2480,plain,
    ( spl0_2
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f3058,plain,
    ( ! [X2: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f3057]) ).

thf(f3057,plain,
    ( spl0_110
  <=> ! [X2: mworld] :
        ( ( ( mrel @ sK2 @ X2 )
          = $false )
        | ( $true
          = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

thf(f4208,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK49 ) )
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f4201]) ).

thf(f4201,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK49 ) )
    | ( $true != $true )
    | ~ spl0_6 ),
    inference(superposition,[],[f3222,f2500]) ).

thf(f2500,plain,
    ( ( ( mrel @ mactual @ sK49 )
      = $true )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f2498]) ).

thf(f2498,plain,
    ( spl0_6
  <=> ( ( mrel @ mactual @ sK49 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f4200,plain,
    ( ~ spl0_74
    | ~ spl0_76
    | ~ spl0_104 ),
    inference(avatar_contradiction_clause,[],[f4199]) ).

thf(f4199,plain,
    ( $false
    | ~ spl0_74
    | ~ spl0_76
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f4198]) ).

thf(f4198,plain,
    ( ( $false = $true )
    | ~ spl0_74
    | ~ spl0_76
    | ~ spl0_104 ),
    inference(backward_demodulation,[],[f4168,f4197]) ).

thf(f4197,plain,
    ( ( ( mrel @ sK2 @ sK14 )
      = $false )
    | ~ spl0_74
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f4195]) ).

thf(f4195,plain,
    ( ( $false = $true )
    | ( ( mrel @ sK2 @ sK14 )
      = $false )
    | ~ spl0_74
    | ~ spl0_104 ),
    inference(superposition,[],[f2950,f2820]) ).

thf(f2820,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK14 ) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f2818]) ).

thf(f2818,plain,
    ( spl0_74
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK14 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

thf(f2950,plain,
    ( ! [X4: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) )
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f2949]) ).

thf(f2949,plain,
    ( spl0_104
  <=> ! [X4: mworld] :
        ( ( $false
          = ( mrel @ sK2 @ X4 ) )
        | ( $true
          = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

thf(f4168,plain,
    ( ( ( mrel @ sK2 @ sK14 )
      = $true )
    | ~ spl0_76 ),
    inference(trivial_inequality_removal,[],[f4163]) ).

thf(f4163,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK14 )
      = $true )
    | ~ spl0_76 ),
    inference(superposition,[],[f3222,f2829]) ).

thf(f2829,plain,
    ( ( $true
      = ( mrel @ mactual @ sK14 ) )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f2827]) ).

thf(f2827,plain,
    ( spl0_76
  <=> ( $true
      = ( mrel @ mactual @ sK14 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

thf(f4160,plain,
    ( ~ spl0_69
    | ~ spl0_73
    | ~ spl0_104 ),
    inference(avatar_contradiction_clause,[],[f4159]) ).

thf(f4159,plain,
    ( $false
    | ~ spl0_69
    | ~ spl0_73
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f4158]) ).

thf(f4158,plain,
    ( ( $false = $true )
    | ~ spl0_69
    | ~ spl0_73
    | ~ spl0_104 ),
    inference(backward_demodulation,[],[f4136,f4157]) ).

thf(f4157,plain,
    ( ( ( mrel @ sK2 @ sK15 )
      = $false )
    | ~ spl0_69
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f4154]) ).

thf(f4154,plain,
    ( ( ( mrel @ sK2 @ sK15 )
      = $false )
    | ( $false = $true )
    | ~ spl0_69
    | ~ spl0_104 ),
    inference(superposition,[],[f2798,f2950]) ).

thf(f2798,plain,
    ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK15 )
      = $false )
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f2796]) ).

thf(f2796,plain,
    ( spl0_69
  <=> ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK15 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

thf(f4136,plain,
    ( ( ( mrel @ sK2 @ sK15 )
      = $true )
    | ~ spl0_73 ),
    inference(trivial_inequality_removal,[],[f4130]) ).

thf(f4130,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK15 )
      = $true )
    | ~ spl0_73 ),
    inference(superposition,[],[f3222,f2815]) ).

thf(f2815,plain,
    ( ( $true
      = ( mrel @ mactual @ sK15 ) )
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f2813]) ).

thf(f2813,plain,
    ( spl0_73
  <=> ( $true
      = ( mrel @ mactual @ sK15 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

thf(f4129,plain,
    ( ~ spl0_79
    | ~ spl0_80
    | ~ spl0_104 ),
    inference(avatar_contradiction_clause,[],[f4128]) ).

thf(f4128,plain,
    ( $false
    | ~ spl0_79
    | ~ spl0_80
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f4127]) ).

thf(f4127,plain,
    ( ( $false = $true )
    | ~ spl0_79
    | ~ spl0_80
    | ~ spl0_104 ),
    inference(backward_demodulation,[],[f4114,f4126]) ).

thf(f4126,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK12 ) )
    | ~ spl0_79
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f4123]) ).

thf(f4123,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK12 ) )
    | ( $false = $true )
    | ~ spl0_79
    | ~ spl0_104 ),
    inference(superposition,[],[f2842,f2950]) ).

thf(f2842,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK12 ) )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f2840]) ).

thf(f2840,plain,
    ( spl0_79
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK12 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

thf(f4114,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK12 ) )
    | ~ spl0_80 ),
    inference(trivial_inequality_removal,[],[f4110]) ).

thf(f4110,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK12 ) )
    | ( $true != $true )
    | ~ spl0_80 ),
    inference(superposition,[],[f3222,f2847]) ).

thf(f2847,plain,
    ( ( ( mrel @ mactual @ sK12 )
      = $true )
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f2845]) ).

thf(f2845,plain,
    ( spl0_80
  <=> ( ( mrel @ mactual @ sK12 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

thf(f4109,plain,
    ( ~ spl0_77
    | ~ spl0_81
    | ~ spl0_103 ),
    inference(avatar_contradiction_clause,[],[f4108]) ).

thf(f4108,plain,
    ( $false
    | ~ spl0_77
    | ~ spl0_81
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f4107]) ).

thf(f4107,plain,
    ( ( $false = $true )
    | ~ spl0_77
    | ~ spl0_81
    | ~ spl0_103 ),
    inference(backward_demodulation,[],[f4086,f4106]) ).

thf(f4106,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK11 ) )
    | ~ spl0_77
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f4104]) ).

thf(f4104,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK11 ) )
    | ( $false = $true )
    | ~ spl0_77
    | ~ spl0_103 ),
    inference(superposition,[],[f2946,f2834]) ).

thf(f2834,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 )
      = $false )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f2832]) ).

thf(f2832,plain,
    ( spl0_77
  <=> ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

thf(f4086,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK11 ) )
    | ~ spl0_81 ),
    inference(trivial_inequality_removal,[],[f4079]) ).

thf(f4079,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK11 ) )
    | ( $true != $true )
    | ~ spl0_81 ),
    inference(superposition,[],[f3222,f2852]) ).

thf(f2852,plain,
    ( ( $true
      = ( mrel @ mactual @ sK11 ) )
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f2850]) ).

thf(f2850,plain,
    ( spl0_81
  <=> ( $true
      = ( mrel @ mactual @ sK11 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

thf(f4078,plain,
    ( ~ spl0_26
    | ~ spl0_28
    | ~ spl0_107 ),
    inference(avatar_contradiction_clause,[],[f4077]) ).

thf(f4077,plain,
    ( $false
    | ~ spl0_26
    | ~ spl0_28
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4076]) ).

thf(f4076,plain,
    ( ( $false = $true )
    | ~ spl0_26
    | ~ spl0_28
    | ~ spl0_107 ),
    inference(backward_demodulation,[],[f4063,f4075]) ).

thf(f4075,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK38 ) )
    | ~ spl0_26
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4072]) ).

thf(f4072,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK38 ) )
    | ( $false = $true )
    | ~ spl0_26
    | ~ spl0_107 ),
    inference(superposition,[],[f2596,f3001]) ).

thf(f2596,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK38 ) )
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f2594]) ).

thf(f2594,plain,
    ( spl0_26
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK38 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

thf(f4063,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK38 ) )
    | ~ spl0_28 ),
    inference(trivial_inequality_removal,[],[f4058]) ).

thf(f4058,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK38 ) )
    | ~ spl0_28 ),
    inference(superposition,[],[f3222,f2605]) ).

thf(f2605,plain,
    ( ( $true
      = ( mrel @ mactual @ sK38 ) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f2603]) ).

thf(f2603,plain,
    ( spl0_28
  <=> ( $true
      = ( mrel @ mactual @ sK38 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

thf(f4055,plain,
    ( ~ spl0_24
    | ~ spl0_27
    | ~ spl0_105 ),
    inference(avatar_contradiction_clause,[],[f4054]) ).

thf(f4054,plain,
    ( $false
    | ~ spl0_24
    | ~ spl0_27
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f4053]) ).

thf(f4053,plain,
    ( ( $false = $true )
    | ~ spl0_24
    | ~ spl0_27
    | ~ spl0_105 ),
    inference(backward_demodulation,[],[f4002,f4052]) ).

thf(f4052,plain,
    ( ( ( mrel @ sK2 @ sK35 )
      = $false )
    | ~ spl0_24
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f4049]) ).

thf(f4049,plain,
    ( ( $false = $true )
    | ( ( mrel @ sK2 @ sK35 )
      = $false )
    | ~ spl0_24
    | ~ spl0_105 ),
    inference(superposition,[],[f2586,f2963]) ).

thf(f2586,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f2584]) ).

thf(f2584,plain,
    ( spl0_24
  <=> ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

thf(f4002,plain,
    ( ( ( mrel @ sK2 @ sK35 )
      = $true )
    | ~ spl0_27 ),
    inference(trivial_inequality_removal,[],[f3996]) ).

thf(f3996,plain,
    ( ( ( mrel @ sK2 @ sK35 )
      = $true )
    | ( $true != $true )
    | ~ spl0_27 ),
    inference(superposition,[],[f3222,f2600]) ).

thf(f2600,plain,
    ( ( ( mrel @ mactual @ sK35 )
      = $true )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f2598]) ).

thf(f2598,plain,
    ( spl0_27
  <=> ( ( mrel @ mactual @ sK35 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

thf(f4039,plain,
    ( ~ spl0_22
    | ~ spl0_25
    | ~ spl0_107 ),
    inference(avatar_contradiction_clause,[],[f4038]) ).

thf(f4038,plain,
    ( $false
    | ~ spl0_22
    | ~ spl0_25
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4037]) ).

thf(f4037,plain,
    ( ( $false = $true )
    | ~ spl0_22
    | ~ spl0_25
    | ~ spl0_107 ),
    inference(backward_demodulation,[],[f3995,f4036]) ).

thf(f4036,plain,
    ( ( ( mrel @ sK2 @ sK39 )
      = $false )
    | ~ spl0_22
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f4034]) ).

thf(f4034,plain,
    ( ( $false = $true )
    | ( ( mrel @ sK2 @ sK39 )
      = $false )
    | ~ spl0_22
    | ~ spl0_107 ),
    inference(superposition,[],[f2578,f3001]) ).

thf(f2578,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK39 ) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f2576]) ).

thf(f2576,plain,
    ( spl0_22
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK39 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

thf(f3995,plain,
    ( ( ( mrel @ sK2 @ sK39 )
      = $true )
    | ~ spl0_25 ),
    inference(trivial_inequality_removal,[],[f3988]) ).

thf(f3988,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK39 )
      = $true )
    | ~ spl0_25 ),
    inference(superposition,[],[f3222,f2591]) ).

thf(f2591,plain,
    ( ( ( mrel @ mactual @ sK39 )
      = $true )
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f2589]) ).

thf(f2589,plain,
    ( spl0_25
  <=> ( ( mrel @ mactual @ sK39 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

thf(f3987,plain,
    ( ~ spl0_58
    | ~ spl0_61
    | ~ spl0_100 ),
    inference(avatar_contradiction_clause,[],[f3986]) ).

thf(f3986,plain,
    ( $false
    | ~ spl0_58
    | ~ spl0_61
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3985]) ).

thf(f3985,plain,
    ( ( $false = $true )
    | ~ spl0_58
    | ~ spl0_61
    | ~ spl0_100 ),
    inference(backward_demodulation,[],[f3977,f3984]) ).

thf(f3984,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK22 ) )
    | ~ spl0_58
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3981]) ).

thf(f3981,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK22 ) )
    | ~ spl0_58
    | ~ spl0_100 ),
    inference(superposition,[],[f2746,f2934]) ).

thf(f2746,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK22 ) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f2744]) ).

thf(f2744,plain,
    ( spl0_58
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK22 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

thf(f3977,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK22 ) )
    | ~ spl0_61 ),
    inference(trivial_inequality_removal,[],[f3973]) ).

thf(f3973,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK22 ) )
    | ( $true != $true )
    | ~ spl0_61 ),
    inference(superposition,[],[f3222,f2759]) ).

thf(f2759,plain,
    ( ( $true
      = ( mrel @ mactual @ sK22 ) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f2757]) ).

thf(f2757,plain,
    ( spl0_61
  <=> ( $true
      = ( mrel @ mactual @ sK22 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

thf(f3972,plain,
    ( ~ spl0_59
    | ~ spl0_63
    | ~ spl0_101 ),
    inference(avatar_contradiction_clause,[],[f3971]) ).

thf(f3971,plain,
    ( $false
    | ~ spl0_59
    | ~ spl0_63
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f3970]) ).

thf(f3970,plain,
    ( ( $false = $true )
    | ~ spl0_59
    | ~ spl0_63
    | ~ spl0_101 ),
    inference(backward_demodulation,[],[f3955,f3969]) ).

thf(f3969,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK20 ) )
    | ~ spl0_59
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f3965]) ).

thf(f3965,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK20 ) )
    | ( $false = $true )
    | ~ spl0_59
    | ~ spl0_101 ),
    inference(superposition,[],[f2938,f2750]) ).

thf(f2750,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f2748]) ).

thf(f2748,plain,
    ( spl0_59
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

thf(f3955,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK20 ) )
    | ~ spl0_63 ),
    inference(trivial_inequality_removal,[],[f3949]) ).

thf(f3949,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK20 ) )
    | ( $true != $true )
    | ~ spl0_63 ),
    inference(superposition,[],[f3222,f2768]) ).

thf(f2768,plain,
    ( ( ( mrel @ mactual @ sK20 )
      = $true )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f2766]) ).

thf(f2766,plain,
    ( spl0_63
  <=> ( ( mrel @ mactual @ sK20 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

thf(f3948,plain,
    ( ~ spl0_62
    | ~ spl0_64
    | ~ spl0_100 ),
    inference(avatar_contradiction_clause,[],[f3947]) ).

thf(f3947,plain,
    ( $false
    | ~ spl0_62
    | ~ spl0_64
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3946]) ).

thf(f3946,plain,
    ( ( $false = $true )
    | ~ spl0_62
    | ~ spl0_64
    | ~ spl0_100 ),
    inference(backward_demodulation,[],[f3915,f3945]) ).

thf(f3945,plain,
    ( ( ( mrel @ sK2 @ sK21 )
      = $false )
    | ~ spl0_62
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3942]) ).

thf(f3942,plain,
    ( ( $false = $true )
    | ( ( mrel @ sK2 @ sK21 )
      = $false )
    | ~ spl0_62
    | ~ spl0_100 ),
    inference(superposition,[],[f2764,f2934]) ).

thf(f2764,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f2762]) ).

thf(f2762,plain,
    ( spl0_62
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

thf(f3915,plain,
    ( ( ( mrel @ sK2 @ sK21 )
      = $true )
    | ~ spl0_64 ),
    inference(trivial_inequality_removal,[],[f3909]) ).

thf(f3909,plain,
    ( ( ( mrel @ sK2 @ sK21 )
      = $true )
    | ( $true != $true )
    | ~ spl0_64 ),
    inference(superposition,[],[f3222,f2773]) ).

thf(f2773,plain,
    ( ( $true
      = ( mrel @ mactual @ sK21 ) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f2771]) ).

thf(f2771,plain,
    ( spl0_64
  <=> ( $true
      = ( mrel @ mactual @ sK21 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

thf(f3902,plain,
    ( ~ spl0_11
    | ~ spl0_12
    | ~ spl0_110 ),
    inference(avatar_contradiction_clause,[],[f3901]) ).

thf(f3901,plain,
    ( $false
    | ~ spl0_11
    | ~ spl0_12
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f3900]) ).

thf(f3900,plain,
    ( ( $false = $true )
    | ~ spl0_11
    | ~ spl0_12
    | ~ spl0_110 ),
    inference(backward_demodulation,[],[f3877,f3899]) ).

thf(f3899,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK46 ) )
    | ~ spl0_11
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f3897]) ).

thf(f3897,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK46 ) )
    | ( $false = $true )
    | ~ spl0_11
    | ~ spl0_110 ),
    inference(superposition,[],[f3058,f2526]) ).

thf(f2526,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK46 ) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f2524]) ).

thf(f2524,plain,
    ( spl0_11
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK46 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

thf(f3877,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK46 ) )
    | ~ spl0_12 ),
    inference(trivial_inequality_removal,[],[f3871]) ).

thf(f3871,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK46 ) )
    | ( $true != $true )
    | ~ spl0_12 ),
    inference(superposition,[],[f3222,f2531]) ).

thf(f2531,plain,
    ( ( ( mrel @ mactual @ sK46 )
      = $true )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f2529]) ).

thf(f2529,plain,
    ( spl0_12
  <=> ( ( mrel @ mactual @ sK46 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

thf(f3870,plain,
    ( ~ spl0_14
    | ~ spl0_15
    | ~ spl0_110 ),
    inference(avatar_contradiction_clause,[],[f3869]) ).

thf(f3869,plain,
    ( $false
    | ~ spl0_14
    | ~ spl0_15
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f3868]) ).

thf(f3868,plain,
    ( ( $false = $true )
    | ~ spl0_14
    | ~ spl0_15
    | ~ spl0_110 ),
    inference(backward_demodulation,[],[f3855,f3867]) ).

thf(f3867,plain,
    ( ( ( mrel @ sK2 @ sK45 )
      = $false )
    | ~ spl0_14
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f3864]) ).

thf(f3864,plain,
    ( ( ( mrel @ sK2 @ sK45 )
      = $false )
    | ( $false = $true )
    | ~ spl0_14
    | ~ spl0_110 ),
    inference(superposition,[],[f2540,f3058]) ).

thf(f2540,plain,
    ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK45 )
      = $false )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f2538]) ).

thf(f2538,plain,
    ( spl0_14
  <=> ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK45 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

thf(f3855,plain,
    ( ( ( mrel @ sK2 @ sK45 )
      = $true )
    | ~ spl0_15 ),
    inference(trivial_inequality_removal,[],[f3850]) ).

thf(f3850,plain,
    ( ( ( mrel @ sK2 @ sK45 )
      = $true )
    | ( $true != $true )
    | ~ spl0_15 ),
    inference(superposition,[],[f3222,f2545]) ).

thf(f2545,plain,
    ( ( ( mrel @ mactual @ sK45 )
      = $true )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f2543]) ).

thf(f2543,plain,
    ( spl0_15
  <=> ( ( mrel @ mactual @ sK45 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

thf(f3847,plain,
    ( ~ spl0_10
    | ~ spl0_13
    | ~ spl0_109 ),
    inference(avatar_contradiction_clause,[],[f3846]) ).

thf(f3846,plain,
    ( $false
    | ~ spl0_10
    | ~ spl0_13
    | ~ spl0_109 ),
    inference(trivial_inequality_removal,[],[f3845]) ).

thf(f3845,plain,
    ( ( $false = $true )
    | ~ spl0_10
    | ~ spl0_13
    | ~ spl0_109 ),
    inference(backward_demodulation,[],[f3815,f3844]) ).

thf(f3844,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK44 ) )
    | ~ spl0_10
    | ~ spl0_109 ),
    inference(trivial_inequality_removal,[],[f3840]) ).

thf(f3840,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK44 ) )
    | ( $false = $true )
    | ~ spl0_10
    | ~ spl0_109 ),
    inference(superposition,[],[f3039,f2522]) ).

thf(f2522,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) )
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f2520]) ).

thf(f2520,plain,
    ( spl0_10
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

thf(f3815,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK44 ) )
    | ~ spl0_13 ),
    inference(trivial_inequality_removal,[],[f3809]) ).

thf(f3809,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK44 ) )
    | ~ spl0_13 ),
    inference(superposition,[],[f3222,f2536]) ).

thf(f2536,plain,
    ( ( $true
      = ( mrel @ mactual @ sK44 ) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f2534]) ).

thf(f2534,plain,
    ( spl0_13
  <=> ( $true
      = ( mrel @ mactual @ sK44 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

thf(f3808,plain,
    ( ~ spl0_8
    | ~ spl0_16
    | ~ spl0_108 ),
    inference(avatar_contradiction_clause,[],[f3807]) ).

thf(f3807,plain,
    ( $false
    | ~ spl0_8
    | ~ spl0_16
    | ~ spl0_108 ),
    inference(trivial_inequality_removal,[],[f3806]) ).

thf(f3806,plain,
    ( ( $false = $true )
    | ~ spl0_8
    | ~ spl0_16
    | ~ spl0_108 ),
    inference(forward_demodulation,[],[f3803,f3461]) ).

thf(f3461,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK41 ) )
    | ~ spl0_8
    | ~ spl0_108 ),
    inference(trivial_inequality_removal,[],[f3458]) ).

thf(f3458,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK41 ) )
    | ~ spl0_8
    | ~ spl0_108 ),
    inference(superposition,[],[f2514,f3020]) ).

thf(f3020,plain,
    ( ! [X2: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) )
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f3019]) ).

thf(f3019,plain,
    ( spl0_108
  <=> ! [X2: mworld] :
        ( ( ( mrel @ sK2 @ X2 )
          = $false )
        | ( $true
          = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

thf(f2514,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f2512]) ).

thf(f2512,plain,
    ( spl0_8
  <=> ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

thf(f3803,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK41 ) )
    | ~ spl0_16 ),
    inference(trivial_inequality_removal,[],[f3798]) ).

thf(f3798,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK41 ) )
    | ( $true != $true )
    | ~ spl0_16 ),
    inference(superposition,[],[f3222,f2550]) ).

thf(f2550,plain,
    ( ( ( mrel @ mactual @ sK41 )
      = $true )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f2548]) ).

thf(f2548,plain,
    ( spl0_16
  <=> ( ( mrel @ mactual @ sK41 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

thf(f3797,plain,
    ( ~ spl0_83
    | ~ spl0_86
    | ~ spl0_103 ),
    inference(avatar_contradiction_clause,[],[f3796]) ).

thf(f3796,plain,
    ( $false
    | ~ spl0_83
    | ~ spl0_86
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f3795]) ).

thf(f3795,plain,
    ( ( $false = $true )
    | ~ spl0_83
    | ~ spl0_86
    | ~ spl0_103 ),
    inference(backward_demodulation,[],[f3779,f3794]) ).

thf(f3794,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK9 ) )
    | ~ spl0_83
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f3792]) ).

thf(f3792,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK9 ) )
    | ~ spl0_83
    | ~ spl0_103 ),
    inference(superposition,[],[f2946,f2862]) ).

thf(f2862,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK9 ) )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f2860]) ).

thf(f2860,plain,
    ( spl0_83
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

thf(f3779,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK9 ) )
    | ~ spl0_86 ),
    inference(trivial_inequality_removal,[],[f3773]) ).

thf(f3773,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK9 ) )
    | ~ spl0_86 ),
    inference(superposition,[],[f3222,f2875]) ).

thf(f2875,plain,
    ( ( $true
      = ( mrel @ mactual @ sK9 ) )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f2873]) ).

thf(f2873,plain,
    ( spl0_86
  <=> ( $true
      = ( mrel @ mactual @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

thf(f3772,plain,
    ( ~ spl0_87
    | ~ spl0_89
    | ~ spl0_103 ),
    inference(avatar_contradiction_clause,[],[f3771]) ).

thf(f3771,plain,
    ( $false
    | ~ spl0_87
    | ~ spl0_89
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f3770]) ).

thf(f3770,plain,
    ( ( $false = $true )
    | ~ spl0_87
    | ~ spl0_89
    | ~ spl0_103 ),
    inference(backward_demodulation,[],[f3758,f3769]) ).

thf(f3769,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK8 ) )
    | ~ spl0_87
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f3766]) ).

thf(f3766,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK8 ) )
    | ~ spl0_87
    | ~ spl0_103 ),
    inference(superposition,[],[f2880,f2946]) ).

thf(f2880,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK8 ) )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f2878]) ).

thf(f2878,plain,
    ( spl0_87
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK8 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

thf(f3758,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK8 ) )
    | ~ spl0_89 ),
    inference(trivial_inequality_removal,[],[f3751]) ).

thf(f3751,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK8 ) )
    | ( $true != $true )
    | ~ spl0_89 ),
    inference(superposition,[],[f3222,f2889]) ).

thf(f2889,plain,
    ( ( $true
      = ( mrel @ mactual @ sK8 ) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f2887]) ).

thf(f2887,plain,
    ( spl0_89
  <=> ( $true
      = ( mrel @ mactual @ sK8 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

thf(f3750,plain,
    ( ~ spl0_82
    | ~ spl0_90
    | ~ spl0_104 ),
    inference(avatar_contradiction_clause,[],[f3749]) ).

thf(f3749,plain,
    ( $false
    | ~ spl0_82
    | ~ spl0_90
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f3748]) ).

thf(f3748,plain,
    ( ( $false = $true )
    | ~ spl0_82
    | ~ spl0_90
    | ~ spl0_104 ),
    inference(backward_demodulation,[],[f3725,f3747]) ).

thf(f3747,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK4 ) )
    | ~ spl0_82
    | ~ spl0_104 ),
    inference(trivial_inequality_removal,[],[f3745]) ).

thf(f3745,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK4 ) )
    | ~ spl0_82
    | ~ spl0_104 ),
    inference(superposition,[],[f2858,f2950]) ).

thf(f2858,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) )
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f2856]) ).

thf(f2856,plain,
    ( spl0_82
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

thf(f3725,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK4 ) )
    | ~ spl0_90 ),
    inference(trivial_inequality_removal,[],[f3720]) ).

thf(f3720,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK4 ) )
    | ( $true != $true )
    | ~ spl0_90 ),
    inference(superposition,[],[f3222,f2894]) ).

thf(f2894,plain,
    ( ( ( mrel @ mactual @ sK4 )
      = $true )
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f2892]) ).

thf(f2892,plain,
    ( spl0_90
  <=> ( ( mrel @ mactual @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

thf(f3715,plain,
    ( ~ spl0_71
    | ~ spl0_78
    | ~ spl0_98 ),
    inference(avatar_contradiction_clause,[],[f3714]) ).

thf(f3714,plain,
    ( $false
    | ~ spl0_71
    | ~ spl0_78
    | ~ spl0_98 ),
    inference(trivial_inequality_removal,[],[f3713]) ).

thf(f3713,plain,
    ( ( $false = $true )
    | ~ spl0_71
    | ~ spl0_78
    | ~ spl0_98 ),
    inference(backward_demodulation,[],[f3674,f3712]) ).

thf(f3712,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK10 ) )
    | ~ spl0_71
    | ~ spl0_98 ),
    inference(trivial_inequality_removal,[],[f3710]) ).

thf(f3710,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK10 ) )
    | ( $false = $true )
    | ~ spl0_71
    | ~ spl0_98 ),
    inference(superposition,[],[f2926,f2806]) ).

thf(f2806,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f2804]) ).

thf(f2804,plain,
    ( spl0_71
  <=> ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

thf(f2926,plain,
    ( ! [X3: mworld] :
        ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X3 ) ) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f2925]) ).

thf(f2925,plain,
    ( spl0_98
  <=> ! [X3: mworld] :
        ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X3 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

thf(f3674,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK10 ) )
    | ~ spl0_78 ),
    inference(trivial_inequality_removal,[],[f3667]) ).

thf(f3667,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK10 ) )
    | ~ spl0_78 ),
    inference(superposition,[],[f3222,f2838]) ).

thf(f2838,plain,
    ( ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f2836]) ).

thf(f2836,plain,
    ( spl0_78
  <=> ( $true
      = ( mrel @ mactual @ sK10 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

thf(f3706,plain,
    ( ~ spl0_72
    | ~ spl0_75
    | ~ spl0_103 ),
    inference(avatar_contradiction_clause,[],[f3705]) ).

thf(f3705,plain,
    ( $false
    | ~ spl0_72
    | ~ spl0_75
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f3704]) ).

thf(f3704,plain,
    ( ( $false = $true )
    | ~ spl0_72
    | ~ spl0_75
    | ~ spl0_103 ),
    inference(backward_demodulation,[],[f3666,f3703]) ).

thf(f3703,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK13 ) )
    | ~ spl0_72
    | ~ spl0_103 ),
    inference(trivial_inequality_removal,[],[f3700]) ).

thf(f3700,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK13 ) )
    | ( $false = $true )
    | ~ spl0_72
    | ~ spl0_103 ),
    inference(superposition,[],[f2946,f2810]) ).

thf(f2810,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) )
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f2808]) ).

thf(f2808,plain,
    ( spl0_72
  <=> ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

thf(f3666,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK13 ) )
    | ~ spl0_75 ),
    inference(trivial_inequality_removal,[],[f3659]) ).

thf(f3659,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK13 ) )
    | ~ spl0_75 ),
    inference(superposition,[],[f3222,f2824]) ).

thf(f2824,plain,
    ( ( $true
      = ( mrel @ mactual @ sK13 ) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f2822]) ).

thf(f2822,plain,
    ( spl0_75
  <=> ( $true
      = ( mrel @ mactual @ sK13 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

thf(f3658,plain,
    ( ~ spl0_85
    | ~ spl0_88
    | ~ spl0_98 ),
    inference(avatar_contradiction_clause,[],[f3657]) ).

thf(f3657,plain,
    ( $false
    | ~ spl0_85
    | ~ spl0_88
    | ~ spl0_98 ),
    inference(trivial_inequality_removal,[],[f3656]) ).

thf(f3656,plain,
    ( ( $false = $true )
    | ~ spl0_85
    | ~ spl0_88
    | ~ spl0_98 ),
    inference(backward_demodulation,[],[f3643,f3655]) ).

thf(f3655,plain,
    ( ( ( mrel @ sK2 @ sK5 )
      = $false )
    | ~ spl0_85
    | ~ spl0_98 ),
    inference(trivial_inequality_removal,[],[f3653]) ).

thf(f3653,plain,
    ( ( ( mrel @ sK2 @ sK5 )
      = $false )
    | ( $false = $true )
    | ~ spl0_85
    | ~ spl0_98 ),
    inference(superposition,[],[f2926,f2870]) ).

thf(f2870,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f2868]) ).

thf(f2868,plain,
    ( spl0_85
  <=> ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

thf(f3643,plain,
    ( ( ( mrel @ sK2 @ sK5 )
      = $true )
    | ~ spl0_88 ),
    inference(trivial_inequality_removal,[],[f3638]) ).

thf(f3638,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK5 )
      = $true )
    | ~ spl0_88 ),
    inference(superposition,[],[f3222,f2884]) ).

thf(f2884,plain,
    ( ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f2882]) ).

thf(f2882,plain,
    ( spl0_88
  <=> ( $true
      = ( mrel @ mactual @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

thf(f3635,plain,
    ( ~ spl0_70
    | ~ spl0_84
    | ~ spl0_102 ),
    inference(avatar_contradiction_clause,[],[f3634]) ).

thf(f3634,plain,
    ( $false
    | ~ spl0_70
    | ~ spl0_84
    | ~ spl0_102 ),
    inference(trivial_inequality_removal,[],[f3633]) ).

thf(f3633,plain,
    ( ( $false = $true )
    | ~ spl0_70
    | ~ spl0_84
    | ~ spl0_102 ),
    inference(backward_demodulation,[],[f3289,f3632]) ).

thf(f3632,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK3 ) )
    | ~ spl0_70
    | ~ spl0_102 ),
    inference(trivial_inequality_removal,[],[f3629]) ).

thf(f3629,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK3 ) )
    | ( $false = $true )
    | ~ spl0_70
    | ~ spl0_102 ),
    inference(superposition,[],[f2942,f2802]) ).

thf(f2802,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f2800]) ).

thf(f2800,plain,
    ( spl0_70
  <=> ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

thf(f2942,plain,
    ( ! [X4: mworld] :
        ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) )
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f2941]) ).

thf(f2941,plain,
    ( spl0_102
  <=> ! [X4: mworld] :
        ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

thf(f3289,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK3 ) )
    | ~ spl0_84 ),
    inference(trivial_inequality_removal,[],[f3280]) ).

thf(f3280,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK3 ) )
    | ~ spl0_84 ),
    inference(superposition,[],[f3222,f2866]) ).

thf(f2866,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f2864]) ).

thf(f2864,plain,
    ( spl0_84
  <=> ( $true
      = ( mrel @ mactual @ sK3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

thf(f3611,plain,
    ( ~ spl0_38
    | ~ spl0_40
    | ~ spl0_105 ),
    inference(avatar_contradiction_clause,[],[f3610]) ).

thf(f3610,plain,
    ( $false
    | ~ spl0_38
    | ~ spl0_40
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f3609]) ).

thf(f3609,plain,
    ( ( $false = $true )
    | ~ spl0_38
    | ~ spl0_40
    | ~ spl0_105 ),
    inference(backward_demodulation,[],[f3598,f3608]) ).

thf(f3608,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK33 ) )
    | ~ spl0_38
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f3606]) ).

thf(f3606,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK33 ) )
    | ~ spl0_38
    | ~ spl0_105 ),
    inference(superposition,[],[f2963,f2652]) ).

thf(f2652,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK33 )
      = $false )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f2650]) ).

thf(f2650,plain,
    ( spl0_38
  <=> ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK33 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

thf(f3598,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK33 ) )
    | ~ spl0_40 ),
    inference(trivial_inequality_removal,[],[f3591]) ).

thf(f3591,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK33 ) )
    | ~ spl0_40 ),
    inference(superposition,[],[f3222,f2661]) ).

thf(f2661,plain,
    ( ( ( mrel @ mactual @ sK33 )
      = $true )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f2659]) ).

thf(f2659,plain,
    ( spl0_40
  <=> ( ( mrel @ mactual @ sK33 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

thf(f3588,plain,
    ( ~ spl0_35
    | ~ spl0_39
    | ~ spl0_107 ),
    inference(avatar_contradiction_clause,[],[f3587]) ).

thf(f3587,plain,
    ( $false
    | ~ spl0_35
    | ~ spl0_39
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f3586]) ).

thf(f3586,plain,
    ( ( $false = $true )
    | ~ spl0_35
    | ~ spl0_39
    | ~ spl0_107 ),
    inference(backward_demodulation,[],[f3557,f3585]) ).

thf(f3585,plain,
    ( ( ( mrel @ sK2 @ sK31 )
      = $false )
    | ~ spl0_35
    | ~ spl0_107 ),
    inference(trivial_inequality_removal,[],[f3583]) ).

thf(f3583,plain,
    ( ( $false = $true )
    | ( ( mrel @ sK2 @ sK31 )
      = $false )
    | ~ spl0_35
    | ~ spl0_107 ),
    inference(superposition,[],[f2638,f3001]) ).

thf(f2638,plain,
    ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false )
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f2636]) ).

thf(f2636,plain,
    ( spl0_35
  <=> ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

thf(f3557,plain,
    ( ( ( mrel @ sK2 @ sK31 )
      = $true )
    | ~ spl0_39 ),
    inference(trivial_inequality_removal,[],[f3552]) ).

thf(f3552,plain,
    ( ( ( mrel @ sK2 @ sK31 )
      = $true )
    | ( $true != $true )
    | ~ spl0_39 ),
    inference(superposition,[],[f3222,f2656]) ).

thf(f2656,plain,
    ( ( $true
      = ( mrel @ mactual @ sK31 ) )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f2654]) ).

thf(f2654,plain,
    ( spl0_39
  <=> ( $true
      = ( mrel @ mactual @ sK31 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

thf(f3566,plain,
    ( ~ spl0_34
    | ~ spl0_37
    | ~ spl0_105 ),
    inference(avatar_contradiction_clause,[],[f3565]) ).

thf(f3565,plain,
    ( $false
    | ~ spl0_34
    | ~ spl0_37
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f3564]) ).

thf(f3564,plain,
    ( ( $false = $true )
    | ~ spl0_34
    | ~ spl0_37
    | ~ spl0_105 ),
    inference(backward_demodulation,[],[f3549,f3563]) ).

thf(f3563,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK34 ) )
    | ~ spl0_34
    | ~ spl0_105 ),
    inference(trivial_inequality_removal,[],[f3560]) ).

thf(f3560,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK34 ) )
    | ( $false = $true )
    | ~ spl0_34
    | ~ spl0_105 ),
    inference(superposition,[],[f2634,f2963]) ).

thf(f2634,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK34 )
      = $false )
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f2632]) ).

thf(f2632,plain,
    ( spl0_34
  <=> ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK34 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

thf(f3549,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK34 ) )
    | ~ spl0_37 ),
    inference(trivial_inequality_removal,[],[f3544]) ).

thf(f3544,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK34 ) )
    | ~ spl0_37 ),
    inference(superposition,[],[f3222,f2647]) ).

thf(f2647,plain,
    ( ( $true
      = ( mrel @ mactual @ sK34 ) )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f2645]) ).

thf(f2645,plain,
    ( spl0_37
  <=> ( $true
      = ( mrel @ mactual @ sK34 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

thf(f3541,plain,
    ( ~ spl0_21
    | ~ spl0_36
    | ~ spl0_106 ),
    inference(avatar_contradiction_clause,[],[f3540]) ).

thf(f3540,plain,
    ( $false
    | ~ spl0_21
    | ~ spl0_36
    | ~ spl0_106 ),
    inference(trivial_inequality_removal,[],[f3539]) ).

thf(f3539,plain,
    ( ( $false = $true )
    | ~ spl0_21
    | ~ spl0_36
    | ~ spl0_106 ),
    inference(backward_demodulation,[],[f3520,f3538]) ).

thf(f3538,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK29 ) )
    | ~ spl0_21
    | ~ spl0_106 ),
    inference(trivial_inequality_removal,[],[f3536]) ).

thf(f3536,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK29 ) )
    | ( $false = $true )
    | ~ spl0_21
    | ~ spl0_106 ),
    inference(superposition,[],[f2574,f2982]) ).

thf(f2982,plain,
    ( ! [X2: mworld] :
        ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
          = $true )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f2981]) ).

thf(f2981,plain,
    ( spl0_106
  <=> ! [X2: mworld] :
        ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
          = $true )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

thf(f2574,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f2572]) ).

thf(f2572,plain,
    ( spl0_21
  <=> ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

thf(f3520,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK29 ) )
    | ~ spl0_36 ),
    inference(trivial_inequality_removal,[],[f3514]) ).

thf(f3514,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK29 ) )
    | ~ spl0_36 ),
    inference(superposition,[],[f3222,f2642]) ).

thf(f2642,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f2640]) ).

thf(f2640,plain,
    ( spl0_36
  <=> ( ( mrel @ mactual @ sK29 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

thf(f3513,plain,
    ( ~ spl0_23
    | ~ spl0_30
    | ~ spl0_96 ),
    inference(avatar_contradiction_clause,[],[f3512]) ).

thf(f3512,plain,
    ( $false
    | ~ spl0_23
    | ~ spl0_30
    | ~ spl0_96 ),
    inference(trivial_inequality_removal,[],[f3511]) ).

thf(f3511,plain,
    ( ( $false = $true )
    | ~ spl0_23
    | ~ spl0_30
    | ~ spl0_96 ),
    inference(backward_demodulation,[],[f3292,f3510]) ).

thf(f3510,plain,
    ( ( ( mrel @ sK2 @ sK30 )
      = $false )
    | ~ spl0_23
    | ~ spl0_96 ),
    inference(trivial_inequality_removal,[],[f3508]) ).

thf(f3508,plain,
    ( ( ( mrel @ sK2 @ sK30 )
      = $false )
    | ( $false = $true )
    | ~ spl0_23
    | ~ spl0_96 ),
    inference(superposition,[],[f2582,f2920]) ).

thf(f2920,plain,
    ( ! [X2: mworld] :
        ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
          = $true )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f2919]) ).

thf(f2919,plain,
    ( spl0_96
  <=> ! [X2: mworld] :
        ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
          = $true )
        | ( ( mrel @ sK2 @ X2 )
          = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

thf(f2582,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f2580]) ).

thf(f2580,plain,
    ( spl0_23
  <=> ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

thf(f3292,plain,
    ( ( ( mrel @ sK2 @ sK30 )
      = $true )
    | ~ spl0_30 ),
    inference(trivial_inequality_removal,[],[f3282]) ).

thf(f3282,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK30 )
      = $true )
    | ~ spl0_30 ),
    inference(superposition,[],[f3222,f2614]) ).

thf(f2614,plain,
    ( ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f2612]) ).

thf(f2612,plain,
    ( spl0_30
  <=> ( $true
      = ( mrel @ mactual @ sK30 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

thf(f3502,plain,
    ( ~ spl0_18
    | ~ spl0_19
    | ~ spl0_109 ),
    inference(avatar_contradiction_clause,[],[f3501]) ).

thf(f3501,plain,
    ( $false
    | ~ spl0_18
    | ~ spl0_19
    | ~ spl0_109 ),
    inference(trivial_inequality_removal,[],[f3500]) ).

thf(f3500,plain,
    ( ( $false = $true )
    | ~ spl0_18
    | ~ spl0_19
    | ~ spl0_109 ),
    inference(backward_demodulation,[],[f3489,f3499]) ).

thf(f3499,plain,
    ( ( ( mrel @ sK2 @ sK43 )
      = $false )
    | ~ spl0_18
    | ~ spl0_109 ),
    inference(trivial_inequality_removal,[],[f3496]) ).

thf(f3496,plain,
    ( ( ( mrel @ sK2 @ sK43 )
      = $false )
    | ( $false = $true )
    | ~ spl0_18
    | ~ spl0_109 ),
    inference(superposition,[],[f2558,f3039]) ).

thf(f2558,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK43 )
      = $false )
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f2556]) ).

thf(f2556,plain,
    ( spl0_18
  <=> ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK43 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

thf(f3489,plain,
    ( ( ( mrel @ sK2 @ sK43 )
      = $true )
    | ~ spl0_19 ),
    inference(trivial_inequality_removal,[],[f3483]) ).

thf(f3483,plain,
    ( ( ( mrel @ sK2 @ sK43 )
      = $true )
    | ( $true != $true )
    | ~ spl0_19 ),
    inference(superposition,[],[f3222,f2563]) ).

thf(f2563,plain,
    ( ( $true
      = ( mrel @ mactual @ sK43 ) )
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f2561]) ).

thf(f2561,plain,
    ( spl0_19
  <=> ( $true
      = ( mrel @ mactual @ sK43 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

thf(f3482,plain,
    ( ~ spl0_17
    | ~ spl0_20
    | ~ spl0_110 ),
    inference(avatar_contradiction_clause,[],[f3481]) ).

thf(f3481,plain,
    ( $false
    | ~ spl0_17
    | ~ spl0_20
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f3480]) ).

thf(f3480,plain,
    ( ( $false = $true )
    | ~ spl0_17
    | ~ spl0_20
    | ~ spl0_110 ),
    inference(backward_demodulation,[],[f3435,f3479]) ).

thf(f3479,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK42 ) )
    | ~ spl0_17
    | ~ spl0_110 ),
    inference(trivial_inequality_removal,[],[f3476]) ).

thf(f3476,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK42 ) )
    | ~ spl0_17
    | ~ spl0_110 ),
    inference(superposition,[],[f3058,f2554]) ).

thf(f2554,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f2552]) ).

thf(f2552,plain,
    ( spl0_17
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

thf(f3435,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK42 ) )
    | ~ spl0_20 ),
    inference(trivial_inequality_removal,[],[f3431]) ).

thf(f3431,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK42 ) )
    | ~ spl0_20 ),
    inference(superposition,[],[f3222,f2568]) ).

thf(f2568,plain,
    ( ( $true
      = ( mrel @ mactual @ sK42 ) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f2566]) ).

thf(f2566,plain,
    ( spl0_20
  <=> ( $true
      = ( mrel @ mactual @ sK42 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

thf(f3428,plain,
    ( ~ spl0_4
    | ~ spl0_5
    | ~ spl0_108 ),
    inference(avatar_contradiction_clause,[],[f3427]) ).

thf(f3427,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_5
    | ~ spl0_108 ),
    inference(trivial_inequality_removal,[],[f3426]) ).

thf(f3426,plain,
    ( ( $false = $true )
    | ~ spl0_4
    | ~ spl0_5
    | ~ spl0_108 ),
    inference(backward_demodulation,[],[f3410,f3425]) ).

thf(f3425,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK47 ) )
    | ~ spl0_4
    | ~ spl0_108 ),
    inference(trivial_inequality_removal,[],[f3423]) ).

thf(f3423,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK47 ) )
    | ( $false = $true )
    | ~ spl0_4
    | ~ spl0_108 ),
    inference(superposition,[],[f2490,f3020]) ).

thf(f2490,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 )
      = $false )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f2488]) ).

thf(f2488,plain,
    ( spl0_4
  <=> ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f3410,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK47 ) )
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f3405]) ).

thf(f3405,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK47 ) )
    | ~ spl0_5 ),
    inference(superposition,[],[f3222,f2495]) ).

thf(f2495,plain,
    ( ( $true
      = ( mrel @ mactual @ sK47 ) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f2493]) ).

thf(f2493,plain,
    ( spl0_5
  <=> ( $true
      = ( mrel @ mactual @ sK47 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f3404,plain,
    ( ~ spl0_3
    | ~ spl0_9
    | ~ spl0_97 ),
    inference(avatar_contradiction_clause,[],[f3403]) ).

thf(f3403,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_9
    | ~ spl0_97 ),
    inference(trivial_inequality_removal,[],[f3402]) ).

thf(f3402,plain,
    ( ( $false = $true )
    | ~ spl0_3
    | ~ spl0_9
    | ~ spl0_97 ),
    inference(backward_demodulation,[],[f3288,f3401]) ).

thf(f3401,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK40 ) )
    | ~ spl0_3
    | ~ spl0_97 ),
    inference(trivial_inequality_removal,[],[f3399]) ).

thf(f3399,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK40 ) )
    | ~ spl0_3
    | ~ spl0_97 ),
    inference(superposition,[],[f2486,f2923]) ).

thf(f2923,plain,
    ( ! [X1: mworld] :
        ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
          = $true )
        | ( $false
          = ( mrel @ sK2 @ X1 ) ) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f2922]) ).

thf(f2922,plain,
    ( spl0_97
  <=> ! [X1: mworld] :
        ( ( $false
          = ( mrel @ sK2 @ X1 ) )
        | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

thf(f2486,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f2484]) ).

thf(f2484,plain,
    ( spl0_3
  <=> ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f3288,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK40 ) )
    | ~ spl0_9 ),
    inference(trivial_inequality_removal,[],[f3283]) ).

thf(f3283,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK40 ) )
    | ~ spl0_9 ),
    inference(superposition,[],[f3222,f2518]) ).

thf(f2518,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f2516]) ).

thf(f2516,plain,
    ( spl0_9
  <=> ( $true
      = ( mrel @ mactual @ sK40 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

thf(f3381,plain,
    ( ~ spl0_48
    | ~ spl0_50
    | ~ spl0_100 ),
    inference(avatar_contradiction_clause,[],[f3380]) ).

thf(f3380,plain,
    ( $false
    | ~ spl0_48
    | ~ spl0_50
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3379]) ).

thf(f3379,plain,
    ( ( $false = $true )
    | ~ spl0_48
    | ~ spl0_50
    | ~ spl0_100 ),
    inference(backward_demodulation,[],[f3355,f3378]) ).

thf(f3378,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK27 ) )
    | ~ spl0_48
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3375]) ).

thf(f3375,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK27 ) )
    | ( $false = $true )
    | ~ spl0_48
    | ~ spl0_100 ),
    inference(superposition,[],[f2700,f2934]) ).

thf(f2700,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK27 )
      = $false )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f2698]) ).

thf(f2698,plain,
    ( spl0_48
  <=> ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK27 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

thf(f3355,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK27 ) )
    | ~ spl0_50 ),
    inference(trivial_inequality_removal,[],[f3350]) ).

thf(f3350,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK27 ) )
    | ( $true != $true )
    | ~ spl0_50 ),
    inference(superposition,[],[f3222,f2709]) ).

thf(f2709,plain,
    ( ( ( mrel @ mactual @ sK27 )
      = $true )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f2707]) ).

thf(f2707,plain,
    ( spl0_50
  <=> ( ( mrel @ mactual @ sK27 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

thf(f3345,plain,
    ( ~ spl0_44
    | ~ spl0_47
    | ~ spl0_100 ),
    inference(avatar_contradiction_clause,[],[f3344]) ).

thf(f3344,plain,
    ( $false
    | ~ spl0_44
    | ~ spl0_47
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3343]) ).

thf(f3343,plain,
    ( ( $false = $true )
    | ~ spl0_44
    | ~ spl0_47
    | ~ spl0_100 ),
    inference(backward_demodulation,[],[f3335,f3342]) ).

thf(f3342,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK28 ) )
    | ~ spl0_44
    | ~ spl0_100 ),
    inference(trivial_inequality_removal,[],[f3339]) ).

thf(f3339,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK28 ) )
    | ~ spl0_44
    | ~ spl0_100 ),
    inference(superposition,[],[f2682,f2934]) ).

thf(f2682,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK28 )
      = $false )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f2680]) ).

thf(f2680,plain,
    ( spl0_44
  <=> ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK28 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

thf(f3335,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK28 ) )
    | ~ spl0_47 ),
    inference(trivial_inequality_removal,[],[f3331]) ).

thf(f3331,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK28 ) )
    | ( $true != $true )
    | ~ spl0_47 ),
    inference(superposition,[],[f3222,f2695]) ).

thf(f2695,plain,
    ( ( $true
      = ( mrel @ mactual @ sK28 ) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f2693]) ).

thf(f2693,plain,
    ( spl0_47
  <=> ( $true
      = ( mrel @ mactual @ sK28 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

thf(f3330,plain,
    ( ~ spl0_45
    | ~ spl0_49
    | ~ spl0_101 ),
    inference(avatar_contradiction_clause,[],[f3329]) ).

thf(f3329,plain,
    ( $false
    | ~ spl0_45
    | ~ spl0_49
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f3328]) ).

thf(f3328,plain,
    ( ( $false = $true )
    | ~ spl0_45
    | ~ spl0_49
    | ~ spl0_101 ),
    inference(backward_demodulation,[],[f3317,f3327]) ).

thf(f3327,plain,
    ( ( ( mrel @ sK2 @ sK26 )
      = $false )
    | ~ spl0_45
    | ~ spl0_101 ),
    inference(trivial_inequality_removal,[],[f3324]) ).

thf(f3324,plain,
    ( ( ( mrel @ sK2 @ sK26 )
      = $false )
    | ( $false = $true )
    | ~ spl0_45
    | ~ spl0_101 ),
    inference(superposition,[],[f2686,f2938]) ).

thf(f2686,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f2684]) ).

thf(f2684,plain,
    ( spl0_45
  <=> ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

thf(f3317,plain,
    ( ( ( mrel @ sK2 @ sK26 )
      = $true )
    | ~ spl0_49 ),
    inference(trivial_inequality_removal,[],[f3311]) ).

thf(f3311,plain,
    ( ( $true != $true )
    | ( ( mrel @ sK2 @ sK26 )
      = $true )
    | ~ spl0_49 ),
    inference(superposition,[],[f3222,f2704]) ).

thf(f2704,plain,
    ( ( $true
      = ( mrel @ mactual @ sK26 ) )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f2702]) ).

thf(f2702,plain,
    ( spl0_49
  <=> ( $true
      = ( mrel @ mactual @ sK26 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

thf(f3310,plain,
    ( ~ spl0_43
    | ~ spl0_60
    | ~ spl0_95 ),
    inference(avatar_contradiction_clause,[],[f3309]) ).

thf(f3309,plain,
    ( $false
    | ~ spl0_43
    | ~ spl0_60
    | ~ spl0_95 ),
    inference(trivial_inequality_removal,[],[f3308]) ).

thf(f3308,plain,
    ( ( $false = $true )
    | ~ spl0_43
    | ~ spl0_60
    | ~ spl0_95 ),
    inference(backward_demodulation,[],[f3302,f3307]) ).

thf(f3307,plain,
    ( ( $false
      = ( mrel @ sK2 @ sK17 ) )
    | ~ spl0_43
    | ~ spl0_95 ),
    inference(trivial_inequality_removal,[],[f3305]) ).

thf(f3305,plain,
    ( ( $false = $true )
    | ( $false
      = ( mrel @ sK2 @ sK17 ) )
    | ~ spl0_43
    | ~ spl0_95 ),
    inference(superposition,[],[f2917,f2678]) ).

thf(f2678,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f2676]) ).

thf(f2676,plain,
    ( spl0_43
  <=> ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

thf(f2917,plain,
    ( ! [X4: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f2916]) ).

thf(f2916,plain,
    ( spl0_95
  <=> ! [X4: mworld] :
        ( ( $false
          = ( mrel @ sK2 @ X4 ) )
        | ( $true
          = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

thf(f3302,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK17 ) )
    | ~ spl0_60 ),
    inference(trivial_inequality_removal,[],[f3296]) ).

thf(f3296,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK17 ) )
    | ~ spl0_60 ),
    inference(superposition,[],[f3222,f2754]) ).

thf(f2754,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f2752]) ).

thf(f2752,plain,
    ( spl0_60
  <=> ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

thf(f3295,plain,
    ( ~ spl0_46
    | ~ spl0_52
    | ~ spl0_99 ),
    inference(avatar_contradiction_clause,[],[f3294]) ).

thf(f3294,plain,
    ( $false
    | ~ spl0_46
    | ~ spl0_52
    | ~ spl0_99 ),
    inference(trivial_inequality_removal,[],[f3293]) ).

thf(f3293,plain,
    ( ( $false = $true )
    | ~ spl0_46
    | ~ spl0_52
    | ~ spl0_99 ),
    inference(forward_demodulation,[],[f3287,f3264]) ).

thf(f3264,plain,
    ( ( ( mrel @ sK2 @ sK16 )
      = $false )
    | ~ spl0_46
    | ~ spl0_99 ),
    inference(trivial_inequality_removal,[],[f3262]) ).

thf(f3262,plain,
    ( ( ( mrel @ sK2 @ sK16 )
      = $false )
    | ( $false = $true )
    | ~ spl0_46
    | ~ spl0_99 ),
    inference(superposition,[],[f2690,f2930]) ).

thf(f2930,plain,
    ( ! [X4: mworld] :
        ( ( $true
          = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        | ( $false
          = ( mrel @ sK2 @ X4 ) ) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f2929]) ).

thf(f2929,plain,
    ( spl0_99
  <=> ! [X4: mworld] :
        ( ( $false
          = ( mrel @ sK2 @ X4 ) )
        | ( $true
          = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

thf(f2690,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f2688]) ).

thf(f2688,plain,
    ( spl0_46
  <=> ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

thf(f3287,plain,
    ( ( ( mrel @ sK2 @ sK16 )
      = $true )
    | ~ spl0_52 ),
    inference(trivial_inequality_removal,[],[f3281]) ).

thf(f3281,plain,
    ( ( ( mrel @ sK2 @ sK16 )
      = $true )
    | ( $true != $true )
    | ~ spl0_52 ),
    inference(superposition,[],[f3222,f2718]) ).

thf(f2718,plain,
    ( ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f2716]) ).

thf(f2716,plain,
    ( spl0_52
  <=> ( $true
      = ( mrel @ mactual @ sK16 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

thf(f3218,plain,
    ( spl0_104
    | spl0_107
    | spl0_101
    | spl0_110 ),
    inference(avatar_split_clause,[],[f220,f3057,f2937,f3000,f2949]) ).

thf(f220,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f219]) ).

thf(f219,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f218]) ).

thf(f218,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f217]) ).

thf(f217,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f215]) ).

thf(f215,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f213]) ).

thf(f213,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f212]) ).

thf(f212,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f211]) ).

thf(f211,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f210]) ).

thf(f210,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f208]) ).

thf(f208,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f206]) ).

thf(f206,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f204]) ).

thf(f204,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f202]) ).

thf(f202,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f201]) ).

thf(f201,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f200]) ).

thf(f200,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f199]) ).

thf(f199,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f198]) ).

thf(f198,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
          @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
    inference(pi_clausification,[],[f197]) ).

thf(f197,plain,
    ! [X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f196]) ).

thf(f196,plain,
    ! [X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X1 ) ) ),
    inference(pi_clausification,[],[f195]) ).

thf(f195,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $true )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f193]) ).

thf(f193,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f191]) ).

thf(f191,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f189]) ).

thf(f189,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f187]) ).

thf(f187,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f185]) ).

thf(f185,plain,
    ( ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f183]) ).

thf(f183,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f182]) ).

thf(f182,plain,
    ( ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) ) )
      = $true )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f181]) ).

thf(f181,plain,
    ( ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) )
    = $true ),
    inference(not_proxy_clausification,[],[f179]) ).

thf(f179,plain,
    ( ( ~ ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f178]) ).

thf(f3217,plain,
    ( spl0_107
    | spl0_101
    | spl0_103
    | spl0_110 ),
    inference(avatar_split_clause,[],[f223,f3057,f2945,f2937,f3000]) ).

thf(f223,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f222]) ).

thf(f222,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f221]) ).

thf(f221,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f216]) ).

thf(f216,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f215]) ).

thf(f3216,plain,
    ( spl0_102
    | spl0_107
    | spl0_101
    | spl0_110 ),
    inference(avatar_split_clause,[],[f226,f3057,f2937,f3000,f2941]) ).

thf(f226,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f225]) ).

thf(f225,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f224]) ).

thf(f224,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(pi_clausification,[],[f214]) ).

thf(f214,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f213]) ).

thf(f3215,plain,
    ( spl0_100
    | spl0_110
    | spl0_107
    | spl0_104 ),
    inference(avatar_split_clause,[],[f236,f2949,f3000,f3057,f2933]) ).

thf(f236,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f235]) ).

thf(f235,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f234]) ).

thf(f234,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f233]) ).

thf(f233,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f231]) ).

thf(f231,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f230]) ).

thf(f230,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f229]) ).

thf(f229,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f228]) ).

thf(f228,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f209]) ).

thf(f209,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f208]) ).

thf(f3214,plain,
    ( spl0_103
    | spl0_100
    | spl0_107
    | spl0_110 ),
    inference(avatar_split_clause,[],[f239,f3057,f3000,f2933,f2945]) ).

thf(f239,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f238]) ).

thf(f238,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f237]) ).

thf(f237,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f232]) ).

thf(f232,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f231]) ).

thf(f3213,plain,
    ( spl0_107
    | spl0_100
    | spl0_102
    | spl0_110 ),
    inference(avatar_split_clause,[],[f245,f3057,f2941,f2933,f3000]) ).

thf(f245,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f244]) ).

thf(f244,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f243]) ).

thf(f243,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f242]) ).

thf(f242,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f241]) ).

thf(f241,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f240]) ).

thf(f240,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f227]) ).

thf(f227,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f209]) ).

thf(f3212,plain,
    ( spl0_107
    | spl0_99
    | spl0_110
    | spl0_104 ),
    inference(avatar_split_clause,[],[f255,f2949,f3057,f2929,f3000]) ).

thf(f255,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f254]) ).

thf(f254,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f253]) ).

thf(f253,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f252]) ).

thf(f252,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f251]) ).

thf(f251,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f249]) ).

thf(f249,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f248]) ).

thf(f248,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f247]) ).

thf(f247,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f207]) ).

thf(f207,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f206]) ).

thf(f3211,plain,
    ( spl0_99
    | spl0_107
    | spl0_110
    | spl0_103 ),
    inference(avatar_split_clause,[],[f259,f2945,f3057,f3000,f2929]) ).

thf(f259,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f258]) ).

thf(f258,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f257]) ).

thf(f257,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f256]) ).

thf(f256,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f250]) ).

thf(f250,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f249]) ).

thf(f3210,plain,
    ( spl0_110
    | spl0_99
    | spl0_102
    | spl0_107 ),
    inference(avatar_split_clause,[],[f265,f3000,f2941,f2929,f3057]) ).

thf(f265,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f264]) ).

thf(f264,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f263]) ).

thf(f263,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f262]) ).

thf(f262,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f261]) ).

thf(f261,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f260]) ).

thf(f260,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f246]) ).

thf(f246,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f207]) ).

thf(f3209,plain,
    ( spl0_110
    | spl0_104
    | spl0_107
    | spl0_95 ),
    inference(avatar_split_clause,[],[f275,f2916,f3000,f2949,f3057]) ).

thf(f275,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f274]) ).

thf(f274,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f273]) ).

thf(f273,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f272]) ).

thf(f272,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f270]) ).

thf(f270,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f268]) ).

thf(f268,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f267]) ).

thf(f267,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f266]) ).

thf(f266,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f205]) ).

thf(f205,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f204]) ).

thf(f3208,plain,
    ( spl0_110
    | spl0_103
    | spl0_95
    | spl0_107 ),
    inference(avatar_split_clause,[],[f278,f3000,f2916,f2945,f3057]) ).

thf(f278,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f277]) ).

thf(f277,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f276]) ).

thf(f276,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f271]) ).

thf(f271,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f270]) ).

thf(f3207,plain,
    ( spl0_102
    | spl0_110
    | spl0_95
    | spl0_107 ),
    inference(avatar_split_clause,[],[f281,f3000,f2916,f3057,f2941]) ).

thf(f281,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f280]) ).

thf(f280,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f279]) ).

thf(f279,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f269]) ).

thf(f269,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f268]) ).

thf(f3206,plain,
    ( spl0_110
    | spl0_101
    | spl0_98
    | spl0_107 ),
    inference(avatar_split_clause,[],[f293,f3000,f2925,f2937,f3057]) ).

thf(f293,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f292]) ).

thf(f292,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f291]) ).

thf(f291,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(pi_clausification,[],[f290]) ).

thf(f290,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f289]) ).

thf(f289,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f288]) ).

thf(f288,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f287]) ).

thf(f287,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f285]) ).

thf(f285,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f283]) ).

thf(f283,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f203]) ).

thf(f203,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f202]) ).

thf(f3205,plain,
    ( spl0_107
    | spl0_110
    | spl0_98
    | spl0_100 ),
    inference(avatar_split_clause,[],[f299,f2933,f2925,f3057,f3000]) ).

thf(f299,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f298]) ).

thf(f298,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f297]) ).

thf(f297,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f296]) ).

thf(f296,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f295]) ).

thf(f295,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f294]) ).

thf(f294,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f286]) ).

thf(f286,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f285]) ).

thf(f3204,plain,
    ( spl0_110
    | spl0_107
    | spl0_99
    | spl0_98 ),
    inference(avatar_split_clause,[],[f305,f2925,f2929,f3000,f3057]) ).

thf(f305,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f304]) ).

thf(f304,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f303]) ).

thf(f303,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f302]) ).

thf(f302,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f301]) ).

thf(f301,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f300]) ).

thf(f300,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f284]) ).

thf(f284,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f283]) ).

thf(f3203,plain,
    ( spl0_107
    | spl0_95
    | spl0_110
    | spl0_98 ),
    inference(avatar_split_clause,[],[f311,f2925,f3057,f2916,f3000]) ).

thf(f311,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f310]) ).

thf(f310,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f309]) ).

thf(f309,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f308]) ).

thf(f308,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f307]) ).

thf(f307,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f306]) ).

thf(f306,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f282]) ).

thf(f282,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f203]) ).

thf(f3202,plain,
    ( spl0_101
    | spl0_107
    | spl0_109
    | spl0_104 ),
    inference(avatar_split_clause,[],[f336,f2949,f3038,f3000,f2937]) ).

thf(f336,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f335]) ).

thf(f335,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f334]) ).

thf(f334,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f333]) ).

thf(f333,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f332]) ).

thf(f332,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f330]) ).

thf(f330,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f329]) ).

thf(f329,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f328]) ).

thf(f328,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f326]) ).

thf(f326,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f324]) ).

thf(f324,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f322]) ).

thf(f322,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f320]) ).

thf(f320,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f318]) ).

thf(f318,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f317]) ).

thf(f317,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f316]) ).

thf(f316,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f315]) ).

thf(f315,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f314]) ).

thf(f314,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f313]) ).

thf(f313,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f312]) ).

thf(f312,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f194]) ).

thf(f194,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f193]) ).

thf(f3201,plain,
    ( spl0_107
    | spl0_104
    | spl0_109
    | spl0_100 ),
    inference(avatar_split_clause,[],[f340,f2933,f3038,f2949,f3000]) ).

thf(f340,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f339]) ).

thf(f339,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f338]) ).

thf(f338,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f337]) ).

thf(f337,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true ) ),
    inference(pi_clausification,[],[f331]) ).

thf(f331,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f330]) ).

thf(f3200,plain,
    ( spl0_107
    | spl0_101
    | spl0_103
    | spl0_109 ),
    inference(avatar_split_clause,[],[f348,f3038,f2945,f2937,f3000]) ).

thf(f348,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f347]) ).

thf(f347,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f346]) ).

thf(f346,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(pi_clausification,[],[f345]) ).

thf(f345,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f344]) ).

thf(f344,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f343]) ).

thf(f343,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f342]) ).

thf(f342,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f327]) ).

thf(f327,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f326]) ).

thf(f3199,plain,
    ( spl0_100
    | spl0_107
    | spl0_103
    | spl0_109 ),
    inference(avatar_split_clause,[],[f354,f3038,f2945,f3000,f2933]) ).

thf(f354,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f353]) ).

thf(f353,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f352]) ).

thf(f352,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f351]) ).

thf(f351,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f350]) ).

thf(f350,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f349]) ).

thf(f349,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f341]) ).

thf(f341,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f327]) ).

thf(f3198,plain,
    ( spl0_99
    | spl0_109
    | spl0_107
    | spl0_104 ),
    inference(avatar_split_clause,[],[f362,f2949,f3000,f3038,f2929]) ).

thf(f362,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f361]) ).

thf(f361,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f360]) ).

thf(f360,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f359]) ).

thf(f359,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f358]) ).

thf(f358,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f357]) ).

thf(f357,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f356]) ).

thf(f356,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f325]) ).

thf(f325,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f324]) ).

thf(f3197,plain,
    ( spl0_107
    | spl0_109
    | spl0_103
    | spl0_99 ),
    inference(avatar_split_clause,[],[f368,f2929,f2945,f3038,f3000]) ).

thf(f368,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f367]) ).

thf(f367,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f366]) ).

thf(f366,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f365]) ).

thf(f365,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f364]) ).

thf(f364,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f363]) ).

thf(f363,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f355]) ).

thf(f355,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f325]) ).

thf(f3196,plain,
    ( spl0_101
    | spl0_102
    | spl0_109
    | spl0_107 ),
    inference(avatar_split_clause,[],[f378,f3000,f3038,f2941,f2937]) ).

thf(f378,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f377]) ).

thf(f377,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f376]) ).

thf(f376,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f375]) ).

thf(f375,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f374]) ).

thf(f374,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f373]) ).

thf(f373,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f372]) ).

thf(f372,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f370]) ).

thf(f370,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f323]) ).

thf(f323,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f322]) ).

thf(f3195,plain,
    ( spl0_100
    | spl0_109
    | spl0_102
    | spl0_107 ),
    inference(avatar_split_clause,[],[f384,f3000,f2941,f3038,f2933]) ).

thf(f384,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f383]) ).

thf(f383,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f382]) ).

thf(f382,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f381]) ).

thf(f381,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f380]) ).

thf(f380,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f379]) ).

thf(f379,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f371]) ).

thf(f371,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f370]) ).

thf(f3194,plain,
    ( spl0_109
    | spl0_99
    | spl0_102
    | spl0_107 ),
    inference(avatar_split_clause,[],[f390,f3000,f2941,f2929,f3038]) ).

thf(f390,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f389]) ).

thf(f389,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f388]) ).

thf(f388,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f387]) ).

thf(f387,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f386]) ).

thf(f386,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f385]) ).

thf(f385,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f369]) ).

thf(f369,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f323]) ).

thf(f3193,plain,
    ( spl0_109
    | spl0_95
    | spl0_104
    | spl0_107 ),
    inference(avatar_split_clause,[],[f400,f3000,f2949,f2916,f3038]) ).

thf(f400,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f399]) ).

thf(f399,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f398]) ).

thf(f398,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f397]) ).

thf(f397,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f395]) ).

thf(f395,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f393]) ).

thf(f393,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f392]) ).

thf(f392,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f391]) ).

thf(f391,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f321]) ).

thf(f321,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f320]) ).

thf(f3192,plain,
    ( spl0_107
    | spl0_103
    | spl0_109
    | spl0_95 ),
    inference(avatar_split_clause,[],[f403,f2916,f3038,f2945,f3000]) ).

thf(f403,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f402]) ).

thf(f402,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f401]) ).

thf(f401,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f396]) ).

thf(f396,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f395]) ).

thf(f3191,plain,
    ( spl0_102
    | spl0_95
    | spl0_107
    | spl0_109 ),
    inference(avatar_split_clause,[],[f406,f3038,f3000,f2916,f2941]) ).

thf(f406,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f405]) ).

thf(f405,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f404]) ).

thf(f404,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f394]) ).

thf(f394,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f393]) ).

thf(f3190,plain,
    ( spl0_98
    | spl0_109
    | spl0_107
    | spl0_101 ),
    inference(avatar_split_clause,[],[f418,f2937,f3000,f3038,f2925]) ).

thf(f418,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f417]) ).

thf(f417,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f416]) ).

thf(f416,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f415]) ).

thf(f415,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f413]) ).

thf(f413,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f411]) ).

thf(f411,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f409]) ).

thf(f409,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f408]) ).

thf(f408,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f407]) ).

thf(f407,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f319]) ).

thf(f319,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f318]) ).

thf(f3189,plain,
    ( spl0_107
    | spl0_100
    | spl0_109
    | spl0_98 ),
    inference(avatar_split_clause,[],[f421,f2925,f3038,f2933,f3000]) ).

thf(f421,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f420]) ).

thf(f420,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f419]) ).

thf(f419,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f414]) ).

thf(f414,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f413]) ).

thf(f3188,plain,
    ( spl0_109
    | spl0_99
    | spl0_98
    | spl0_107 ),
    inference(avatar_split_clause,[],[f424,f3000,f2925,f2929,f3038]) ).

thf(f424,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f423]) ).

thf(f423,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f422]) ).

thf(f422,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f412]) ).

thf(f412,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f411]) ).

thf(f3187,plain,
    ( spl0_95
    | spl0_107
    | spl0_98
    | spl0_109 ),
    inference(avatar_split_clause,[],[f427,f3038,f2925,f3000,f2916]) ).

thf(f427,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f426]) ).

thf(f426,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f425]) ).

thf(f425,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f410]) ).

thf(f410,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f409]) ).

thf(f3186,plain,
    ( spl0_106
    | spl0_104
    | spl0_110
    | spl0_101 ),
    inference(avatar_split_clause,[],[f454,f2937,f3057,f2949,f2981]) ).

thf(f454,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f453]) ).

thf(f453,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f452]) ).

thf(f452,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f451]) ).

thf(f451,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
    inference(pi_clausification,[],[f450]) ).

thf(f450,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f448]) ).

thf(f448,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f447]) ).

thf(f447,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f446]) ).

thf(f446,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f445]) ).

thf(f445,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f443]) ).

thf(f443,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f441]) ).

thf(f441,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f439]) ).

thf(f439,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f438]) ).

thf(f438,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
          @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f437]) ).

thf(f437,plain,
    ! [X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f435]) ).

thf(f435,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f433]) ).

thf(f433,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f432]) ).

thf(f432,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f430]) ).

thf(f430,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f429]) ).

thf(f429,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f428]) ).

thf(f428,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f192]) ).

thf(f192,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f191]) ).

thf(f3185,plain,
    ( spl0_106
    | spl0_110
    | spl0_104
    | spl0_100 ),
    inference(avatar_split_clause,[],[f458,f2933,f2949,f3057,f2981]) ).

thf(f458,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f457]) ).

thf(f457,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f456]) ).

thf(f456,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f455]) ).

thf(f455,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f449]) ).

thf(f449,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f448]) ).

thf(f3184,plain,
    ( spl0_110
    | spl0_101
    | spl0_103
    | spl0_106 ),
    inference(avatar_split_clause,[],[f467,f2981,f2945,f2937,f3057]) ).

thf(f467,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f466]) ).

thf(f466,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f465]) ).

thf(f465,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f464]) ).

thf(f464,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f463]) ).

thf(f463,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f462]) ).

thf(f462,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f461]) ).

thf(f461,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f460]) ).

thf(f460,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f444]) ).

thf(f444,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f443]) ).

thf(f3183,plain,
    ( spl0_103
    | spl0_106
    | spl0_100
    | spl0_110 ),
    inference(avatar_split_clause,[],[f474,f3057,f2933,f2981,f2945]) ).

thf(f474,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f473]) ).

thf(f473,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f472]) ).

thf(f472,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f471]) ).

thf(f471,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f470]) ).

thf(f470,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f469]) ).

thf(f469,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f468]) ).

thf(f468,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f459]) ).

thf(f459,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f444]) ).

thf(f3182,plain,
    ( spl0_99
    | spl0_104
    | spl0_106
    | spl0_110 ),
    inference(avatar_split_clause,[],[f483,f3057,f2981,f2949,f2929]) ).

thf(f483,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f482]) ).

thf(f482,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f481]) ).

thf(f481,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f480]) ).

thf(f480,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f478]) ).

thf(f478,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f477]) ).

thf(f477,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f476]) ).

thf(f476,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f475]) ).

thf(f475,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f442]) ).

thf(f442,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f441]) ).

thf(f3181,plain,
    ( spl0_103
    | spl0_106
    | spl0_99
    | spl0_110 ),
    inference(avatar_split_clause,[],[f486,f3057,f2929,f2981,f2945]) ).

thf(f486,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f485]) ).

thf(f485,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f484]) ).

thf(f484,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f479]) ).

thf(f479,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f478]) ).

thf(f3180,plain,
    ( spl0_101
    | spl0_106
    | spl0_102
    | spl0_110 ),
    inference(avatar_split_clause,[],[f497,f3057,f2941,f2981,f2937]) ).

thf(f497,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f496]) ).

thf(f496,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f495]) ).

thf(f495,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f494]) ).

thf(f494,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f493]) ).

thf(f493,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f491]) ).

thf(f491,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f490]) ).

thf(f490,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f489]) ).

thf(f489,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f487]) ).

thf(f487,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f440]) ).

thf(f440,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f439]) ).

thf(f3179,plain,
    ( spl0_100
    | spl0_110
    | spl0_102
    | spl0_106 ),
    inference(avatar_split_clause,[],[f501,f2981,f2941,f3057,f2933]) ).

thf(f501,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f500]) ).

thf(f500,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f499]) ).

thf(f499,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f498]) ).

thf(f498,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f492]) ).

thf(f492,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f491]) ).

thf(f3178,plain,
    ( spl0_106
    | spl0_102
    | spl0_99
    | spl0_110 ),
    inference(avatar_split_clause,[],[f507,f3057,f2929,f2941,f2981]) ).

thf(f507,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f506]) ).

thf(f506,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f505]) ).

thf(f505,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f504]) ).

thf(f504,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f503]) ).

thf(f503,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f502]) ).

thf(f502,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f488]) ).

thf(f488,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f487]) ).

thf(f3177,plain,
    ( spl0_95
    | spl0_106
    | spl0_110
    | spl0_104 ),
    inference(avatar_split_clause,[],[f520,f2949,f3057,f2981,f2916]) ).

thf(f520,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f519]) ).

thf(f519,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f518]) ).

thf(f518,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(pi_clausification,[],[f517]) ).

thf(f517,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f516]) ).

thf(f516,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f514]) ).

thf(f514,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f513]) ).

thf(f513,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f512]) ).

thf(f512,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f510]) ).

thf(f510,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f509]) ).

thf(f509,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f508]) ).

thf(f508,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
          @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f436]) ).

thf(f436,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f435]) ).

thf(f3176,plain,
    ( spl0_103
    | spl0_110
    | spl0_106
    | spl0_95 ),
    inference(avatar_split_clause,[],[f524,f2916,f2981,f3057,f2945]) ).

thf(f524,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f523]) ).

thf(f523,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f522]) ).

thf(f522,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(pi_clausification,[],[f521]) ).

thf(f521,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f515]) ).

thf(f515,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f514]) ).

thf(f3175,plain,
    ( spl0_102
    | spl0_110
    | spl0_95
    | spl0_106 ),
    inference(avatar_split_clause,[],[f530,f2981,f2916,f3057,f2941]) ).

thf(f530,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f529]) ).

thf(f529,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f528]) ).

thf(f528,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f527]) ).

thf(f527,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f526]) ).

thf(f526,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f525]) ).

thf(f525,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f511]) ).

thf(f511,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f510]) ).

thf(f3174,plain,
    ( spl0_101
    | spl0_106
    | spl0_110
    | spl0_98 ),
    inference(avatar_split_clause,[],[f545,f2925,f3057,f2981,f2937]) ).

thf(f545,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f544]) ).

thf(f544,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f543]) ).

thf(f543,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f542]) ).

thf(f542,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f540]) ).

thf(f540,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f538]) ).

thf(f538,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f537]) ).

thf(f537,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f535]) ).

thf(f535,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f534]) ).

thf(f534,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f533]) ).

thf(f533,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f532]) ).

thf(f532,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f531]) ).

thf(f531,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f434]) ).

thf(f434,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f433]) ).

thf(f3173,plain,
    ( spl0_106
    | spl0_98
    | spl0_110
    | spl0_100 ),
    inference(avatar_split_clause,[],[f548,f2933,f3057,f2925,f2981]) ).

thf(f548,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f547]) ).

thf(f547,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f546]) ).

thf(f546,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f541]) ).

thf(f541,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f540]) ).

thf(f3172,plain,
    ( spl0_99
    | spl0_98
    | spl0_106
    | spl0_110 ),
    inference(avatar_split_clause,[],[f551,f3057,f2981,f2925,f2929]) ).

thf(f551,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f550]) ).

thf(f550,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f549]) ).

thf(f549,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f539]) ).

thf(f539,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f538]) ).

thf(f3171,plain,
    ( spl0_106
    | spl0_110
    | spl0_95
    | spl0_98 ),
    inference(avatar_split_clause,[],[f555,f2925,f2916,f3057,f2981]) ).

thf(f555,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f554]) ).

thf(f554,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f553]) ).

thf(f553,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f552]) ).

thf(f552,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f536]) ).

thf(f536,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X3 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f535]) ).

thf(f3170,plain,
    ( spl0_106
    | spl0_101
    | spl0_104
    | spl0_109 ),
    inference(avatar_split_clause,[],[f577,f3038,f2949,f2937,f2981]) ).

thf(f577,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f576]) ).

thf(f576,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f575]) ).

thf(f575,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f574]) ).

thf(f574,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f573]) ).

thf(f573,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f572]) ).

thf(f572,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f571]) ).

thf(f571,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f569]) ).

thf(f569,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f568]) ).

thf(f568,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f566]) ).

thf(f566,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f564]) ).

thf(f564,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f562]) ).

thf(f562,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f560]) ).

thf(f560,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f559]) ).

thf(f559,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f558]) ).

thf(f558,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f556]) ).

thf(f556,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f431]) ).

thf(f431,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f430]) ).

thf(f3169,plain,
    ( spl0_104
    | spl0_100
    | spl0_106
    | spl0_109 ),
    inference(avatar_split_clause,[],[f583,f3038,f2981,f2933,f2949]) ).

thf(f583,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f582]) ).

thf(f582,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f581]) ).

thf(f581,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true ) ),
    inference(pi_clausification,[],[f580]) ).

thf(f580,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f579]) ).

thf(f579,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f578]) ).

thf(f578,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f570]) ).

thf(f570,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f569]) ).

thf(f3168,plain,
    ( spl0_106
    | spl0_101
    | spl0_109
    | spl0_103 ),
    inference(avatar_split_clause,[],[f592,f2945,f3038,f2937,f2981]) ).

thf(f592,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f591]) ).

thf(f591,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f590]) ).

thf(f590,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(pi_clausification,[],[f589]) ).

thf(f589,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f588]) ).

thf(f588,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f587]) ).

thf(f587,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f586]) ).

thf(f586,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f585]) ).

thf(f585,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f567]) ).

thf(f567,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f566]) ).

thf(f3167,plain,
    ( spl0_106
    | spl0_109
    | spl0_100
    | spl0_103 ),
    inference(avatar_split_clause,[],[f599,f2945,f2933,f3038,f2981]) ).

thf(f599,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f598]) ).

thf(f598,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f597]) ).

thf(f597,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f596]) ).

thf(f596,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f595]) ).

thf(f595,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(pi_clausification,[],[f594]) ).

thf(f594,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f593]) ).

thf(f593,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f584]) ).

thf(f584,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f567]) ).

thf(f3166,plain,
    ( spl0_104
    | spl0_109
    | spl0_106
    | spl0_99 ),
    inference(avatar_split_clause,[],[f608,f2929,f2981,f3038,f2949]) ).

thf(f608,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f607]) ).

thf(f607,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f606]) ).

thf(f606,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f605]) ).

thf(f605,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f604]) ).

thf(f604,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f602]) ).

thf(f602,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f601]) ).

thf(f601,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f600]) ).

thf(f600,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f565]) ).

thf(f565,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f564]) ).

thf(f3165,plain,
    ( spl0_103
    | spl0_106
    | spl0_109
    | spl0_99 ),
    inference(avatar_split_clause,[],[f612,f2929,f3038,f2981,f2945]) ).

thf(f612,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f611]) ).

thf(f611,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f610]) ).

thf(f610,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f609]) ).

thf(f609,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f603]) ).

thf(f603,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f602]) ).

thf(f3164,plain,
    ( spl0_101
    | spl0_102
    | spl0_109
    | spl0_106 ),
    inference(avatar_split_clause,[],[f623,f2981,f3038,f2941,f2937]) ).

thf(f623,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f622]) ).

thf(f622,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f621]) ).

thf(f621,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f620]) ).

thf(f620,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f618]) ).

thf(f618,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f616]) ).

thf(f616,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f615]) ).

thf(f615,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f614]) ).

thf(f614,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f613]) ).

thf(f613,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f563]) ).

thf(f563,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f562]) ).

thf(f3163,plain,
    ( spl0_102
    | spl0_109
    | spl0_106
    | spl0_100 ),
    inference(avatar_split_clause,[],[f626,f2933,f2981,f3038,f2941]) ).

thf(f626,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f625]) ).

thf(f625,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f624]) ).

thf(f624,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true ) ),
    inference(pi_clausification,[],[f619]) ).

thf(f619,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f618]) ).

thf(f3162,plain,
    ( spl0_106
    | spl0_99
    | spl0_102
    | spl0_109 ),
    inference(avatar_split_clause,[],[f629,f3038,f2941,f2929,f2981]) ).

thf(f629,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f628]) ).

thf(f628,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f627]) ).

thf(f627,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f617]) ).

thf(f617,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f616]) ).

thf(f3161,plain,
    ( spl0_106
    | spl0_95
    | spl0_104
    | spl0_109 ),
    inference(avatar_split_clause,[],[f640,f3038,f2949,f2916,f2981]) ).

thf(f640,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f639]) ).

thf(f639,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f638]) ).

thf(f638,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f637]) ).

thf(f637,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f635]) ).

thf(f635,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f634]) ).

thf(f634,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f633]) ).

thf(f633,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f632]) ).

thf(f632,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f630]) ).

thf(f630,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f561]) ).

thf(f561,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f560]) ).

thf(f3160,plain,
    ( spl0_106
    | spl0_109
    | spl0_103
    | spl0_95 ),
    inference(avatar_split_clause,[],[f643,f2916,f2945,f3038,f2981]) ).

thf(f643,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f642]) ).

thf(f642,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f641]) ).

thf(f641,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f636]) ).

thf(f636,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f635]) ).

thf(f3159,plain,
    ( spl0_106
    | spl0_102
    | spl0_109
    | spl0_95 ),
    inference(avatar_split_clause,[],[f649,f2916,f3038,f2941,f2981]) ).

thf(f649,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f648]) ).

thf(f648,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f647]) ).

thf(f647,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f646]) ).

thf(f646,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f645]) ).

thf(f645,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f644]) ).

thf(f644,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f631]) ).

thf(f631,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f630]) ).

thf(f3158,plain,
    ( spl0_106
    | spl0_109
    | spl0_101
    | spl0_98 ),
    inference(avatar_split_clause,[],[f664,f2925,f2937,f3038,f2981]) ).

thf(f664,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f663]) ).

thf(f663,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f662]) ).

thf(f662,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f661]) ).

thf(f661,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f659]) ).

thf(f659,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f658]) ).

thf(f658,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f657]) ).

thf(f657,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f656]) ).

thf(f656,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f654]) ).

thf(f654,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f653]) ).

thf(f653,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f652]) ).

thf(f652,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f651]) ).

thf(f651,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f557]) ).

thf(f557,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f556]) ).

thf(f3157,plain,
    ( spl0_98
    | spl0_100
    | spl0_106
    | spl0_109 ),
    inference(avatar_split_clause,[],[f667,f3038,f2981,f2933,f2925]) ).

thf(f667,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f666]) ).

thf(f666,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f665]) ).

thf(f665,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(pi_clausification,[],[f660]) ).

thf(f660,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f659]) ).

thf(f3156,plain,
    ( spl0_109
    | spl0_99
    | spl0_98
    | spl0_106 ),
    inference(avatar_split_clause,[],[f673,f2981,f2925,f2929,f3038]) ).

thf(f673,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f672]) ).

thf(f672,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f671]) ).

thf(f671,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f670]) ).

thf(f670,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f669]) ).

thf(f669,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f668]) ).

thf(f668,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f655]) ).

thf(f655,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f654]) ).

thf(f3155,plain,
    ( spl0_106
    | spl0_95
    | spl0_109
    | spl0_98 ),
    inference(avatar_split_clause,[],[f682,f2925,f3038,f2916,f2981]) ).

thf(f682,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f681]) ).

thf(f681,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f680]) ).

thf(f680,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f679]) ).

thf(f679,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f678]) ).

thf(f678,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f677]) ).

thf(f677,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f676]) ).

thf(f676,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(pi_clausification,[],[f675]) ).

thf(f675,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f674]) ).

thf(f674,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f650]) ).

thf(f650,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f557]) ).

thf(f3154,plain,
    ( spl0_104
    | spl0_110
    | spl0_101
    | spl0_105 ),
    inference(avatar_split_clause,[],[f709,f2962,f2937,f3057,f2949]) ).

thf(f709,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f708]) ).

thf(f708,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f707]) ).

thf(f707,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f706]) ).

thf(f706,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f705]) ).

thf(f705,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f703]) ).

thf(f703,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f702]) ).

thf(f702,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f701]) ).

thf(f701,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f699]) ).

thf(f699,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f697]) ).

thf(f697,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f695]) ).

thf(f695,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f694]) ).

thf(f694,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f693]) ).

thf(f693,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f692]) ).

thf(f692,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f691]) ).

thf(f691,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f689]) ).

thf(f689,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f687]) ).

thf(f687,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f686]) ).

thf(f686,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
          @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f685]) ).

thf(f685,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $true )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f684]) ).

thf(f684,plain,
    ( ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f190]) ).

thf(f190,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f189]) ).

thf(f3153,plain,
    ( spl0_101
    | spl0_105
    | spl0_110
    | spl0_103 ),
    inference(avatar_split_clause,[],[f713,f2945,f3057,f2962,f2937]) ).

thf(f713,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f712]) ).

thf(f712,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f711]) ).

thf(f711,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f710]) ).

thf(f710,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f704]) ).

thf(f704,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f703]) ).

thf(f3152,plain,
    ( spl0_110
    | spl0_101
    | spl0_102
    | spl0_105 ),
    inference(avatar_split_clause,[],[f719,f2962,f2941,f2937,f3057]) ).

thf(f719,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f718]) ).

thf(f718,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f717]) ).

thf(f717,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f716]) ).

thf(f716,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f715]) ).

thf(f715,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f714]) ).

thf(f714,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f700]) ).

thf(f700,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f699]) ).

thf(f3151,plain,
    ( spl0_110
    | spl0_105
    | spl0_104
    | spl0_100 ),
    inference(avatar_split_clause,[],[f729,f2933,f2949,f2962,f3057]) ).

thf(f729,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f728]) ).

thf(f728,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f727]) ).

thf(f727,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f726]) ).

thf(f726,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f725]) ).

thf(f725,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f723]) ).

thf(f723,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f722]) ).

thf(f722,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f721]) ).

thf(f721,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f698]) ).

thf(f698,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f697]) ).

thf(f3150,plain,
    ( spl0_103
    | spl0_105
    | spl0_110
    | spl0_100 ),
    inference(avatar_split_clause,[],[f733,f2933,f3057,f2962,f2945]) ).

thf(f733,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f732]) ).

thf(f732,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f731]) ).

thf(f731,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f730]) ).

thf(f730,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f724]) ).

thf(f724,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f723]) ).

thf(f3149,plain,
    ( spl0_100
    | spl0_110
    | spl0_105
    | spl0_102 ),
    inference(avatar_split_clause,[],[f739,f2941,f2962,f3057,f2933]) ).

thf(f739,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f738]) ).

thf(f738,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f737]) ).

thf(f737,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f736]) ).

thf(f736,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f735]) ).

thf(f735,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f734]) ).

thf(f734,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f720]) ).

thf(f720,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f698]) ).

thf(f3148,plain,
    ( spl0_98
    | spl0_101
    | spl0_110
    | spl0_105 ),
    inference(avatar_split_clause,[],[f747,f2962,f3057,f2937,f2925]) ).

thf(f747,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f746]) ).

thf(f746,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f745]) ).

thf(f745,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f744]) ).

thf(f744,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f743]) ).

thf(f743,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f742]) ).

thf(f742,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f741]) ).

thf(f741,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f696]) ).

thf(f696,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f695]) ).

thf(f3147,plain,
    ( spl0_110
    | spl0_98
    | spl0_105
    | spl0_100 ),
    inference(avatar_split_clause,[],[f753,f2933,f2962,f2925,f3057]) ).

thf(f753,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f752]) ).

thf(f752,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f751]) ).

thf(f751,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f750]) ).

thf(f750,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f749]) ).

thf(f749,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f748]) ).

thf(f748,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f740]) ).

thf(f740,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f696]) ).

thf(f3146,plain,
    ( spl0_110
    | spl0_105
    | spl0_99
    | spl0_104 ),
    inference(avatar_split_clause,[],[f769,f2949,f2929,f2962,f3057]) ).

thf(f769,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f768]) ).

thf(f768,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f767]) ).

thf(f767,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f766]) ).

thf(f766,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f764]) ).

thf(f764,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f763]) ).

thf(f763,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f761]) ).

thf(f761,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f759]) ).

thf(f759,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f758]) ).

thf(f758,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f757]) ).

thf(f757,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f756]) ).

thf(f756,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f755]) ).

thf(f755,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f754]) ).

thf(f754,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f690]) ).

thf(f690,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f689]) ).

thf(f3145,plain,
    ( spl0_110
    | spl0_99
    | spl0_103
    | spl0_105 ),
    inference(avatar_split_clause,[],[f772,f2962,f2945,f2929,f3057]) ).

thf(f772,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f771]) ).

thf(f771,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f770]) ).

thf(f770,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true ) ),
    inference(pi_clausification,[],[f765]) ).

thf(f765,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f764]) ).

thf(f3144,plain,
    ( spl0_110
    | spl0_102
    | spl0_105
    | spl0_99 ),
    inference(avatar_split_clause,[],[f776,f2929,f2962,f2941,f3057]) ).

thf(f776,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f775]) ).

thf(f775,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f774]) ).

thf(f774,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f773]) ).

thf(f773,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f762]) ).

thf(f762,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f761]) ).

thf(f3143,plain,
    ( spl0_98
    | spl0_99
    | spl0_110
    | spl0_105 ),
    inference(avatar_split_clause,[],[f780,f2962,f3057,f2929,f2925]) ).

thf(f780,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f779]) ).

thf(f779,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f778]) ).

thf(f778,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f777]) ).

thf(f777,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f760]) ).

thf(f760,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f759]) ).

thf(f3142,plain,
    ( spl0_104
    | spl0_105
    | spl0_95
    | spl0_110 ),
    inference(avatar_split_clause,[],[f796,f3057,f2916,f2962,f2949]) ).

thf(f796,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f795]) ).

thf(f795,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f794]) ).

thf(f794,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f793]) ).

thf(f793,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f792]) ).

thf(f792,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f791]) ).

thf(f791,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f790]) ).

thf(f790,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f788]) ).

thf(f788,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f786]) ).

thf(f786,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f784]) ).

thf(f784,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f783]) ).

thf(f783,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f782]) ).

thf(f782,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f781]) ).

thf(f781,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f688]) ).

thf(f688,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f687]) ).

thf(f3141,plain,
    ( spl0_95
    | spl0_110
    | spl0_103
    | spl0_105 ),
    inference(avatar_split_clause,[],[f802,f2962,f2945,f3057,f2916]) ).

thf(f802,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f801]) ).

thf(f801,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f800]) ).

thf(f800,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f799]) ).

thf(f799,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f798]) ).

thf(f798,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f797]) ).

thf(f797,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f789]) ).

thf(f789,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f788]) ).

thf(f3140,plain,
    ( spl0_105
    | spl0_95
    | spl0_102
    | spl0_110 ),
    inference(avatar_split_clause,[],[f808,f3057,f2941,f2916,f2962]) ).

thf(f808,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f807]) ).

thf(f807,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f806]) ).

thf(f806,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f805]) ).

thf(f805,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f804]) ).

thf(f804,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f803]) ).

thf(f803,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f787]) ).

thf(f787,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f786]) ).

thf(f3139,plain,
    ( spl0_95
    | spl0_110
    | spl0_105
    | spl0_98 ),
    inference(avatar_split_clause,[],[f814,f2925,f2962,f3057,f2916]) ).

thf(f814,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f813]) ).

thf(f813,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f812]) ).

thf(f812,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f811]) ).

thf(f811,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f810]) ).

thf(f810,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f809]) ).

thf(f809,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f785]) ).

thf(f785,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f784]) ).

thf(f3138,plain,
    ( spl0_109
    | spl0_104
    | spl0_101
    | spl0_105 ),
    inference(avatar_split_clause,[],[f839,f2962,f2937,f2949,f3038]) ).

thf(f839,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f838]) ).

thf(f838,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f837]) ).

thf(f837,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f836]) ).

thf(f836,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
    inference(pi_clausification,[],[f835]) ).

thf(f835,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f834]) ).

thf(f834,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f833]) ).

thf(f833,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f832]) ).

thf(f832,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f831]) ).

thf(f831,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f830]) ).

thf(f830,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
        = $true ) ),
    inference(pi_clausification,[],[f829]) ).

thf(f829,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f828]) ).

thf(f828,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f827]) ).

thf(f827,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f825]) ).

thf(f825,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f823]) ).

thf(f823,plain,
    ( ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f821]) ).

thf(f821,plain,
    ( ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      = $true )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f819]) ).

thf(f819,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f817]) ).

thf(f817,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f815]) ).

thf(f815,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f683]) ).

thf(f683,plain,
    ( ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f190]) ).

thf(f3137,plain,
    ( spl0_103
    | spl0_101
    | spl0_109
    | spl0_105 ),
    inference(avatar_split_clause,[],[f851,f2962,f3038,f2937,f2945]) ).

thf(f851,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f850]) ).

thf(f850,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f849]) ).

thf(f849,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f848]) ).

thf(f848,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f847]) ).

thf(f847,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f846]) ).

thf(f846,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f845]) ).

thf(f845,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f844]) ).

thf(f844,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f843]) ).

thf(f843,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f842]) ).

thf(f842,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
        = $true ) ),
    inference(pi_clausification,[],[f841]) ).

thf(f841,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f840]) ).

thf(f840,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f826]) ).

thf(f826,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f825]) ).

thf(f3136,plain,
    ( spl0_104
    | spl0_100
    | spl0_109
    | spl0_105 ),
    inference(avatar_split_clause,[],[f865,f2962,f3038,f2933,f2949]) ).

thf(f865,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f864]) ).

thf(f864,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f863]) ).

thf(f863,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f862]) ).

thf(f862,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f861]) ).

thf(f861,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f860]) ).

thf(f860,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
    inference(pi_clausification,[],[f859]) ).

thf(f859,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f858]) ).

thf(f858,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f857]) ).

thf(f857,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f856]) ).

thf(f856,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f855]) ).

thf(f855,plain,
    ! [X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f854]) ).

thf(f854,plain,
    ! [X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f853]) ).

thf(f853,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f824]) ).

thf(f824,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f823]) ).

thf(f3135,plain,
    ( spl0_109
    | spl0_105
    | spl0_103
    | spl0_100 ),
    inference(avatar_split_clause,[],[f877,f2933,f2945,f2962,f3038]) ).

thf(f877,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f876]) ).

thf(f876,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f875]) ).

thf(f875,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
    inference(pi_clausification,[],[f874]) ).

thf(f874,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f873]) ).

thf(f873,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f872]) ).

thf(f872,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f871]) ).

thf(f871,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f870]) ).

thf(f870,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f869]) ).

thf(f869,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f868]) ).

thf(f868,plain,
    ! [X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f867]) ).

thf(f867,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f866]) ).

thf(f866,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X1 ) ) ),
    inference(pi_clausification,[],[f852]) ).

thf(f852,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f824]) ).

thf(f3134,plain,
    ( spl0_105
    | spl0_109
    | spl0_101
    | spl0_102 ),
    inference(avatar_split_clause,[],[f891,f2941,f2937,f3038,f2962]) ).

thf(f891,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f890]) ).

thf(f890,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f889]) ).

thf(f889,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f888]) ).

thf(f888,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f886]) ).

thf(f886,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f885]) ).

thf(f885,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f884]) ).

thf(f884,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f883]) ).

thf(f883,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f882]) ).

thf(f882,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f881]) ).

thf(f881,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f880]) ).

thf(f880,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X2 ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f879]) ).

thf(f879,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f878]) ).

thf(f878,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X1 ) ) ),
    inference(pi_clausification,[],[f822]) ).

thf(f822,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f821]) ).

thf(f3133,plain,
    ( spl0_102
    | spl0_105
    | spl0_109
    | spl0_100 ),
    inference(avatar_split_clause,[],[f894,f2933,f3038,f2962,f2941]) ).

thf(f894,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f893]) ).

thf(f893,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f892]) ).

thf(f892,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f887]) ).

thf(f887,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f886]) ).

thf(f3132,plain,
    ( spl0_109
    | spl0_99
    | spl0_105
    | spl0_104 ),
    inference(avatar_split_clause,[],[f910,f2949,f2962,f2929,f3038]) ).

thf(f910,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f909]) ).

thf(f909,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f908]) ).

thf(f908,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f907]) ).

thf(f907,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f906]) ).

thf(f906,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f905]) ).

thf(f905,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f903]) ).

thf(f903,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f902]) ).

thf(f902,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f901]) ).

thf(f901,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f900]) ).

thf(f900,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f899]) ).

thf(f899,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f897]) ).

thf(f897,plain,
    ! [X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f896]) ).

thf(f896,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f895]) ).

thf(f895,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f820]) ).

thf(f820,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f819]) ).

thf(f3131,plain,
    ( spl0_105
    | spl0_109
    | spl0_99
    | spl0_103 ),
    inference(avatar_split_clause,[],[f915,f2945,f2929,f3038,f2962]) ).

thf(f915,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f914]) ).

thf(f914,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f913]) ).

thf(f913,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f912]) ).

thf(f912,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f911]) ).

thf(f911,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f904]) ).

thf(f904,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f903]) ).

thf(f3130,plain,
    ( spl0_109
    | spl0_99
    | spl0_102
    | spl0_105 ),
    inference(avatar_split_clause,[],[f924,f2962,f2941,f2929,f3038]) ).

thf(f924,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f923]) ).

thf(f923,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f922]) ).

thf(f922,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f921]) ).

thf(f921,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f920]) ).

thf(f920,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f919]) ).

thf(f919,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f918]) ).

thf(f918,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f917]) ).

thf(f917,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f916]) ).

thf(f916,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f898]) ).

thf(f898,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f897]) ).

thf(f3129,plain,
    ( spl0_105
    | spl0_98
    | spl0_101
    | spl0_109 ),
    inference(avatar_split_clause,[],[f940,f3038,f2937,f2925,f2962]) ).

thf(f940,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f939]) ).

thf(f939,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f938]) ).

thf(f938,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f937]) ).

thf(f937,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f936]) ).

thf(f936,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f935]) ).

thf(f935,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f934]) ).

thf(f934,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f933]) ).

thf(f933,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f932]) ).

thf(f932,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f931]) ).

thf(f931,plain,
    ! [X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f929]) ).

thf(f929,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f928]) ).

thf(f928,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f927]) ).

thf(f927,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f926]) ).

thf(f926,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f818]) ).

thf(f818,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f817]) ).

thf(f3128,plain,
    ( spl0_98
    | spl0_105
    | spl0_109
    | spl0_100 ),
    inference(avatar_split_clause,[],[f949,f2933,f3038,f2962,f2925]) ).

thf(f949,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f948]) ).

thf(f948,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f947]) ).

thf(f947,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f946]) ).

thf(f946,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f945]) ).

thf(f945,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f944]) ).

thf(f944,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f943]) ).

thf(f943,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f942]) ).

thf(f942,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f941]) ).

thf(f941,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f930]) ).

thf(f930,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f929]) ).

thf(f3127,plain,
    ( spl0_98
    | spl0_99
    | spl0_109
    | spl0_105 ),
    inference(avatar_split_clause,[],[f961,f2962,f3038,f2929,f2925]) ).

thf(f961,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f960]) ).

thf(f960,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f959]) ).

thf(f959,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f958]) ).

thf(f958,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f957]) ).

thf(f957,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f956]) ).

thf(f956,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f955]) ).

thf(f955,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ) ),
    inference(pi_clausification,[],[f954]) ).

thf(f954,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f953]) ).

thf(f953,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f952]) ).

thf(f952,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ) ),
    inference(pi_clausification,[],[f951]) ).

thf(f951,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f950]) ).

thf(f950,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f925]) ).

thf(f925,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f818]) ).

thf(f3126,plain,
    ( spl0_95
    | spl0_109
    | spl0_105
    | spl0_104 ),
    inference(avatar_split_clause,[],[f979,f2949,f2962,f3038,f2916]) ).

thf(f979,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f978]) ).

thf(f978,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f977]) ).

thf(f977,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(pi_clausification,[],[f976]) ).

thf(f976,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f974]) ).

thf(f974,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f973]) ).

thf(f973,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f972]) ).

thf(f972,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f971]) ).

thf(f971,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f970]) ).

thf(f970,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f969]) ).

thf(f969,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f967]) ).

thf(f967,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f966]) ).

thf(f966,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f965]) ).

thf(f965,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f964]) ).

thf(f964,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f963]) ).

thf(f963,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
      = $true )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f816]) ).

thf(f816,plain,
    ( ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
      = $true )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f815]) ).

thf(f3125,plain,
    ( spl0_109
    | spl0_105
    | spl0_95
    | spl0_103 ),
    inference(avatar_split_clause,[],[f982,f2945,f2916,f2962,f3038]) ).

thf(f982,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f981]) ).

thf(f981,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f980]) ).

thf(f980,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f975]) ).

thf(f975,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f974]) ).

thf(f3124,plain,
    ( spl0_102
    | spl0_95
    | spl0_105
    | spl0_109 ),
    inference(avatar_split_clause,[],[f990,f3038,f2962,f2916,f2941]) ).

thf(f990,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f989]) ).

thf(f989,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f988]) ).

thf(f988,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f987]) ).

thf(f987,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f986]) ).

thf(f986,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f985]) ).

thf(f985,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f984]) ).

thf(f984,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f983]) ).

thf(f983,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f968]) ).

thf(f968,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X1 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f967]) ).

thf(f3123,plain,
    ( spl0_109
    | spl0_98
    | spl0_105
    | spl0_95 ),
    inference(avatar_split_clause,[],[f1002,f2916,f2962,f2925,f3038]) ).

thf(f1002,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1001]) ).

thf(f1001,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1000]) ).

thf(f1000,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f999]) ).

thf(f999,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(pi_clausification,[],[f998]) ).

thf(f998,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f997]) ).

thf(f997,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f996]) ).

thf(f996,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f995]) ).

thf(f995,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f994]) ).

thf(f994,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f993]) ).

thf(f993,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f992]) ).

thf(f992,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f991]) ).

thf(f991,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f962]) ).

thf(f962,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f816]) ).

thf(f3122,plain,
    ( spl0_108
    | spl0_107
    | spl0_104
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1031,f2937,f2949,f3000,f3019]) ).

thf(f1031,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1030]) ).

thf(f1030,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1029]) ).

thf(f1029,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1028]) ).

thf(f1028,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1027]) ).

thf(f1027,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1025]) ).

thf(f1025,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1024]) ).

thf(f1024,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1023]) ).

thf(f1023,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1022]) ).

thf(f1022,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f1021]) ).

thf(f1021,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1020]) ).

thf(f1020,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1018]) ).

thf(f1018,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1016]) ).

thf(f1016,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1014]) ).

thf(f1014,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1012]) ).

thf(f1012,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1010]) ).

thf(f1010,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1008]) ).

thf(f1008,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1006]) ).

thf(f1006,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1005]) ).

thf(f1005,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1004]) ).

thf(f1004,plain,
    ! [X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1003]) ).

thf(f1003,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
          @ X1 )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(pi_clausification,[],[f188]) ).

thf(f188,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f187]) ).

thf(f3121,plain,
    ( spl0_104
    | spl0_107
    | spl0_108
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1035,f2933,f3019,f3000,f2949]) ).

thf(f1035,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1034]) ).

thf(f1034,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1033]) ).

thf(f1033,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1032]) ).

thf(f1032,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1026]) ).

thf(f1026,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1025]) ).

thf(f3120,plain,
    ( spl0_104
    | spl0_108
    | spl0_106
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1046,f2937,f2981,f3019,f2949]) ).

thf(f1046,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1045]) ).

thf(f1045,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1044]) ).

thf(f1044,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
    inference(pi_clausification,[],[f1043]) ).

thf(f1043,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1041]) ).

thf(f1041,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1040]) ).

thf(f1040,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1039]) ).

thf(f1039,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1038]) ).

thf(f1038,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1037]) ).

thf(f1037,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1036]) ).

thf(f1036,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1019]) ).

thf(f1019,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1018]) ).

thf(f3119,plain,
    ( spl0_106
    | spl0_104
    | spl0_100
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1049,f3019,f2933,f2949,f2981]) ).

thf(f1049,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1048]) ).

thf(f1048,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1047]) ).

thf(f1047,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) ) ),
    inference(pi_clausification,[],[f1042]) ).

thf(f1042,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1041]) ).

thf(f3118,plain,
    ( spl0_103
    | spl0_107
    | spl0_101
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1062,f3019,f2937,f3000,f2945]) ).

thf(f1062,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1061]) ).

thf(f1061,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1060]) ).

thf(f1060,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(pi_clausification,[],[f1059]) ).

thf(f1059,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1058]) ).

thf(f1058,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1056]) ).

thf(f1056,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1055]) ).

thf(f1055,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1054]) ).

thf(f1054,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1053]) ).

thf(f1053,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1052]) ).

thf(f1052,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f1051]) ).

thf(f1051,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1017]) ).

thf(f1017,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1016]) ).

thf(f3117,plain,
    ( spl0_103
    | spl0_101
    | spl0_108
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1066,f2981,f3019,f2937,f2945]) ).

thf(f1066,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1065]) ).

thf(f1065,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1064]) ).

thf(f1064,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1063]) ).

thf(f1063,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X4 )
        = $true ) ),
    inference(pi_clausification,[],[f1057]) ).

thf(f1057,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1056]) ).

thf(f3116,plain,
    ( spl0_100
    | spl0_103
    | spl0_107
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1077,f3019,f3000,f2945,f2933]) ).

thf(f1077,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1076]) ).

thf(f1076,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1075]) ).

thf(f1075,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
    inference(pi_clausification,[],[f1074]) ).

thf(f1074,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1073]) ).

thf(f1073,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1072]) ).

thf(f1072,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1071]) ).

thf(f1071,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1070]) ).

thf(f1070,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1069]) ).

thf(f1069,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f1068]) ).

thf(f1068,plain,
    ! [X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1050]) ).

thf(f1050,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1017]) ).

thf(f3115,plain,
    ( spl0_100
    | spl0_108
    | spl0_103
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1086,f2981,f2945,f3019,f2933]) ).

thf(f1086,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1085]) ).

thf(f1085,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1084]) ).

thf(f1084,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1083]) ).

thf(f1083,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1082]) ).

thf(f1082,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1081]) ).

thf(f1081,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1080]) ).

thf(f1080,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1079]) ).

thf(f1079,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1078]) ).

thf(f1078,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1067]) ).

thf(f1067,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1050]) ).

thf(f3114,plain,
    ( spl0_108
    | spl0_107
    | spl0_104
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1099,f2929,f2949,f3000,f3019]) ).

thf(f1099,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1098]) ).

thf(f1098,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1097]) ).

thf(f1097,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1096]) ).

thf(f1096,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1094]) ).

thf(f1094,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1093]) ).

thf(f1093,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1092]) ).

thf(f1092,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1091]) ).

thf(f1091,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1090]) ).

thf(f1090,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1088]) ).

thf(f1088,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1087]) ).

thf(f1087,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1015]) ).

thf(f1015,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1014]) ).

thf(f3113,plain,
    ( spl0_108
    | spl0_103
    | spl0_99
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1102,f3000,f2929,f2945,f3019]) ).

thf(f1102,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1101]) ).

thf(f1101,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1100]) ).

thf(f1100,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1095]) ).

thf(f1095,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1094]) ).

thf(f3112,plain,
    ( spl0_104
    | spl0_108
    | spl0_106
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1111,f2929,f2981,f3019,f2949]) ).

thf(f1111,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1110]) ).

thf(f1110,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1109]) ).

thf(f1109,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1108]) ).

thf(f1108,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1106]) ).

thf(f1106,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1105]) ).

thf(f1105,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1104]) ).

thf(f1104,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1103]) ).

thf(f1103,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f1089]) ).

thf(f1089,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1088]) ).

thf(f3111,plain,
    ( spl0_106
    | spl0_108
    | spl0_99
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1114,f2945,f2929,f3019,f2981]) ).

thf(f1114,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1113]) ).

thf(f1113,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1112]) ).

thf(f1112,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1107]) ).

thf(f1107,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1106]) ).

thf(f3110,plain,
    ( spl0_104
    | spl0_101
    | spl0_108
    | spl0_105 ),
    inference(avatar_split_clause,[],[f1129,f2962,f3019,f2937,f2949]) ).

thf(f1129,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1128]) ).

thf(f1128,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1127]) ).

thf(f1127,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1126]) ).

thf(f1126,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1124]) ).

thf(f1124,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1122]) ).

thf(f1122,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1121]) ).

thf(f1121,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1120]) ).

thf(f1120,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1119]) ).

thf(f1119,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1118]) ).

thf(f1118,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1117]) ).

thf(f1117,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1116]) ).

thf(f1116,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1013]) ).

thf(f1013,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1012]) ).

thf(f3109,plain,
    ( spl0_108
    | spl0_104
    | spl0_100
    | spl0_105 ),
    inference(avatar_split_clause,[],[f1132,f2962,f2933,f2949,f3019]) ).

thf(f1132,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1131]) ).

thf(f1131,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1130]) ).

thf(f1130,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1125]) ).

thf(f1125,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1124]) ).

thf(f3108,plain,
    ( spl0_108
    | spl0_104
    | spl0_105
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1135,f2929,f2962,f2949,f3019]) ).

thf(f1135,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1134]) ).

thf(f1134,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1133]) ).

thf(f1133,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1123]) ).

thf(f1123,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1122]) ).

thf(f3107,plain,
    ( spl0_101
    | spl0_105
    | spl0_108
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1148,f2945,f3019,f2962,f2937]) ).

thf(f1148,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1147]) ).

thf(f1147,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1146]) ).

thf(f1146,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1145]) ).

thf(f1145,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1144]) ).

thf(f1144,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1143]) ).

thf(f1143,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
    inference(pi_clausification,[],[f1142]) ).

thf(f1142,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1140]) ).

thf(f1140,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1139]) ).

thf(f1139,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1137]) ).

thf(f1137,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1136]) ).

thf(f1136,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f1115]) ).

thf(f1115,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1013]) ).

thf(f3106,plain,
    ( spl0_100
    | spl0_108
    | spl0_105
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1154,f2945,f2962,f3019,f2933]) ).

thf(f1154,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1153]) ).

thf(f1153,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1152]) ).

thf(f1152,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1151]) ).

thf(f1151,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1150]) ).

thf(f1150,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1149]) ).

thf(f1149,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1141]) ).

thf(f1141,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1140]) ).

thf(f3105,plain,
    ( spl0_108
    | spl0_105
    | spl0_99
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1161,f2945,f2929,f2962,f3019]) ).

thf(f1161,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1160]) ).

thf(f1160,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1159]) ).

thf(f1159,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1158]) ).

thf(f1158,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f1157]) ).

thf(f1157,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1156]) ).

thf(f1156,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1155]) ).

thf(f1155,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1138]) ).

thf(f1138,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1137]) ).

thf(f3104,plain,
    ( spl0_107
    | spl0_108
    | spl0_101
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1178,f2941,f2937,f3019,f3000]) ).

thf(f1178,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1177]) ).

thf(f1177,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1176]) ).

thf(f1176,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1175]) ).

thf(f1175,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1173]) ).

thf(f1173,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1172]) ).

thf(f1172,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1171]) ).

thf(f1171,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1170]) ).

thf(f1170,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1168]) ).

thf(f1168,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1167]) ).

thf(f1167,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1165]) ).

thf(f1165,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1163]) ).

thf(f1163,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1162]) ).

thf(f1162,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1011]) ).

thf(f1011,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1010]) ).

thf(f3103,plain,
    ( spl0_102
    | spl0_101
    | spl0_108
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1181,f2981,f3019,f2937,f2941]) ).

thf(f1181,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1180]) ).

thf(f1180,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1179]) ).

thf(f1179,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1174]) ).

thf(f1174,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1173]) ).

thf(f3102,plain,
    ( spl0_100
    | spl0_107
    | spl0_102
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1189,f3019,f2941,f3000,f2933]) ).

thf(f1189,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1188]) ).

thf(f1188,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1187]) ).

thf(f1187,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1186]) ).

thf(f1186,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1185]) ).

thf(f1185,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1184]) ).

thf(f1184,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1183]) ).

thf(f1183,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1169]) ).

thf(f1169,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1168]) ).

thf(f3101,plain,
    ( spl0_102
    | spl0_106
    | spl0_108
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1195,f2933,f3019,f2981,f2941]) ).

thf(f1195,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1194]) ).

thf(f1194,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1193]) ).

thf(f1193,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1192]) ).

thf(f1192,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1191]) ).

thf(f1191,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1190]) ).

thf(f1190,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1182]) ).

thf(f1182,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1169]) ).

thf(f3100,plain,
    ( spl0_101
    | spl0_105
    | spl0_102
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1204,f3019,f2941,f2962,f2937]) ).

thf(f1204,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1203]) ).

thf(f1203,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1202]) ).

thf(f1202,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1201]) ).

thf(f1201,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1200]) ).

thf(f1200,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1199]) ).

thf(f1199,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1197]) ).

thf(f1197,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f1196]) ).

thf(f1196,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f1166]) ).

thf(f1166,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1165]) ).

thf(f3099,plain,
    ( spl0_105
    | spl0_108
    | spl0_102
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1209,f2933,f2941,f3019,f2962]) ).

thf(f1209,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1208]) ).

thf(f1208,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1207]) ).

thf(f1207,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1206]) ).

thf(f1206,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f1205]) ).

thf(f1205,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1198]) ).

thf(f1198,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1197]) ).

thf(f3098,plain,
    ( spl0_108
    | spl0_107
    | spl0_99
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1220,f2941,f2929,f3000,f3019]) ).

thf(f1220,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1219]) ).

thf(f1219,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1218]) ).

thf(f1218,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1217]) ).

thf(f1217,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1215]) ).

thf(f1215,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1214]) ).

thf(f1214,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1213]) ).

thf(f1213,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1212]) ).

thf(f1212,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1211]) ).

thf(f1211,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1164]) ).

thf(f1164,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1163]) ).

thf(f3097,plain,
    ( spl0_108
    | spl0_102
    | spl0_99
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1223,f2981,f2929,f2941,f3019]) ).

thf(f1223,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1222]) ).

thf(f1222,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1221]) ).

thf(f1221,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1216]) ).

thf(f1216,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1215]) ).

thf(f3096,plain,
    ( spl0_99
    | spl0_102
    | spl0_108
    | spl0_105 ),
    inference(avatar_split_clause,[],[f1230,f2962,f3019,f2941,f2929]) ).

thf(f1230,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1229]) ).

thf(f1229,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1228]) ).

thf(f1228,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1227]) ).

thf(f1227,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1226]) ).

thf(f1226,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1225]) ).

thf(f1225,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1224]) ).

thf(f1224,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1210]) ).

thf(f1210,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1164]) ).

thf(f3095,plain,
    ( spl0_108
    | spl0_95
    | spl0_104
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1247,f3000,f2949,f2916,f3019]) ).

thf(f1247,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1246]) ).

thf(f1246,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1245]) ).

thf(f1245,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1244]) ).

thf(f1244,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1243]) ).

thf(f1243,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1242]) ).

thf(f1242,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1241]) ).

thf(f1241,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1240]) ).

thf(f1240,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1238]) ).

thf(f1238,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1236]) ).

thf(f1236,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1234]) ).

thf(f1234,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1233]) ).

thf(f1233,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1232]) ).

thf(f1232,plain,
    ! [X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1009]) ).

thf(f1009,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1008]) ).

thf(f3094,plain,
    ( spl0_106
    | spl0_108
    | spl0_95
    | spl0_104 ),
    inference(avatar_split_clause,[],[f1254,f2949,f2916,f3019,f2981]) ).

thf(f1254,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1253]) ).

thf(f1253,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1252]) ).

thf(f1252,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1251]) ).

thf(f1251,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1250]) ).

thf(f1250,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1249]) ).

thf(f1249,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1248]) ).

thf(f1248,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1239]) ).

thf(f1239,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1238]) ).

thf(f3093,plain,
    ( spl0_95
    | spl0_105
    | spl0_108
    | spl0_104 ),
    inference(avatar_split_clause,[],[f1261,f2949,f3019,f2962,f2916]) ).

thf(f1261,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1260]) ).

thf(f1260,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1259]) ).

thf(f1259,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1258]) ).

thf(f1258,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1257]) ).

thf(f1257,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1256]) ).

thf(f1256,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1255]) ).

thf(f1255,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f1237]) ).

thf(f1237,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1236]) ).

thf(f3092,plain,
    ( spl0_95
    | spl0_107
    | spl0_108
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1272,f2945,f3019,f3000,f2916]) ).

thf(f1272,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1271]) ).

thf(f1271,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1270]) ).

thf(f1270,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1269]) ).

thf(f1269,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1267]) ).

thf(f1267,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1265]) ).

thf(f1265,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1264]) ).

thf(f1264,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1263]) ).

thf(f1263,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1262]) ).

thf(f1262,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1235]) ).

thf(f1235,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1234]) ).

thf(f3091,plain,
    ( spl0_95
    | spl0_103
    | spl0_106
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1275,f3019,f2981,f2945,f2916]) ).

thf(f1275,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1274]) ).

thf(f1274,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1273]) ).

thf(f1273,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1268]) ).

thf(f1268,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1267]) ).

thf(f3090,plain,
    ( spl0_108
    | spl0_95
    | spl0_105
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1278,f2945,f2962,f2916,f3019]) ).

thf(f1278,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1277]) ).

thf(f1277,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1276]) ).

thf(f1276,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
    inference(pi_clausification,[],[f1266]) ).

thf(f1266,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1265]) ).

thf(f3089,plain,
    ( spl0_108
    | spl0_95
    | spl0_102
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1291,f3000,f2941,f2916,f3019]) ).

thf(f1291,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1290]) ).

thf(f1290,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1289]) ).

thf(f1289,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1288]) ).

thf(f1288,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f1287]) ).

thf(f1287,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1285]) ).

thf(f1285,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1284]) ).

thf(f1284,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1283]) ).

thf(f1283,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1282]) ).

thf(f1282,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1281]) ).

thf(f1281,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1280]) ).

thf(f1280,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1231]) ).

thf(f1231,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1009]) ).

thf(f3088,plain,
    ( spl0_102
    | spl0_95
    | spl0_106
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1295,f3019,f2981,f2916,f2941]) ).

thf(f1295,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1294]) ).

thf(f1294,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1293]) ).

thf(f1293,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1292]) ).

thf(f1292,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1286]) ).

thf(f1286,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1285]) ).

thf(f3087,plain,
    ( spl0_95
    | spl0_105
    | spl0_108
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1304,f2941,f3019,f2962,f2916]) ).

thf(f1304,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1303]) ).

thf(f1303,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1302]) ).

thf(f1302,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1301]) ).

thf(f1301,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1300]) ).

thf(f1300,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1299]) ).

thf(f1299,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f1298]) ).

thf(f1298,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1297]) ).

thf(f1297,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1296]) ).

thf(f1296,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1279]) ).

thf(f1279,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1231]) ).

thf(f3086,plain,
    ( spl0_98
    | spl0_108
    | spl0_107
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1323,f2937,f3000,f3019,f2925]) ).

thf(f1323,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1322]) ).

thf(f1322,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1321]) ).

thf(f1321,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1320]) ).

thf(f1320,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1318]) ).

thf(f1318,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1317]) ).

thf(f1317,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1316]) ).

thf(f1316,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1315]) ).

thf(f1315,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1313]) ).

thf(f1313,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1311]) ).

thf(f1311,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1309]) ).

thf(f1309,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1307]) ).

thf(f1307,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1306]) ).

thf(f1306,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1305]) ).

thf(f1305,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1007]) ).

thf(f1007,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1006]) ).

thf(f3085,plain,
    ( spl0_108
    | spl0_98
    | spl0_100
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1326,f3000,f2933,f2925,f3019]) ).

thf(f1326,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1325]) ).

thf(f1325,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1324]) ).

thf(f1324,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true ) ),
    inference(pi_clausification,[],[f1319]) ).

thf(f1319,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1318]) ).

thf(f3084,plain,
    ( spl0_99
    | spl0_108
    | spl0_107
    | spl0_98 ),
    inference(avatar_split_clause,[],[f1332,f2925,f3000,f3019,f2929]) ).

thf(f1332,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1331]) ).

thf(f1331,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1330]) ).

thf(f1330,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1329]) ).

thf(f1329,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1328]) ).

thf(f1328,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1327]) ).

thf(f1327,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1314]) ).

thf(f1314,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1313]) ).

thf(f3083,plain,
    ( spl0_108
    | spl0_106
    | spl0_101
    | spl0_98 ),
    inference(avatar_split_clause,[],[f1342,f2925,f2937,f2981,f3019]) ).

thf(f1342,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1341]) ).

thf(f1341,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1340]) ).

thf(f1340,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1339]) ).

thf(f1339,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1337]) ).

thf(f1337,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1335]) ).

thf(f1335,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1334]) ).

thf(f1334,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1333]) ).

thf(f1333,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f1312]) ).

thf(f1312,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1311]) ).

thf(f3082,plain,
    ( spl0_108
    | spl0_98
    | spl0_100
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1345,f2981,f2933,f2925,f3019]) ).

thf(f1345,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1344]) ).

thf(f1344,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1343]) ).

thf(f1343,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1338]) ).

thf(f1338,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1337]) ).

thf(f3081,plain,
    ( spl0_108
    | spl0_106
    | spl0_99
    | spl0_98 ),
    inference(avatar_split_clause,[],[f1348,f2925,f2929,f2981,f3019]) ).

thf(f1348,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1347]) ).

thf(f1347,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1346]) ).

thf(f1346,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1336]) ).

thf(f1336,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1335]) ).

thf(f3080,plain,
    ( spl0_105
    | spl0_101
    | spl0_98
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1358,f3019,f2925,f2937,f2962]) ).

thf(f1358,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1357]) ).

thf(f1357,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1356]) ).

thf(f1356,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1355]) ).

thf(f1355,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1354]) ).

thf(f1354,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1352]) ).

thf(f1352,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1350]) ).

thf(f1350,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1349]) ).

thf(f1349,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1310]) ).

thf(f1310,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1309]) ).

thf(f3079,plain,
    ( spl0_100
    | spl0_105
    | spl0_108
    | spl0_98 ),
    inference(avatar_split_clause,[],[f1362,f2925,f3019,f2962,f2933]) ).

thf(f1362,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1361]) ).

thf(f1361,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1360]) ).

thf(f1360,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1359]) ).

thf(f1359,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f1353]) ).

thf(f1353,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1352]) ).

thf(f3078,plain,
    ( spl0_98
    | spl0_99
    | spl0_108
    | spl0_105 ),
    inference(avatar_split_clause,[],[f1366,f2962,f3019,f2929,f2925]) ).

thf(f1366,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1365]) ).

thf(f1365,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1364]) ).

thf(f1364,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1363]) ).

thf(f1363,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1351]) ).

thf(f1351,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1350]) ).

thf(f3077,plain,
    ( spl0_108
    | spl0_107
    | spl0_95
    | spl0_98 ),
    inference(avatar_split_clause,[],[f1376,f2925,f2916,f3000,f3019]) ).

thf(f1376,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1375]) ).

thf(f1375,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1374]) ).

thf(f1374,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(pi_clausification,[],[f1373]) ).

thf(f1373,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1371]) ).

thf(f1371,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1370]) ).

thf(f1370,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1368]) ).

thf(f1368,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1367]) ).

thf(f1367,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1308]) ).

thf(f1308,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1307]) ).

thf(f3076,plain,
    ( spl0_98
    | spl0_106
    | spl0_95
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1379,f3019,f2916,f2981,f2925]) ).

thf(f1379,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1378]) ).

thf(f1378,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1377]) ).

thf(f1377,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1372]) ).

thf(f1372,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1371]) ).

thf(f3075,plain,
    ( spl0_95
    | spl0_108
    | spl0_98
    | spl0_105 ),
    inference(avatar_split_clause,[],[f1383,f2962,f2925,f3019,f2916]) ).

thf(f1383,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1382]) ).

thf(f1382,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1381]) ).

thf(f1381,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1380]) ).

thf(f1380,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1369]) ).

thf(f1369,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1368]) ).

thf(f3074,plain,
    ( spl0_96
    | spl0_110
    | spl0_101
    | spl0_104 ),
    inference(avatar_split_clause,[],[f1412,f2949,f2937,f3057,f2919]) ).

thf(f1412,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1411]) ).

thf(f1411,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1410]) ).

thf(f1410,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1409]) ).

thf(f1409,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1408]) ).

thf(f1408,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1407]) ).

thf(f1407,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1406]) ).

thf(f1406,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1404]) ).

thf(f1404,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1402]) ).

thf(f1402,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1400]) ).

thf(f1400,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1398]) ).

thf(f1398,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1396]) ).

thf(f1396,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1395]) ).

thf(f1395,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1393]) ).

thf(f1393,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f1392]) ).

thf(f1392,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
          @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1391]) ).

thf(f1391,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1389]) ).

thf(f1389,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1388]) ).

thf(f1388,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1387]) ).

thf(f1387,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1385]) ).

thf(f1385,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1384]) ).

thf(f1384,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
          @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(pi_clausification,[],[f186]) ).

thf(f186,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f185]) ).

thf(f3073,plain,
    ( spl0_103
    | spl0_110
    | spl0_101
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1418,f2919,f2937,f3057,f2945]) ).

thf(f1418,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1417]) ).

thf(f1417,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1416]) ).

thf(f1416,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1415]) ).

thf(f1415,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1414]) ).

thf(f1414,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1413]) ).

thf(f1413,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f1405]) ).

thf(f1405,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1404]) ).

thf(f3072,plain,
    ( spl0_102
    | spl0_110
    | spl0_96
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1424,f2937,f2919,f3057,f2941]) ).

thf(f1424,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1423]) ).

thf(f1423,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1422]) ).

thf(f1422,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1421]) ).

thf(f1421,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1420]) ).

thf(f1420,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1419]) ).

thf(f1419,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1403]) ).

thf(f1403,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1402]) ).

thf(f3071,plain,
    ( spl0_98
    | spl0_96
    | spl0_101
    | spl0_110 ),
    inference(avatar_split_clause,[],[f1430,f3057,f2937,f2919,f2925]) ).

thf(f1430,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1429]) ).

thf(f1429,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1428]) ).

thf(f1428,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1427]) ).

thf(f1427,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1426]) ).

thf(f1426,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1425]) ).

thf(f1425,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1401]) ).

thf(f1401,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1400]) ).

thf(f3070,plain,
    ( spl0_104
    | spl0_96
    | spl0_100
    | spl0_110 ),
    inference(avatar_split_clause,[],[f1442,f3057,f2933,f2919,f2949]) ).

thf(f1442,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1441]) ).

thf(f1441,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1440]) ).

thf(f1440,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1439]) ).

thf(f1439,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1437]) ).

thf(f1437,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1435]) ).

thf(f1435,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1433]) ).

thf(f1433,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1432]) ).

thf(f1432,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1431]) ).

thf(f1431,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1399]) ).

thf(f1399,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1398]) ).

thf(f3069,plain,
    ( spl0_110
    | spl0_96
    | spl0_103
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1445,f2933,f2945,f2919,f3057]) ).

thf(f1445,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1444]) ).

thf(f1444,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1443]) ).

thf(f1443,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1438]) ).

thf(f1438,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1437]) ).

thf(f3068,plain,
    ( spl0_102
    | spl0_110
    | spl0_96
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1448,f2933,f2919,f3057,f2941]) ).

thf(f1448,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1447]) ).

thf(f1447,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1446]) ).

thf(f1446,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1436]) ).

thf(f1436,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1435]) ).

thf(f3067,plain,
    ( spl0_100
    | spl0_110
    | spl0_98
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1451,f2919,f2925,f3057,f2933]) ).

thf(f1451,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1450]) ).

thf(f1450,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1449]) ).

thf(f1449,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1434]) ).

thf(f1434,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1433]) ).

thf(f3066,plain,
    ( spl0_110
    | spl0_96
    | spl0_104
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1463,f2929,f2949,f2919,f3057]) ).

thf(f1463,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1462]) ).

thf(f1462,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1461]) ).

thf(f1461,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f1460]) ).

thf(f1460,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1459]) ).

thf(f1459,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1458]) ).

thf(f1458,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1457]) ).

thf(f1457,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1455]) ).

thf(f1455,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1453]) ).

thf(f1453,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1397]) ).

thf(f1397,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1396]) ).

thf(f3065,plain,
    ( spl0_96
    | spl0_110
    | spl0_103
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1469,f2929,f2945,f3057,f2919]) ).

thf(f1469,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1468]) ).

thf(f1468,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1467]) ).

thf(f1467,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1466]) ).

thf(f1466,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1465]) ).

thf(f1465,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1464]) ).

thf(f1464,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1456]) ).

thf(f1456,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1455]) ).

thf(f3064,plain,
    ( spl0_96
    | spl0_99
    | spl0_102
    | spl0_110 ),
    inference(avatar_split_clause,[],[f1475,f3057,f2941,f2929,f2919]) ).

thf(f1475,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1474]) ).

thf(f1474,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1473]) ).

thf(f1473,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1472]) ).

thf(f1472,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1471]) ).

thf(f1471,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1470]) ).

thf(f1470,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1454]) ).

thf(f1454,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1453]) ).

thf(f3063,plain,
    ( spl0_96
    | spl0_99
    | spl0_98
    | spl0_110 ),
    inference(avatar_split_clause,[],[f1481,f3057,f2925,f2929,f2919]) ).

thf(f1481,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1480]) ).

thf(f1480,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1479]) ).

thf(f1479,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1478]) ).

thf(f1478,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1477]) ).

thf(f1477,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1476]) ).

thf(f1476,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1452]) ).

thf(f1452,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1397]) ).

thf(f3062,plain,
    ( spl0_96
    | spl0_104
    | spl0_110
    | spl0_95 ),
    inference(avatar_split_clause,[],[f1494,f2916,f3057,f2949,f2919]) ).

thf(f1494,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1493]) ).

thf(f1493,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1492]) ).

thf(f1492,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1491]) ).

thf(f1491,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f1490]) ).

thf(f1490,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1489]) ).

thf(f1489,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1488]) ).

thf(f1488,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1486]) ).

thf(f1486,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1484]) ).

thf(f1484,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1483]) ).

thf(f1483,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1394]) ).

thf(f1394,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1393]) ).

thf(f3061,plain,
    ( spl0_95
    | spl0_103
    | spl0_96
    | spl0_110 ),
    inference(avatar_split_clause,[],[f1500,f3057,f2919,f2945,f2916]) ).

thf(f1500,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1499]) ).

thf(f1499,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1498]) ).

thf(f1498,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1497]) ).

thf(f1497,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f1496]) ).

thf(f1496,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1495]) ).

thf(f1495,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1487]) ).

thf(f1487,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1486]) ).

thf(f3060,plain,
    ( spl0_95
    | spl0_102
    | spl0_96
    | spl0_110 ),
    inference(avatar_split_clause,[],[f1506,f3057,f2919,f2941,f2916]) ).

thf(f1506,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1505]) ).

thf(f1505,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1504]) ).

thf(f1504,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1503]) ).

thf(f1503,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1502]) ).

thf(f1502,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1501]) ).

thf(f1501,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1485]) ).

thf(f1485,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1484]) ).

thf(f3059,plain,
    ( spl0_98
    | spl0_110
    | spl0_96
    | spl0_95 ),
    inference(avatar_split_clause,[],[f1513,f2916,f2919,f3057,f2925]) ).

thf(f1513,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1512]) ).

thf(f1512,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1511]) ).

thf(f1511,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1510]) ).

thf(f1510,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f1509]) ).

thf(f1509,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1508]) ).

thf(f1508,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1507]) ).

thf(f1507,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1482]) ).

thf(f1482,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1394]) ).

thf(f3055,plain,
    ( spl0_104
    | spl0_109
    | spl0_101
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1534,f2919,f2937,f3038,f2949]) ).

thf(f1534,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1533]) ).

thf(f1533,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1532]) ).

thf(f1532,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1531]) ).

thf(f1531,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1529]) ).

thf(f1529,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1528]) ).

thf(f1528,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1526]) ).

thf(f1526,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1525]) ).

thf(f1525,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1524]) ).

thf(f1524,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1523]) ).

thf(f1523,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1522]) ).

thf(f1522,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f1521]) ).

thf(f1521,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1519]) ).

thf(f1519,plain,
    ! [X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1517]) ).

thf(f1517,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1515]) ).

thf(f1515,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1390]) ).

thf(f1390,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1389]) ).

thf(f3054,plain,
    ( spl0_109
    | spl0_96
    | spl0_101
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1537,f2945,f2937,f2919,f3038]) ).

thf(f1537,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1536]) ).

thf(f1536,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1535]) ).

thf(f1535,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1530]) ).

thf(f1530,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1529]) ).

thf(f3053,plain,
    ( spl0_102
    | spl0_101
    | spl0_109
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1541,f2919,f3038,f2937,f2941]) ).

thf(f1541,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1540]) ).

thf(f1540,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1539]) ).

thf(f1539,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1538]) ).

thf(f1538,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) ) ),
    inference(pi_clausification,[],[f1527]) ).

thf(f1527,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1526]) ).

thf(f3052,plain,
    ( spl0_104
    | spl0_109
    | spl0_100
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1554,f2919,f2933,f3038,f2949]) ).

thf(f1554,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1553]) ).

thf(f1553,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1552]) ).

thf(f1552,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1551]) ).

thf(f1551,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1550]) ).

thf(f1550,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1549]) ).

thf(f1549,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1548]) ).

thf(f1548,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1546]) ).

thf(f1546,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1544]) ).

thf(f1544,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1543]) ).

thf(f1543,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1542]) ).

thf(f1542,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f1520]) ).

thf(f1520,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1519]) ).

thf(f3051,plain,
    ( spl0_103
    | spl0_100
    | spl0_109
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1560,f2919,f3038,f2933,f2945]) ).

thf(f1560,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1559]) ).

thf(f1559,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1558]) ).

thf(f1558,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1557]) ).

thf(f1557,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
    inference(pi_clausification,[],[f1556]) ).

thf(f1556,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1555]) ).

thf(f1555,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1547]) ).

thf(f1547,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1546]) ).

thf(f3050,plain,
    ( spl0_102
    | spl0_109
    | spl0_100
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1566,f2919,f2933,f3038,f2941]) ).

thf(f1566,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1565]) ).

thf(f1565,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1564]) ).

thf(f1564,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1563]) ).

thf(f1563,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1562]) ).

thf(f1562,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1561]) ).

thf(f1561,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1545]) ).

thf(f1545,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1544]) ).

thf(f3049,plain,
    ( spl0_96
    | spl0_99
    | spl0_104
    | spl0_109 ),
    inference(avatar_split_clause,[],[f1579,f3038,f2949,f2929,f2919]) ).

thf(f1579,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1578]) ).

thf(f1578,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1577]) ).

thf(f1577,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1576]) ).

thf(f1576,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1575]) ).

thf(f1575,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1574]) ).

thf(f1574,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1573]) ).

thf(f1573,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1571]) ).

thf(f1571,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1570]) ).

thf(f1570,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1569]) ).

thf(f1569,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1568]) ).

thf(f1568,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1518]) ).

thf(f1518,plain,
    ! [X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1517]) ).

thf(f3048,plain,
    ( spl0_103
    | spl0_109
    | spl0_99
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1585,f2919,f2929,f3038,f2945]) ).

thf(f1585,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1584]) ).

thf(f1584,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1583]) ).

thf(f1583,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) ) ),
    inference(pi_clausification,[],[f1582]) ).

thf(f1582,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1581]) ).

thf(f1581,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1580]) ).

thf(f1580,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1572]) ).

thf(f1572,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1571]) ).

thf(f3047,plain,
    ( spl0_109
    | spl0_99
    | spl0_96
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1594,f2941,f2919,f2929,f3038]) ).

thf(f1594,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1593]) ).

thf(f1593,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1592]) ).

thf(f1592,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1591]) ).

thf(f1591,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1590]) ).

thf(f1590,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1589]) ).

thf(f1589,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1588]) ).

thf(f1588,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1587]) ).

thf(f1587,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1586]) ).

thf(f1586,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f1567]) ).

thf(f1567,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1518]) ).

thf(f3046,plain,
    ( spl0_96
    | spl0_95
    | spl0_109
    | spl0_104 ),
    inference(avatar_split_clause,[],[f1607,f2949,f3038,f2916,f2919]) ).

thf(f1607,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1606]) ).

thf(f1606,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1605]) ).

thf(f1605,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1604]) ).

thf(f1604,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1603]) ).

thf(f1603,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1602]) ).

thf(f1602,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1601]) ).

thf(f1601,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1600]) ).

thf(f1600,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1598]) ).

thf(f1598,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1596]) ).

thf(f1596,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1595]) ).

thf(f1595,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X2 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1516]) ).

thf(f1516,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1515]) ).

thf(f3045,plain,
    ( spl0_103
    | spl0_96
    | spl0_95
    | spl0_109 ),
    inference(avatar_split_clause,[],[f1614,f3038,f2916,f2919,f2945]) ).

thf(f1614,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1613]) ).

thf(f1613,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1612]) ).

thf(f1612,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1611]) ).

thf(f1611,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1610]) ).

thf(f1610,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1609]) ).

thf(f1609,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1608]) ).

thf(f1608,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(pi_clausification,[],[f1599]) ).

thf(f1599,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1598]) ).

thf(f3044,plain,
    ( spl0_96
    | spl0_95
    | spl0_109
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1621,f2941,f3038,f2916,f2919]) ).

thf(f1621,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1620]) ).

thf(f1620,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1619]) ).

thf(f1619,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1618]) ).

thf(f1618,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1617]) ).

thf(f1617,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1616]) ).

thf(f1616,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1615]) ).

thf(f1615,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1597]) ).

thf(f1597,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1596]) ).

thf(f3043,plain,
    ( spl0_96
    | spl0_109
    | spl0_98
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1636,f2937,f2925,f3038,f2919]) ).

thf(f1636,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1635]) ).

thf(f1635,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1634]) ).

thf(f1634,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1633]) ).

thf(f1633,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1631]) ).

thf(f1631,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1629]) ).

thf(f1629,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1628]) ).

thf(f1628,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1627]) ).

thf(f1627,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1625]) ).

thf(f1625,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1624]) ).

thf(f1624,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
          @ X3 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true ) ),
    inference(pi_clausification,[],[f1623]) ).

thf(f1623,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1622]) ).

thf(f1622,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f1514]) ).

thf(f1514,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1390]) ).

thf(f3042,plain,
    ( spl0_96
    | spl0_109
    | spl0_100
    | spl0_98 ),
    inference(avatar_split_clause,[],[f1639,f2925,f2933,f3038,f2919]) ).

thf(f1639,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1638]) ).

thf(f1638,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1637]) ).

thf(f1637,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1632]) ).

thf(f1632,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1631]) ).

thf(f3041,plain,
    ( spl0_96
    | spl0_98
    | spl0_99
    | spl0_109 ),
    inference(avatar_split_clause,[],[f1642,f3038,f2929,f2925,f2919]) ).

thf(f1642,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1641]) ).

thf(f1641,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1640]) ).

thf(f1640,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1630]) ).

thf(f1630,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1629]) ).

thf(f3040,plain,
    ( spl0_96
    | spl0_98
    | spl0_109
    | spl0_95 ),
    inference(avatar_split_clause,[],[f1647,f2916,f3038,f2925,f2919]) ).

thf(f1647,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1646]) ).

thf(f1646,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1645]) ).

thf(f1645,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) ),
    inference(pi_clausification,[],[f1644]) ).

thf(f1644,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1643]) ).

thf(f1643,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1626]) ).

thf(f1626,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X3 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1625]) ).

thf(f3036,plain,
    ( spl0_108
    | spl0_104
    | spl0_101
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1670,f2919,f2937,f2949,f3019]) ).

thf(f1670,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1669]) ).

thf(f1669,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1668]) ).

thf(f1668,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1667]) ).

thf(f1667,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f1666]) ).

thf(f1666,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1665]) ).

thf(f1665,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(pi_clausification,[],[f1664]) ).

thf(f1664,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1662]) ).

thf(f1662,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1660]) ).

thf(f1660,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1658]) ).

thf(f1658,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1657]) ).

thf(f1657,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1655]) ).

thf(f1655,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1654]) ).

thf(f1654,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1652]) ).

thf(f1652,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1651]) ).

thf(f1651,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
          @ X2 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ) ),
    inference(pi_clausification,[],[f1650]) ).

thf(f1650,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1648]) ).

thf(f1648,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1386]) ).

thf(f1386,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1385]) ).

thf(f3035,plain,
    ( spl0_96
    | spl0_108
    | spl0_104
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1676,f2933,f2949,f3019,f2919]) ).

thf(f1676,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1675]) ).

thf(f1675,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1674]) ).

thf(f1674,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1673]) ).

thf(f1673,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true ) ),
    inference(pi_clausification,[],[f1672]) ).

thf(f1672,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1671]) ).

thf(f1671,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f1663]) ).

thf(f1663,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1662]) ).

thf(f3034,plain,
    ( spl0_96
    | spl0_108
    | spl0_103
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1684,f2937,f2945,f3019,f2919]) ).

thf(f1684,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1683]) ).

thf(f1683,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1682]) ).

thf(f1682,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1681]) ).

thf(f1681,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1679]) ).

thf(f1679,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1678]) ).

thf(f1678,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1677]) ).

thf(f1677,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1661]) ).

thf(f1661,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1660]) ).

thf(f3033,plain,
    ( spl0_103
    | spl0_100
    | spl0_96
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1687,f3019,f2919,f2933,f2945]) ).

thf(f1687,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1686]) ).

thf(f1686,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1685]) ).

thf(f1685,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1680]) ).

thf(f1680,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1679]) ).

thf(f3032,plain,
    ( spl0_99
    | spl0_108
    | spl0_104
    | spl0_96 ),
    inference(avatar_split_clause,[],[f1695,f2919,f2949,f3019,f2929]) ).

thf(f1695,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1694]) ).

thf(f1694,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1693]) ).

thf(f1693,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1692]) ).

thf(f1692,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1690]) ).

thf(f1690,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1689]) ).

thf(f1689,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1688]) ).

thf(f1688,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f1659]) ).

thf(f1659,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1658]) ).

thf(f3031,plain,
    ( spl0_103
    | spl0_99
    | spl0_96
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1698,f3019,f2919,f2929,f2945]) ).

thf(f1698,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1697]) ).

thf(f1697,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1696]) ).

thf(f1696,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1691]) ).

thf(f1691,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1690]) ).

thf(f3030,plain,
    ( spl0_108
    | spl0_104
    | spl0_96
    | spl0_95 ),
    inference(avatar_split_clause,[],[f1707,f2916,f2919,f2949,f3019]) ).

thf(f1707,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1706]) ).

thf(f1706,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1705]) ).

thf(f1705,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1704]) ).

thf(f1704,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f1703]) ).

thf(f1703,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1701]) ).

thf(f1701,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1700]) ).

thf(f1700,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1699]) ).

thf(f1699,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f1656]) ).

thf(f1656,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1655]) ).

thf(f3029,plain,
    ( spl0_108
    | spl0_96
    | spl0_103
    | spl0_95 ),
    inference(avatar_split_clause,[],[f1711,f2916,f2945,f2919,f3019]) ).

thf(f1711,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1710]) ).

thf(f1710,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1709]) ).

thf(f1709,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1708]) ).

thf(f1708,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f1702]) ).

thf(f1702,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1701]) ).

thf(f3028,plain,
    ( spl0_108
    | spl0_101
    | spl0_96
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1725,f2941,f2919,f2937,f3019]) ).

thf(f1725,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1724]) ).

thf(f1724,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f1723]) ).

thf(f1723,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1722]) ).

thf(f1722,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1720]) ).

thf(f1720,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1718]) ).

thf(f1718,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1716]) ).

thf(f1716,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1715]) ).

thf(f1715,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1714]) ).

thf(f1714,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1713]) ).

thf(f1713,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1712]) ).

thf(f1712,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(pi_clausification,[],[f1653]) ).

thf(f1653,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1652]) ).

thf(f3027,plain,
    ( spl0_96
    | spl0_108
    | spl0_102
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1728,f2933,f2941,f3019,f2919]) ).

thf(f1728,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f1727]) ).

thf(f1727,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1726]) ).

thf(f1726,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1721]) ).

thf(f1721,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1720]) ).

thf(f3026,plain,
    ( spl0_102
    | spl0_96
    | spl0_108
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1731,f2929,f3019,f2919,f2941]) ).

thf(f1731,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1730]) ).

thf(f1730,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1729]) ).

thf(f1729,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1719]) ).

thf(f1719,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1718]) ).

thf(f3025,plain,
    ( spl0_96
    | spl0_102
    | spl0_95
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1734,f3019,f2916,f2941,f2919]) ).

thf(f1734,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1733]) ).

thf(f1733,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1732]) ).

thf(f1732,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
    inference(pi_clausification,[],[f1717]) ).

thf(f1717,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1716]) ).

thf(f3024,plain,
    ( spl0_108
    | spl0_96
    | spl0_98
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1750,f2937,f2925,f2919,f3019]) ).

thf(f1750,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1749]) ).

thf(f1749,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1748]) ).

thf(f1748,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1747]) ).

thf(f1747,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1746]) ).

thf(f1746,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1744]) ).

thf(f1744,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1742]) ).

thf(f1742,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1741]) ).

thf(f1741,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1739]) ).

thf(f1739,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1738]) ).

thf(f1738,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1737]) ).

thf(f1737,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f1736]) ).

thf(f1736,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f1735]) ).

thf(f1735,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
          @ X2 ) ) ),
    inference(pi_clausification,[],[f1649]) ).

thf(f1649,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1648]) ).

thf(f3023,plain,
    ( spl0_100
    | spl0_96
    | spl0_98
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1754,f3019,f2925,f2919,f2933]) ).

thf(f1754,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1753]) ).

thf(f1753,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1752]) ).

thf(f1752,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1751]) ).

thf(f1751,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1745]) ).

thf(f1745,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1744]) ).

thf(f3022,plain,
    ( spl0_99
    | spl0_108
    | spl0_96
    | spl0_98 ),
    inference(avatar_split_clause,[],[f1758,f2925,f2919,f3019,f2929]) ).

thf(f1758,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1757]) ).

thf(f1757,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1756]) ).

thf(f1756,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1755]) ).

thf(f1755,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1743]) ).

thf(f1743,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1742]) ).

thf(f3021,plain,
    ( spl0_98
    | spl0_96
    | spl0_95
    | spl0_108 ),
    inference(avatar_split_clause,[],[f1763,f3019,f2916,f2919,f2925]) ).

thf(f1763,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1762]) ).

thf(f1762,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1761]) ).

thf(f1761,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1760]) ).

thf(f1760,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1759]) ).

thf(f1759,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(pi_clausification,[],[f1740]) ).

thf(f1740,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1739]) ).

thf(f3017,plain,
    ( spl0_107
    | spl0_97
    | spl0_104
    | spl0_101 ),
    inference(avatar_split_clause,[],[f1794,f2937,f2949,f2922,f3000]) ).

thf(f1794,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1793]) ).

thf(f1793,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1792]) ).

thf(f1792,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1791]) ).

thf(f1791,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1789]) ).

thf(f1789,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1788]) ).

thf(f1788,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1786]) ).

thf(f1786,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1785]) ).

thf(f1785,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f1784]) ).

thf(f1784,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1782]) ).

thf(f1782,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1780]) ).

thf(f1780,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1779]) ).

thf(f1779,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1778]) ).

thf(f1778,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f1777]) ).

thf(f1777,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1775]) ).

thf(f1775,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1773]) ).

thf(f1773,plain,
    ! [X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1772]) ).

thf(f1772,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1770]) ).

thf(f1770,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1768]) ).

thf(f1768,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1766]) ).

thf(f1766,plain,
    ! [X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1765]) ).

thf(f1765,plain,
    ! [X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X1 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1764]) ).

thf(f1764,plain,
    ! [X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
          @ X1 )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f184]) ).

thf(f184,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
      = $true )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
      = $true )
    | ( $true
      = ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
        | ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f183]) ).

thf(f3016,plain,
    ( spl0_107
    | spl0_97
    | spl0_101
    | spl0_103 ),
    inference(avatar_split_clause,[],[f1797,f2945,f2937,f2922,f3000]) ).

thf(f1797,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1796]) ).

thf(f1796,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1795]) ).

thf(f1795,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1790]) ).

thf(f1790,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1789]) ).

thf(f3015,plain,
    ( spl0_102
    | spl0_107
    | spl0_101
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1801,f2922,f2937,f3000,f2941]) ).

thf(f1801,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1800]) ).

thf(f1800,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1799]) ).

thf(f1799,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1798]) ).

thf(f1798,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1787]) ).

thf(f1787,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1786]) ).

thf(f3014,plain,
    ( spl0_98
    | spl0_101
    | spl0_97
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1807,f3000,f2922,f2937,f2925]) ).

thf(f1807,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1806]) ).

thf(f1806,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1805]) ).

thf(f1805,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1804]) ).

thf(f1804,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1803]) ).

thf(f1803,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1802]) ).

thf(f1802,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1783]) ).

thf(f1783,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1782]) ).

thf(f3013,plain,
    ( spl0_107
    | spl0_97
    | spl0_100
    | spl0_104 ),
    inference(avatar_split_clause,[],[f1819,f2949,f2933,f2922,f3000]) ).

thf(f1819,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1818]) ).

thf(f1818,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1817]) ).

thf(f1817,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1816]) ).

thf(f1816,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1814]) ).

thf(f1814,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1812]) ).

thf(f1812,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1811]) ).

thf(f1811,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1810]) ).

thf(f1810,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1809]) ).

thf(f1809,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1781]) ).

thf(f1781,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1780]) ).

thf(f3012,plain,
    ( spl0_107
    | spl0_103
    | spl0_100
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1822,f2922,f2933,f2945,f3000]) ).

thf(f1822,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1821]) ).

thf(f1821,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1820]) ).

thf(f1820,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1815]) ).

thf(f1815,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1814]) ).

thf(f3011,plain,
    ( spl0_102
    | spl0_100
    | spl0_107
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1825,f2922,f3000,f2933,f2941]) ).

thf(f1825,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1824]) ).

thf(f1824,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1823]) ).

thf(f1823,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1813]) ).

thf(f1813,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1812]) ).

thf(f3010,plain,
    ( spl0_97
    | spl0_100
    | spl0_98
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1831,f3000,f2925,f2933,f2922]) ).

thf(f1831,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1830]) ).

thf(f1830,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1829]) ).

thf(f1829,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1828]) ).

thf(f1828,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1827]) ).

thf(f1827,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1826]) ).

thf(f1826,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1808]) ).

thf(f1808,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1781]) ).

thf(f3009,plain,
    ( spl0_107
    | spl0_99
    | spl0_104
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1846,f2922,f2949,f2929,f3000]) ).

thf(f1846,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1845]) ).

thf(f1845,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1844]) ).

thf(f1844,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1843]) ).

thf(f1843,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1841]) ).

thf(f1841,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1839]) ).

thf(f1839,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1838]) ).

thf(f1838,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1836]) ).

thf(f1836,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1835]) ).

thf(f1835,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1834]) ).

thf(f1834,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1833]) ).

thf(f1833,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1832]) ).

thf(f1832,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1776]) ).

thf(f1776,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1775]) ).

thf(f3008,plain,
    ( spl0_99
    | spl0_97
    | spl0_103
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1849,f3000,f2945,f2922,f2929]) ).

thf(f1849,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1848]) ).

thf(f1848,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1847]) ).

thf(f1847,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1842]) ).

thf(f1842,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1841]) ).

thf(f3007,plain,
    ( spl0_102
    | spl0_107
    | spl0_97
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1852,f2929,f2922,f3000,f2941]) ).

thf(f1852,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1851]) ).

thf(f1851,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1850]) ).

thf(f1850,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f1840]) ).

thf(f1840,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1839]) ).

thf(f3006,plain,
    ( spl0_98
    | spl0_97
    | spl0_107
    | spl0_99 ),
    inference(avatar_split_clause,[],[f1856,f2929,f3000,f2922,f2925]) ).

thf(f1856,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1855]) ).

thf(f1855,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1854]) ).

thf(f1854,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1853]) ).

thf(f1853,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1837]) ).

thf(f1837,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1836]) ).

thf(f3005,plain,
    ( spl0_107
    | spl0_97
    | spl0_104
    | spl0_95 ),
    inference(avatar_split_clause,[],[f1871,f2916,f2949,f2922,f3000]) ).

thf(f1871,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1870]) ).

thf(f1870,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1869]) ).

thf(f1869,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1868]) ).

thf(f1868,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1867]) ).

thf(f1867,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1866]) ).

thf(f1866,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1865]) ).

thf(f1865,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1864]) ).

thf(f1864,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1862]) ).

thf(f1862,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1860]) ).

thf(f1860,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1859]) ).

thf(f1859,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1858]) ).

thf(f1858,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1774]) ).

thf(f1774,plain,
    ! [X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1773]) ).

thf(f3004,plain,
    ( spl0_95
    | spl0_97
    | spl0_103
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1878,f3000,f2945,f2922,f2916]) ).

thf(f1878,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1877]) ).

thf(f1877,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f1876]) ).

thf(f1876,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1875]) ).

thf(f1875,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1874]) ).

thf(f1874,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1873]) ).

thf(f1873,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f1872]) ).

thf(f1872,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f1863]) ).

thf(f1863,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1862]) ).

thf(f3003,plain,
    ( spl0_97
    | spl0_95
    | spl0_102
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1885,f3000,f2941,f2916,f2922]) ).

thf(f1885,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1884]) ).

thf(f1884,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1883]) ).

thf(f1883,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(pi_clausification,[],[f1882]) ).

thf(f1882,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1881]) ).

thf(f1881,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1880]) ).

thf(f1880,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1879]) ).

thf(f1879,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1861]) ).

thf(f1861,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1860]) ).

thf(f3002,plain,
    ( spl0_97
    | spl0_95
    | spl0_98
    | spl0_107 ),
    inference(avatar_split_clause,[],[f1894,f3000,f2925,f2916,f2922]) ).

thf(f1894,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1893]) ).

thf(f1893,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1892]) ).

thf(f1892,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1891]) ).

thf(f1891,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1890]) ).

thf(f1890,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1889]) ).

thf(f1889,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1888]) ).

thf(f1888,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1887]) ).

thf(f1887,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f1886]) ).

thf(f1886,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
          @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(pi_clausification,[],[f1857]) ).

thf(f1857,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1774]) ).

thf(f2998,plain,
    ( spl0_106
    | spl0_104
    | spl0_101
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1916,f2922,f2937,f2949,f2981]) ).

thf(f1916,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1915]) ).

thf(f1915,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1914]) ).

thf(f1914,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1913]) ).

thf(f1913,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1911]) ).

thf(f1911,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1909]) ).

thf(f1909,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1908]) ).

thf(f1908,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1906]) ).

thf(f1906,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1905]) ).

thf(f1905,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1904]) ).

thf(f1904,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1902]) ).

thf(f1902,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1901]) ).

thf(f1901,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1899]) ).

thf(f1899,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1897]) ).

thf(f1897,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f1896]) ).

thf(f1896,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f1895]) ).

thf(f1895,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1771]) ).

thf(f1771,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1770]) ).

thf(f2997,plain,
    ( spl0_106
    | spl0_103
    | spl0_101
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1919,f2922,f2937,f2945,f2981]) ).

thf(f1919,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1918]) ).

thf(f1918,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1917]) ).

thf(f1917,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1912]) ).

thf(f1912,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1911]) ).

thf(f2996,plain,
    ( spl0_97
    | spl0_101
    | spl0_102
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1922,f2981,f2941,f2937,f2922]) ).

thf(f1922,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1921]) ).

thf(f1921,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1920]) ).

thf(f1920,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1910]) ).

thf(f1910,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1909]) ).

thf(f2995,plain,
    ( spl0_98
    | spl0_106
    | spl0_101
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1926,f2922,f2937,f2981,f2925]) ).

thf(f1926,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1925]) ).

thf(f1925,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1924]) ).

thf(f1924,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1923]) ).

thf(f1923,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1907]) ).

thf(f1907,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1906]) ).

thf(f2994,plain,
    ( spl0_100
    | spl0_104
    | spl0_106
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1938,f2922,f2981,f2949,f2933]) ).

thf(f1938,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1937]) ).

thf(f1937,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1936]) ).

thf(f1936,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1935]) ).

thf(f1935,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1933]) ).

thf(f1933,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1932]) ).

thf(f1932,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1931]) ).

thf(f1931,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1930]) ).

thf(f1930,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1928]) ).

thf(f1928,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1903]) ).

thf(f1903,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1902]) ).

thf(f2993,plain,
    ( spl0_106
    | spl0_97
    | spl0_103
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1941,f2933,f2945,f2922,f2981]) ).

thf(f1941,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1940]) ).

thf(f1940,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1939]) ).

thf(f1939,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1934]) ).

thf(f1934,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1933]) ).

thf(f2992,plain,
    ( spl0_100
    | spl0_97
    | spl0_106
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1947,f2941,f2981,f2922,f2933]) ).

thf(f1947,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1946]) ).

thf(f1946,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1945]) ).

thf(f1945,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1944]) ).

thf(f1944,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f1943]) ).

thf(f1943,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1942]) ).

thf(f1942,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1929]) ).

thf(f1929,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1928]) ).

thf(f2991,plain,
    ( spl0_106
    | spl0_97
    | spl0_98
    | spl0_100 ),
    inference(avatar_split_clause,[],[f1953,f2933,f2925,f2922,f2981]) ).

thf(f1953,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1952]) ).

thf(f1952,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1951]) ).

thf(f1951,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1950]) ).

thf(f1950,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1949]) ).

thf(f1949,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1948]) ).

thf(f1948,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1927]) ).

thf(f1927,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1903]) ).

thf(f2990,plain,
    ( spl0_99
    | spl0_104
    | spl0_106
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1966,f2922,f2981,f2949,f2929]) ).

thf(f1966,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1965]) ).

thf(f1965,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1964]) ).

thf(f1964,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1963]) ).

thf(f1963,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1961]) ).

thf(f1961,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1959]) ).

thf(f1959,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1958]) ).

thf(f1958,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1957]) ).

thf(f1957,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1956]) ).

thf(f1956,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f1954]) ).

thf(f1954,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1900]) ).

thf(f1900,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1899]) ).

thf(f2989,plain,
    ( spl0_103
    | spl0_99
    | spl0_97
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1969,f2981,f2922,f2929,f2945]) ).

thf(f1969,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1968]) ).

thf(f1968,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f1967]) ).

thf(f1967,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1962]) ).

thf(f1962,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1961]) ).

thf(f2988,plain,
    ( spl0_97
    | spl0_106
    | spl0_99
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1972,f2941,f2929,f2981,f2922]) ).

thf(f1972,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1971]) ).

thf(f1971,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1970]) ).

thf(f1970,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1960]) ).

thf(f1960,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1959]) ).

thf(f2987,plain,
    ( spl0_98
    | spl0_106
    | spl0_99
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1978,f2922,f2929,f2981,f2925]) ).

thf(f1978,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1977]) ).

thf(f1977,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1976]) ).

thf(f1976,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f1975]) ).

thf(f1975,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1974]) ).

thf(f1974,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1973]) ).

thf(f1973,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1955]) ).

thf(f1955,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1954]) ).

thf(f2986,plain,
    ( spl0_106
    | spl0_104
    | spl0_95
    | spl0_97 ),
    inference(avatar_split_clause,[],[f1991,f2922,f2916,f2949,f2981]) ).

thf(f1991,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1990]) ).

thf(f1990,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f1989]) ).

thf(f1989,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1988]) ).

thf(f1988,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f1987]) ).

thf(f1987,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1985]) ).

thf(f1985,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1984]) ).

thf(f1984,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f1983]) ).

thf(f1983,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1981]) ).

thf(f1981,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1980]) ).

thf(f1980,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1898]) ).

thf(f1898,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1897]) ).

thf(f2985,plain,
    ( spl0_95
    | spl0_97
    | spl0_103
    | spl0_106 ),
    inference(avatar_split_clause,[],[f1995,f2981,f2945,f2922,f2916]) ).

thf(f1995,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1994]) ).

thf(f1994,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1993]) ).

thf(f1993,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f1992]) ).

thf(f1992,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f1986]) ).

thf(f1986,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1985]) ).

thf(f2984,plain,
    ( spl0_95
    | spl0_106
    | spl0_102
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2001,f2922,f2941,f2981,f2916]) ).

thf(f2001,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2000]) ).

thf(f2000,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f1999]) ).

thf(f1999,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f1998]) ).

thf(f1998,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f1997]) ).

thf(f1997,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f1996]) ).

thf(f1996,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1982]) ).

thf(f1982,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1981]) ).

thf(f2983,plain,
    ( spl0_95
    | spl0_97
    | spl0_106
    | spl0_98 ),
    inference(avatar_split_clause,[],[f2008,f2925,f2981,f2922,f2916]) ).

thf(f2008,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f2007]) ).

thf(f2007,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2006]) ).

thf(f2006,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2005]) ).

thf(f2005,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2004]) ).

thf(f2004,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2003]) ).

thf(f2003,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2002]) ).

thf(f2002,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1979]) ).

thf(f1979,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1898]) ).

thf(f2979,plain,
    ( spl0_104
    | spl0_105
    | spl0_101
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2030,f2922,f2937,f2962,f2949]) ).

thf(f2030,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2029]) ).

thf(f2029,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2028]) ).

thf(f2028,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2027]) ).

thf(f2027,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2026]) ).

thf(f2026,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2025]) ).

thf(f2025,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2024]) ).

thf(f2024,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2022]) ).

thf(f2022,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2020]) ).

thf(f2020,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2018]) ).

thf(f2018,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2016]) ).

thf(f2016,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2015]) ).

thf(f2015,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2013]) ).

thf(f2013,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2011]) ).

thf(f2011,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2010]) ).

thf(f2010,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2009]) ).

thf(f2009,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f1769]) ).

thf(f1769,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f1768]) ).

thf(f2978,plain,
    ( spl0_104
    | spl0_100
    | spl0_105
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2036,f2922,f2962,f2933,f2949]) ).

thf(f2036,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2035]) ).

thf(f2035,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2034]) ).

thf(f2034,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2033]) ).

thf(f2033,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f2032]) ).

thf(f2032,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2031]) ).

thf(f2031,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f2023]) ).

thf(f2023,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2022]) ).

thf(f2977,plain,
    ( spl0_97
    | spl0_99
    | spl0_105
    | spl0_104 ),
    inference(avatar_split_clause,[],[f2042,f2949,f2962,f2929,f2922]) ).

thf(f2042,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2041]) ).

thf(f2041,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2040]) ).

thf(f2040,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2039]) ).

thf(f2039,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2038]) ).

thf(f2038,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2037]) ).

thf(f2037,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2021]) ).

thf(f2021,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2020]) ).

thf(f2976,plain,
    ( spl0_97
    | spl0_105
    | spl0_95
    | spl0_104 ),
    inference(avatar_split_clause,[],[f2048,f2949,f2916,f2962,f2922]) ).

thf(f2048,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2047]) ).

thf(f2047,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2046]) ).

thf(f2046,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f2045]) ).

thf(f2045,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2044]) ).

thf(f2044,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2043]) ).

thf(f2043,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2019]) ).

thf(f2019,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2018]) ).

thf(f2975,plain,
    ( spl0_101
    | spl0_103
    | spl0_97
    | spl0_105 ),
    inference(avatar_split_clause,[],[f2060,f2962,f2922,f2945,f2937]) ).

thf(f2060,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2059]) ).

thf(f2059,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2058]) ).

thf(f2058,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f2057]) ).

thf(f2057,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f2055]) ).

thf(f2055,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2054]) ).

thf(f2054,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f2053]) ).

thf(f2053,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2052]) ).

thf(f2052,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2050]) ).

thf(f2050,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2017]) ).

thf(f2017,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2016]) ).

thf(f2974,plain,
    ( spl0_105
    | spl0_100
    | spl0_103
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2063,f2922,f2945,f2933,f2962]) ).

thf(f2063,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2062]) ).

thf(f2062,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f2061]) ).

thf(f2061,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2056]) ).

thf(f2056,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2055]) ).

thf(f2973,plain,
    ( spl0_99
    | spl0_103
    | spl0_105
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2069,f2922,f2962,f2945,f2929]) ).

thf(f2069,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2068]) ).

thf(f2068,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2067]) ).

thf(f2067,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f2066]) ).

thf(f2066,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2065]) ).

thf(f2065,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2064]) ).

thf(f2064,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f2051]) ).

thf(f2051,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2050]) ).

thf(f2972,plain,
    ( spl0_95
    | spl0_105
    | spl0_103
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2075,f2922,f2945,f2962,f2916]) ).

thf(f2075,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2074]) ).

thf(f2074,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2073]) ).

thf(f2073,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2072]) ).

thf(f2072,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2071]) ).

thf(f2071,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2070]) ).

thf(f2070,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f2049]) ).

thf(f2049,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2017]) ).

thf(f2971,plain,
    ( spl0_102
    | spl0_105
    | spl0_101
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2088,f2922,f2937,f2962,f2941]) ).

thf(f2088,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2087]) ).

thf(f2087,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2086]) ).

thf(f2086,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f2085]) ).

thf(f2085,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2083]) ).

thf(f2083,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2082]) ).

thf(f2082,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2081]) ).

thf(f2081,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2079]) ).

thf(f2079,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2077]) ).

thf(f2077,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2076]) ).

thf(f2076,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2014]) ).

thf(f2014,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2013]) ).

thf(f2970,plain,
    ( spl0_100
    | spl0_105
    | spl0_102
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2091,f2922,f2941,f2962,f2933]) ).

thf(f2091,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2090]) ).

thf(f2090,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2089]) ).

thf(f2089,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2084]) ).

thf(f2084,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2083]) ).

thf(f2969,plain,
    ( spl0_105
    | spl0_102
    | spl0_97
    | spl0_99 ),
    inference(avatar_split_clause,[],[f2096,f2929,f2922,f2941,f2962]) ).

thf(f2096,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2095]) ).

thf(f2095,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2094]) ).

thf(f2094,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f2093]) ).

thf(f2093,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2092]) ).

thf(f2092,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2080]) ).

thf(f2080,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2079]) ).

thf(f2968,plain,
    ( spl0_105
    | spl0_102
    | spl0_97
    | spl0_95 ),
    inference(avatar_split_clause,[],[f2101,f2916,f2922,f2941,f2962]) ).

thf(f2101,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2100]) ).

thf(f2100,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2099]) ).

thf(f2099,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2098]) ).

thf(f2098,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2097]) ).

thf(f2097,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2078]) ).

thf(f2078,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2077]) ).

thf(f2967,plain,
    ( spl0_105
    | spl0_98
    | spl0_101
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2114,f2922,f2937,f2925,f2962]) ).

thf(f2114,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2113]) ).

thf(f2113,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f2112]) ).

thf(f2112,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(pi_clausification,[],[f2111]) ).

thf(f2111,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2109]) ).

thf(f2109,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2108]) ).

thf(f2108,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2107]) ).

thf(f2107,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2105]) ).

thf(f2105,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f2104]) ).

thf(f2104,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(pi_clausification,[],[f2103]) ).

thf(f2103,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2012]) ).

thf(f2012,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2011]) ).

thf(f2966,plain,
    ( spl0_105
    | spl0_98
    | spl0_100
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2117,f2922,f2933,f2925,f2962]) ).

thf(f2117,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2116]) ).

thf(f2116,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2115]) ).

thf(f2115,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f2110]) ).

thf(f2110,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2109]) ).

thf(f2965,plain,
    ( spl0_97
    | spl0_105
    | spl0_98
    | spl0_99 ),
    inference(avatar_split_clause,[],[f2122,f2929,f2925,f2962,f2922]) ).

thf(f2122,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2121]) ).

thf(f2121,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f2120]) ).

thf(f2120,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2119]) ).

thf(f2119,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(pi_clausification,[],[f2118]) ).

thf(f2118,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2106]) ).

thf(f2106,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2105]) ).

thf(f2964,plain,
    ( spl0_97
    | spl0_98
    | spl0_95
    | spl0_105 ),
    inference(avatar_split_clause,[],[f2129,f2962,f2916,f2925,f2922]) ).

thf(f2129,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2128]) ).

thf(f2128,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2127]) ).

thf(f2127,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2126]) ).

thf(f2126,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f2125]) ).

thf(f2125,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2124]) ).

thf(f2124,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2123]) ).

thf(f2123,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2102]) ).

thf(f2102,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X2 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2012]) ).

thf(f2960,plain,
    ( spl0_96
    | spl0_101
    | spl0_97
    | spl0_104 ),
    inference(avatar_split_clause,[],[f2151,f2949,f2922,f2937,f2919]) ).

thf(f2151,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2150]) ).

thf(f2150,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2149]) ).

thf(f2149,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2148]) ).

thf(f2148,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2147]) ).

thf(f2147,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2146]) ).

thf(f2146,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X3 ) ) ),
    inference(pi_clausification,[],[f2145]) ).

thf(f2145,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2143]) ).

thf(f2143,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2141]) ).

thf(f2141,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2139]) ).

thf(f2139,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2138]) ).

thf(f2138,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2136]) ).

thf(f2136,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2134]) ).

thf(f2134,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2132]) ).

thf(f2132,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2131]) ).

thf(f2131,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
          @ X2 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2130]) ).

thf(f2130,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f1767]) ).

thf(f1767,plain,
    ! [X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
          | ( ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
            & ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ sK2 @ Y0 )
                 => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f1766]) ).

thf(f2959,plain,
    ( spl0_104
    | spl0_100
    | spl0_97
    | spl0_96 ),
    inference(avatar_split_clause,[],[f2157,f2919,f2922,f2933,f2949]) ).

thf(f2157,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2156]) ).

thf(f2156,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2155]) ).

thf(f2155,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2154]) ).

thf(f2154,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f2153]) ).

thf(f2153,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2152]) ).

thf(f2152,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2144]) ).

thf(f2144,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2143]) ).

thf(f2958,plain,
    ( spl0_101
    | spl0_96
    | spl0_97
    | spl0_103 ),
    inference(avatar_split_clause,[],[f2165,f2945,f2922,f2919,f2937]) ).

thf(f2165,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2164]) ).

thf(f2164,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f2163]) ).

thf(f2163,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2162]) ).

thf(f2162,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f2161]) ).

thf(f2161,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2160]) ).

thf(f2160,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2159]) ).

thf(f2159,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2142]) ).

thf(f2142,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2141]) ).

thf(f2957,plain,
    ( spl0_97
    | spl0_103
    | spl0_96
    | spl0_100 ),
    inference(avatar_split_clause,[],[f2171,f2933,f2919,f2945,f2922]) ).

thf(f2171,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2170]) ).

thf(f2170,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2169]) ).

thf(f2169,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2168]) ).

thf(f2168,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) ) ),
    inference(pi_clausification,[],[f2167]) ).

thf(f2167,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2166]) ).

thf(f2166,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2158]) ).

thf(f2158,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2142]) ).

thf(f2956,plain,
    ( spl0_97
    | spl0_102
    | spl0_96
    | spl0_101 ),
    inference(avatar_split_clause,[],[f2179,f2937,f2919,f2941,f2922]) ).

thf(f2179,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2178]) ).

thf(f2178,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2177]) ).

thf(f2177,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f2176]) ).

thf(f2176,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2174]) ).

thf(f2174,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2173]) ).

thf(f2173,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f2172]) ).

thf(f2172,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2140]) ).

thf(f2140,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2139]) ).

thf(f2955,plain,
    ( spl0_97
    | spl0_96
    | spl0_102
    | spl0_100 ),
    inference(avatar_split_clause,[],[f2182,f2933,f2941,f2919,f2922]) ).

thf(f2182,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2181]) ).

thf(f2181,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f2180]) ).

thf(f2180,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2175]) ).

thf(f2175,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2174]) ).

thf(f2954,plain,
    ( spl0_97
    | spl0_99
    | spl0_96
    | spl0_104 ),
    inference(avatar_split_clause,[],[f2193,f2949,f2919,f2929,f2922]) ).

thf(f2193,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(binary_proxy_clausification,[],[f2192]) ).

thf(f2192,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ) ),
    inference(beta_eta_normalization,[],[f2191]) ).

thf(f2191,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(pi_clausification,[],[f2190]) ).

thf(f2190,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2188]) ).

thf(f2188,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2186]) ).

thf(f2186,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2185]) ).

thf(f2185,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2184]) ).

thf(f2184,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2183]) ).

thf(f2183,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) ) ),
    inference(pi_clausification,[],[f2137]) ).

thf(f2137,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2136]) ).

thf(f2953,plain,
    ( spl0_97
    | spl0_103
    | spl0_99
    | spl0_96 ),
    inference(avatar_split_clause,[],[f2196,f2919,f2929,f2945,f2922]) ).

thf(f2196,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2195]) ).

thf(f2195,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f2194]) ).

thf(f2194,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2189]) ).

thf(f2189,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2188]) ).

thf(f2952,plain,
    ( spl0_97
    | spl0_96
    | spl0_102
    | spl0_99 ),
    inference(avatar_split_clause,[],[f2199,f2929,f2941,f2919,f2922]) ).

thf(f2199,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2198]) ).

thf(f2198,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2197]) ).

thf(f2197,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2187]) ).

thf(f2187,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2186]) ).

thf(f2951,plain,
    ( spl0_97
    | spl0_95
    | spl0_104
    | spl0_96 ),
    inference(avatar_split_clause,[],[f2210,f2919,f2949,f2916,f2922]) ).

thf(f2210,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2209]) ).

thf(f2209,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2208]) ).

thf(f2208,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2207]) ).

thf(f2207,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2206]) ).

thf(f2206,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2204]) ).

thf(f2204,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2202]) ).

thf(f2202,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2201]) ).

thf(f2201,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) ) ),
    inference(beta_eta_normalization,[],[f2200]) ).

thf(f2200,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X3 )
        = $true )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true ) ),
    inference(pi_clausification,[],[f2135]) ).

thf(f2135,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2134]) ).

thf(f2947,plain,
    ( spl0_97
    | spl0_103
    | spl0_96
    | spl0_95 ),
    inference(avatar_split_clause,[],[f2214,f2916,f2919,f2945,f2922]) ).

thf(f2214,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2213]) ).

thf(f2213,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X4 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f2212]) ).

thf(f2212,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
          @ X4 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2211]) ).

thf(f2211,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2205]) ).

thf(f2205,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2204]) ).

thf(f2943,plain,
    ( spl0_102
    | spl0_95
    | spl0_97
    | spl0_96 ),
    inference(avatar_split_clause,[],[f2218,f2919,f2922,f2916,f2941]) ).

thf(f2218,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2217]) ).

thf(f2217,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f2216]) ).

thf(f2216,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2215]) ).

thf(f2215,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2203]) ).

thf(f2203,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X3 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2202]) ).

thf(f2939,plain,
    ( spl0_97
    | spl0_101
    | spl0_98
    | spl0_96 ),
    inference(avatar_split_clause,[],[f2231,f2919,f2925,f2937,f2922]) ).

thf(f2231,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2230]) ).

thf(f2230,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) ) ),
    inference(beta_eta_normalization,[],[f2229]) ).

thf(f2229,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f2228]) ).

thf(f2228,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2227]) ).

thf(f2227,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2225]) ).

thf(f2225,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2223]) ).

thf(f2223,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2222]) ).

thf(f2222,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2221]) ).

thf(f2221,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2220]) ).

thf(f2220,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2133]) ).

thf(f2133,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
          & ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ sK2 @ Y0 )
               => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2132]) ).

thf(f2935,plain,
    ( spl0_96
    | spl0_97
    | spl0_98
    | spl0_100 ),
    inference(avatar_split_clause,[],[f2235,f2933,f2925,f2922,f2919]) ).

thf(f2235,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2234]) ).

thf(f2234,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2233]) ).

thf(f2233,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f2232]) ).

thf(f2232,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
          @ X4 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(pi_clausification,[],[f2226]) ).

thf(f2226,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2225]) ).

thf(f2931,plain,
    ( spl0_98
    | spl0_99
    | spl0_96
    | spl0_97 ),
    inference(avatar_split_clause,[],[f2239,f2922,f2919,f2929,f2925]) ).

thf(f2239,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2238]) ).

thf(f2238,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2237]) ).

thf(f2237,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2236]) ).

thf(f2236,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2224]) ).

thf(f2224,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f2223]) ).

thf(f2927,plain,
    ( spl0_95
    | spl0_96
    | spl0_97
    | spl0_98 ),
    inference(avatar_split_clause,[],[f2246,f2925,f2922,f2919,f2916]) ).

thf(f2246,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $false
        = ( mrel @ sK2 @ X4 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f2245]) ).

thf(f2245,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X3 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f2244]) ).

thf(f2244,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( $true
        = ( ( mrel @ sK2 @ X4 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2243]) ).

thf(f2243,plain,
    ! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
      ( ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
          @ X4 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(pi_clausification,[],[f2242]) ).

thf(f2242,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( ( mrel @ sK2 @ X3 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X3 ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true ) ),
    inference(beta_eta_normalization,[],[f2241]) ).

thf(f2241,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
          @ X3 ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true ) ),
    inference(pi_clausification,[],[f2240]) ).

thf(f2240,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( ( mrel @ sK2 @ X2 )
        = $false )
      | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f2219]) ).

thf(f2219,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ sK2 @ X1 ) )
      | ( $true
        = ( ( mrel @ sK2 @ X2 )
         => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X2 ) ) )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
        = $true )
      | ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2133]) ).

thf(f2914,plain,
    ( spl0_84
    | spl0_94
    | spl0_88
    | spl0_90 ),
    inference(avatar_split_clause,[],[f2265,f2892,f2882,f2911,f2864]) ).

thf(f2265,plain,
    ( ( ( mrel @ mactual @ sK4 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ( ( mrel @ mactual @ sK6 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f2263]) ).

thf(f2263,plain,
    ( ( ( mrel @ mactual @ sK4 )
      = $true )
    | ( ( ( mrel @ mactual @ sK6 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK6 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) ) ),
    inference(beta_eta_normalization,[],[f2262]) ).

thf(f2262,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( mrel @ mactual @ sK4 )
      = $true )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
        @ sK6 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK5 ) ) ),
    inference(sigma_clausification,[],[f2261]) ).

thf(f2261,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( ( mrel @ mactual @ sK4 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f2259]) ).

thf(f2259,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( ( mrel @ mactual @ sK5 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
      = $false )
    | ( ( mrel @ mactual @ sK4 )
      = $true )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2257]) ).

thf(f2257,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK4 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( ( mrel @ mactual @ sK5 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2256]) ).

thf(f2256,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK4 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
        @ sK5 ) ) ),
    inference(sigma_clausification,[],[f2255]) ).

thf(f2255,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK4 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2254]) ).

thf(f2254,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
        @ sK4 )
      = $false ) ),
    inference(sigma_clausification,[],[f2253]) ).

thf(f2253,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2252]) ).

thf(f2252,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2250]) ).

thf(f2250,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK3 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2249]) ).

thf(f2249,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
        @ sK3 )
      = $false )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(sigma_clausification,[],[f2248]) ).

thf(f2248,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2247]) ).

thf(f2247,plain,
    ( ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f175]) ).

thf(f175,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f174]) ).

thf(f2909,plain,
    ( spl0_93
    | spl0_84
    | spl0_88
    | spl0_90 ),
    inference(avatar_split_clause,[],[f2264,f2892,f2882,f2864,f2906]) ).

thf(f2264,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK6 ) )
    | ( ( mrel @ mactual @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2263]) ).

thf(f2904,plain,
    ( spl0_92
    | spl0_84
    | spl0_90
    | spl0_85 ),
    inference(avatar_split_clause,[],[f2269,f2868,f2892,f2864,f2901]) ).

thf(f2269,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
    | ( ( mrel @ mactual @ sK7 )
      = $true )
    | ( ( mrel @ mactual @ sK4 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f2267]) ).

thf(f2267,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK7 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK7 ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( mrel @ mactual @ sK4 )
      = $true ) ),
    inference(beta_eta_normalization,[],[f2266]) ).

thf(f2266,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
        @ sK7 ) )
    | ( ( mrel @ mactual @ sK4 )
      = $true ) ),
    inference(sigma_clausification,[],[f2260]) ).

thf(f2260,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( mrel @ mactual @ sK4 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f2259]) ).

thf(f2899,plain,
    ( spl0_85
    | spl0_90
    | spl0_91
    | spl0_84 ),
    inference(avatar_split_clause,[],[f2268,f2864,f2896,f2892,f2868]) ).

thf(f2268,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK7 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
    | ( ( mrel @ mactual @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2267]) ).

thf(f2890,plain,
    ( spl0_82
    | spl0_89
    | spl0_88
    | spl0_84 ),
    inference(avatar_split_clause,[],[f2275,f2864,f2882,f2887,f2856]) ).

thf(f2275,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK8 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) )
    | ( $true
      = ( mrel @ mactual @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f2273]) ).

thf(f2273,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ( ( ( mrel @ mactual @ sK8 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK8 ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) ),
    inference(beta_eta_normalization,[],[f2272]) ).

thf(f2272,plain,
    ( ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
        @ sK8 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) ),
    inference(sigma_clausification,[],[f2271]) ).

thf(f2271,plain,
    ( ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2258]) ).

thf(f2258,plain,
    ( ( ( ( mrel @ mactual @ sK5 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f2257]) ).

thf(f2885,plain,
    ( spl0_87
    | spl0_88
    | spl0_84
    | spl0_82 ),
    inference(avatar_split_clause,[],[f2274,f2856,f2864,f2882,f2878]) ).

thf(f2274,plain,
    ( ( $true
      = ( mrel @ mactual @ sK5 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK8 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f2273]) ).

thf(f2876,plain,
    ( spl0_82
    | spl0_84
    | spl0_86
    | spl0_85 ),
    inference(avatar_split_clause,[],[f2279,f2868,f2873,f2864,f2856]) ).

thf(f2279,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK9 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f2277]) ).

thf(f2277,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( ( ( mrel @ mactual @ sK9 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK9 ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) ) ),
    inference(beta_eta_normalization,[],[f2276]) ).

thf(f2276,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
        @ sK9 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK3 ) ) ),
    inference(sigma_clausification,[],[f2270]) ).

thf(f2270,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) )
    | ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f2258]) ).

thf(f2871,plain,
    ( spl0_82
    | spl0_83
    | spl0_84
    | spl0_85 ),
    inference(avatar_split_clause,[],[f2278,f2868,f2864,f2860,f2856]) ).

thf(f2278,plain,
    ( ( $true
      = ( mrel @ mactual @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK9 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK4 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f2277]) ).

thf(f2854,plain,
    ( spl0_80
    | spl0_70
    | spl0_78
    | spl0_81 ),
    inference(avatar_split_clause,[],[f2292,f2850,f2836,f2800,f2845]) ).

thf(f2292,plain,
    ( ( $true
      = ( mrel @ mactual @ sK11 ) )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( ( mrel @ mactual @ sK12 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f2290]) ).

thf(f2290,plain,
    ( ( $true
      = ( mrel @ mactual @ sK11 ) )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( ( ( mrel @ mactual @ sK12 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK12 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2288]) ).

thf(f2288,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK11 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 ) ) )
    | ( ( ( mrel @ mactual @ sK12 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK12 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(beta_eta_normalization,[],[f2287]) ).

thf(f2287,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK11 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 ) ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
        @ sK12 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK10 ) ) ),
    inference(sigma_clausification,[],[f2286]) ).

thf(f2286,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK11 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 ) ) ) ),
    inference(beta_eta_normalization,[],[f2285]) ).

thf(f2285,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
        @ sK11 ) ) ),
    inference(sigma_clausification,[],[f2284]) ).

thf(f2284,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2283]) ).

thf(f2283,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2281]) ).

thf(f2281,plain,
    ( ( ( ( mrel @ mactual @ sK10 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
      = $false )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(beta_eta_normalization,[],[f2280]) ).

thf(f2280,plain,
    ( ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
        @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(sigma_clausification,[],[f2251]) ).

thf(f2251,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2250]) ).

thf(f2853,plain,
    ( spl0_79
    | spl0_78
    | spl0_81
    | spl0_70 ),
    inference(avatar_split_clause,[],[f2291,f2800,f2850,f2836,f2840]) ).

thf(f2291,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $true
      = ( mrel @ mactual @ sK11 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK12 ) ) ),
    inference(binary_proxy_clausification,[],[f2290]) ).

thf(f2848,plain,
    ( spl0_70
    | spl0_80
    | spl0_77
    | spl0_78 ),
    inference(avatar_split_clause,[],[f2294,f2836,f2832,f2845,f2800]) ).

thf(f2294,plain,
    ( ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 )
      = $false )
    | ( ( mrel @ mactual @ sK12 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2289]) ).

thf(f2289,plain,
    ( ( ( ( mrel @ mactual @ sK12 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK12 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2288]) ).

thf(f2843,plain,
    ( spl0_77
    | spl0_78
    | spl0_79
    | spl0_70 ),
    inference(avatar_split_clause,[],[f2293,f2800,f2840,f2836,f2832]) ).

thf(f2293,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK10 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK11 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK12 ) ) ),
    inference(binary_proxy_clausification,[],[f2289]) ).

thf(f2830,plain,
    ( spl0_70
    | spl0_71
    | spl0_76
    | spl0_75 ),
    inference(avatar_split_clause,[],[f2303,f2822,f2827,f2804,f2800]) ).

thf(f2303,plain,
    ( ( $true
      = ( mrel @ mactual @ sK13 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $true
      = ( mrel @ mactual @ sK14 ) ) ),
    inference(binary_proxy_clausification,[],[f2301]) ).

thf(f2301,plain,
    ( ( $true
      = ( mrel @ mactual @ sK13 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK14 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK14 ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) ) ),
    inference(beta_eta_normalization,[],[f2300]) ).

thf(f2300,plain,
    ( ( $true
      = ( mrel @ mactual @ sK13 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
        @ sK14 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(sigma_clausification,[],[f2299]) ).

thf(f2299,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $true
      = ( mrel @ mactual @ sK13 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f2297]) ).

thf(f2297,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( ( ( mrel @ mactual @ sK13 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2296]) ).

thf(f2296,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
        @ sK13 )
      = $false ) ),
    inference(sigma_clausification,[],[f2295]) ).

thf(f2295,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) ) ),
    inference(binary_proxy_clausification,[],[f2282]) ).

thf(f2282,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f2281]) ).

thf(f2825,plain,
    ( spl0_74
    | spl0_70
    | spl0_71
    | spl0_75 ),
    inference(avatar_split_clause,[],[f2302,f2822,f2804,f2800,f2818]) ).

thf(f2302,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK14 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $true
      = ( mrel @ mactual @ sK13 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f2301]) ).

thf(f2816,plain,
    ( spl0_73
    | spl0_72
    | spl0_71
    | spl0_70 ),
    inference(avatar_split_clause,[],[f2307,f2800,f2804,f2808,f2813]) ).

thf(f2307,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $true
      = ( mrel @ mactual @ sK15 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f2305]) ).

thf(f2305,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK15 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK15 ) ) ) ),
    inference(beta_eta_normalization,[],[f2304]) ).

thf(f2304,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
        @ sK15 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) ) ),
    inference(sigma_clausification,[],[f2298]) ).

thf(f2298,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2297]) ).

thf(f2811,plain,
    ( spl0_69
    | spl0_70
    | spl0_71
    | spl0_72 ),
    inference(avatar_split_clause,[],[f2306,f2808,f2804,f2800,f2796]) ).

thf(f2306,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sK13 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ sK10 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ sK3 ) )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ sK15 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2305]) ).

thf(f2794,plain,
    ( spl0_52
    | spl0_60
    | spl0_67
    | spl0_68 ),
    inference(avatar_split_clause,[],[f2326,f2790,f2785,f2752,f2716]) ).

thf(f2326,plain,
    ( ( $true
      = ( mrel @ mactual @ sK18 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( ( mrel @ mactual @ sK19 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2324]) ).

thf(f2324,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( ( ( mrel @ mactual @ sK19 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK19 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK18 ) ) ),
    inference(binary_proxy_clausification,[],[f2322]) ).

thf(f2322,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK18 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) ) )
    | ( ( ( mrel @ mactual @ sK19 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK19 ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2321]) ).

thf(f2321,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK18 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
        @ sK19 )
      = $false ) ),
    inference(sigma_clausification,[],[f2320]) ).

thf(f2320,plain,
    ( ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK18 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(beta_eta_normalization,[],[f2319]) ).

thf(f2319,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
        @ sK18 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(sigma_clausification,[],[f2318]) ).

thf(f2318,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2316]) ).

thf(f2316,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK16 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2314]) ).

thf(f2314,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK17 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK16 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2313]) ).

thf(f2313,plain,
    ( ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK16 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK17 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ) ),
    inference(beta_eta_normalization,[],[f2312]) ).

thf(f2312,plain,
    ( ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
        @ sK17 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK16 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $false ) ),
    inference(sigma_clausification,[],[f2311]) ).

thf(f2311,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK16 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) ) ),
    inference(beta_eta_normalization,[],[f2310]) ).

thf(f2310,plain,
    ( ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
        @ sK16 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $false ) ),
    inference(sigma_clausification,[],[f2309]) ).

thf(f2309,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
    | ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2308]) ).

thf(f2308,plain,
    ( ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f173]) ).

thf(f173,plain,
    ( $false
    = ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f172]) ).

thf(f2793,plain,
    ( spl0_52
    | spl0_65
    | spl0_68
    | spl0_60 ),
    inference(avatar_split_clause,[],[f2325,f2752,f2790,f2776,f2716]) ).

thf(f2325,plain,
    ( ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK18 ) )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK19 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2324]) ).

thf(f2788,plain,
    ( spl0_66
    | spl0_60
    | spl0_67
    | spl0_52 ),
    inference(avatar_split_clause,[],[f2328,f2716,f2785,f2752,f2780]) ).

thf(f2328,plain,
    ( ( ( mrel @ mactual @ sK19 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) ) ),
    inference(binary_proxy_clausification,[],[f2323]) ).

thf(f2323,plain,
    ( ( ( ( mrel @ mactual @ sK19 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK19 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2322]) ).

thf(f2783,plain,
    ( spl0_65
    | spl0_60
    | spl0_66
    | spl0_52 ),
    inference(avatar_split_clause,[],[f2327,f2716,f2780,f2752,f2776]) ).

thf(f2327,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK18 ) )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK19 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2323]) ).

thf(f2774,plain,
    ( spl0_60
    | spl0_63
    | spl0_46
    | spl0_64 ),
    inference(avatar_split_clause,[],[f2336,f2771,f2688,f2766,f2752]) ).

thf(f2336,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( ( mrel @ mactual @ sK20 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK21 ) ) ),
    inference(binary_proxy_clausification,[],[f2334]) ).

thf(f2334,plain,
    ( ( ( mrel @ mactual @ sK20 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( ( ( mrel @ mactual @ sK21 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(beta_eta_normalization,[],[f2333]) ).

thf(f2333,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
        @ sK21 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( ( mrel @ mactual @ sK20 )
      = $true ) ),
    inference(sigma_clausification,[],[f2332]) ).

thf(f2332,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( ( mrel @ mactual @ sK20 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2330]) ).

thf(f2330,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK20 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) ),
    inference(beta_eta_normalization,[],[f2329]) ).

thf(f2329,plain,
    ( ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
        @ sK20 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(sigma_clausification,[],[f2317]) ).

thf(f2317,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2316]) ).

thf(f2769,plain,
    ( spl0_62
    | spl0_46
    | spl0_60
    | spl0_63 ),
    inference(avatar_split_clause,[],[f2335,f2766,f2752,f2688,f2762]) ).

thf(f2335,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK21 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( ( mrel @ mactual @ sK20 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2334]) ).

thf(f2760,plain,
    ( spl0_60
    | spl0_59
    | spl0_46
    | spl0_61 ),
    inference(avatar_split_clause,[],[f2340,f2757,f2688,f2748,f2752]) ).

thf(f2340,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK22 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2338]) ).

thf(f2338,plain,
    ( ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK22 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK22 ) ) ) ),
    inference(beta_eta_normalization,[],[f2337]) ).

thf(f2337,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
        @ sK22 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) ) ),
    inference(sigma_clausification,[],[f2331]) ).

thf(f2331,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) ),
    inference(binary_proxy_clausification,[],[f2330]) ).

thf(f2755,plain,
    ( spl0_58
    | spl0_59
    | spl0_60
    | spl0_46 ),
    inference(avatar_split_clause,[],[f2339,f2688,f2752,f2748,f2744]) ).

thf(f2339,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK22 ) )
    | ( $true
      = ( mrel @ mactual @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK20 ) ) ),
    inference(binary_proxy_clausification,[],[f2338]) ).

thf(f2742,plain,
    ( spl0_52
    | spl0_43
    | spl0_57
    | spl0_56 ),
    inference(avatar_split_clause,[],[f2350,f2734,f2739,f2676,f2716]) ).

thf(f2350,plain,
    ( ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK24 ) )
    | ( $true
      = ( mrel @ mactual @ sK23 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2348]) ).

thf(f2348,plain,
    ( ( $true
      = ( mrel @ mactual @ sK23 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK24 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK24 ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) ) ),
    inference(beta_eta_normalization,[],[f2347]) ).

thf(f2347,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK23 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
        @ sK24 ) ) ),
    inference(sigma_clausification,[],[f2346]) ).

thf(f2346,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $true
      = ( mrel @ mactual @ sK23 ) ) ),
    inference(binary_proxy_clausification,[],[f2344]) ).

thf(f2344,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK23 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2343]) ).

thf(f2343,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
        @ sK23 ) ) ),
    inference(sigma_clausification,[],[f2342]) ).

thf(f2342,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2315]) ).

thf(f2315,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK16 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2314]) ).

thf(f2737,plain,
    ( spl0_43
    | spl0_52
    | spl0_55
    | spl0_56 ),
    inference(avatar_split_clause,[],[f2349,f2734,f2730,f2716,f2676]) ).

thf(f2349,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK24 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK23 ) ) ),
    inference(binary_proxy_clausification,[],[f2348]) ).

thf(f2728,plain,
    ( spl0_52
    | spl0_54
    | spl0_51
    | spl0_43 ),
    inference(avatar_split_clause,[],[f2354,f2676,f2712,f2725,f2716]) ).

thf(f2354,plain,
    ( ( ( mrel @ mactual @ sK25 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2352]) ).

thf(f2352,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) )
    | ( ( ( mrel @ mactual @ sK25 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK25 ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2351]) ).

thf(f2351,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
        @ sK25 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) ) ),
    inference(sigma_clausification,[],[f2345]) ).

thf(f2345,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2344]) ).

thf(f2723,plain,
    ( spl0_51
    | spl0_52
    | spl0_53
    | spl0_43 ),
    inference(avatar_split_clause,[],[f2353,f2676,f2720,f2716,f2712]) ).

thf(f2353,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK25 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK23 ) )
    | ( $true
      = ( mrel @ mactual @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2352]) ).

thf(f2710,plain,
    ( spl0_43
    | spl0_46
    | spl0_49
    | spl0_50 ),
    inference(avatar_split_clause,[],[f2362,f2707,f2702,f2688,f2676]) ).

thf(f2362,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( ( mrel @ mactual @ sK27 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK26 ) ) ),
    inference(binary_proxy_clausification,[],[f2360]) ).

thf(f2360,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK26 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK27 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK27 ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(beta_eta_normalization,[],[f2359]) ).

thf(f2359,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
        @ sK27 ) )
    | ( $true
      = ( mrel @ mactual @ sK26 ) ) ),
    inference(sigma_clausification,[],[f2358]) ).

thf(f2358,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK26 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2356]) ).

thf(f2356,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( ( ( mrel @ mactual @ sK26 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2355]) ).

thf(f2355,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
        @ sK26 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) ) ),
    inference(sigma_clausification,[],[f2341]) ).

thf(f2341,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2315]) ).

thf(f2705,plain,
    ( spl0_48
    | spl0_43
    | spl0_49
    | spl0_46 ),
    inference(avatar_split_clause,[],[f2361,f2688,f2702,f2676,f2698]) ).

thf(f2361,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $true
      = ( mrel @ mactual @ sK26 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK27 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2360]) ).

thf(f2696,plain,
    ( spl0_45
    | spl0_43
    | spl0_46
    | spl0_47 ),
    inference(avatar_split_clause,[],[f2366,f2693,f2688,f2676,f2684]) ).

thf(f2366,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) )
    | ( $true
      = ( mrel @ mactual @ sK28 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2364]) ).

thf(f2364,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK28 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK28 ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) ) ),
    inference(beta_eta_normalization,[],[f2363]) ).

thf(f2363,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
        @ sK28 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) ) ),
    inference(sigma_clausification,[],[f2357]) ).

thf(f2357,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) ) ),
    inference(binary_proxy_clausification,[],[f2356]) ).

thf(f2691,plain,
    ( spl0_43
    | spl0_44
    | spl0_45
    | spl0_46 ),
    inference(avatar_split_clause,[],[f2365,f2688,f2684,f2680,f2676]) ).

thf(f2365,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sK16 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ sK17 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ sK28 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ sK26 ) ) ),
    inference(binary_proxy_clausification,[],[f2364]) ).

thf(f2674,plain,
    ( spl0_42
    | spl0_30
    | spl0_39
    | spl0_36 ),
    inference(avatar_split_clause,[],[f2385,f2640,f2654,f2612,f2670]) ).

thf(f2385,plain,
    ( ( ( mrel @ mactual @ sK32 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK31 ) ) ),
    inference(binary_proxy_clausification,[],[f2383]) ).

thf(f2383,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( ( mrel @ mactual @ sK31 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
      = $false )
    | ( ( mrel @ mactual @ sK32 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK30 ) ) ),
    inference(binary_proxy_clausification,[],[f2381]) ).

thf(f2381,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( ( mrel @ mactual @ sK32 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK32 ) ) )
    | ( ( ( mrel @ mactual @ sK31 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) ) ),
    inference(beta_eta_normalization,[],[f2380]) ).

thf(f2380,plain,
    ( ( ( ( mrel @ mactual @ sK31 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
        @ sK32 )
      = $false ) ),
    inference(sigma_clausification,[],[f2379]) ).

thf(f2379,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( ( mrel @ mactual @ sK31 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2377]) ).

thf(f2377,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK30 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( ( mrel @ mactual @ sK31 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2376]) ).

thf(f2376,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
        @ sK31 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK30 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) ) ),
    inference(sigma_clausification,[],[f2375]) ).

thf(f2375,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( ( mrel @ mactual @ sK30 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2373]) ).

thf(f2373,plain,
    ( ( ( ( mrel @ mactual @ sK29 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 ) )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK30 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2372]) ).

thf(f2372,plain,
    ( ( ( ( mrel @ mactual @ sK29 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 ) )
      = $false )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
        @ sK30 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false ) ),
    inference(sigma_clausification,[],[f2371]) ).

thf(f2371,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( ( ( mrel @ mactual @ sK29 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2370]) ).

thf(f2370,plain,
    ( ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
        @ sK29 )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(sigma_clausification,[],[f2369]) ).

thf(f2369,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2368]) ).

thf(f2368,plain,
    ( ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2367]) ).

thf(f2367,plain,
    ( ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f171]) ).

thf(f171,plain,
    ( $false
    = ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f170]) ).

thf(f2673,plain,
    ( spl0_36
    | spl0_42
    | spl0_35
    | spl0_30 ),
    inference(avatar_split_clause,[],[f2384,f2612,f2636,f2670,f2640]) ).

thf(f2384,plain,
    ( ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( mrel @ mactual @ sK32 )
      = $true )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2383]) ).

thf(f2668,plain,
    ( spl0_41
    | spl0_36
    | spl0_39
    | spl0_30 ),
    inference(avatar_split_clause,[],[f2387,f2612,f2654,f2640,f2664]) ).

thf(f2387,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK32 ) )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( $true
      = ( mrel @ mactual @ sK31 ) ) ),
    inference(binary_proxy_clausification,[],[f2382]) ).

thf(f2382,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK32 ) )
    | ( ( ( mrel @ mactual @ sK31 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
      = $false )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK30 ) ) ),
    inference(binary_proxy_clausification,[],[f2381]) ).

thf(f2667,plain,
    ( spl0_36
    | spl0_41
    | spl0_35
    | spl0_30 ),
    inference(avatar_split_clause,[],[f2386,f2612,f2636,f2664,f2640]) ).

thf(f2386,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK32 ) ) ),
    inference(binary_proxy_clausification,[],[f2382]) ).

thf(f2662,plain,
    ( spl0_39
    | spl0_23
    | spl0_40
    | spl0_36 ),
    inference(avatar_split_clause,[],[f2393,f2640,f2659,f2580,f2654]) ).

thf(f2393,plain,
    ( ( $true
      = ( mrel @ mactual @ sK31 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( mrel @ mactual @ sK33 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2391]) ).

thf(f2391,plain,
    ( ( ( ( mrel @ mactual @ sK33 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK33 ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK31 ) ) ),
    inference(beta_eta_normalization,[],[f2390]) ).

thf(f2390,plain,
    ( ( $true
      = ( mrel @ mactual @ sK31 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
        @ sK33 ) ) ),
    inference(sigma_clausification,[],[f2389]) ).

thf(f2389,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK31 ) ) ),
    inference(binary_proxy_clausification,[],[f2378]) ).

thf(f2378,plain,
    ( ( ( ( mrel @ mactual @ sK31 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) ),
    inference(binary_proxy_clausification,[],[f2377]) ).

thf(f2657,plain,
    ( spl0_38
    | spl0_23
    | spl0_39
    | spl0_36 ),
    inference(avatar_split_clause,[],[f2392,f2640,f2654,f2580,f2650]) ).

thf(f2392,plain,
    ( ( $true
      = ( mrel @ mactual @ sK31 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK33 )
      = $false )
    | ( ( mrel @ mactual @ sK29 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2391]) ).

thf(f2648,plain,
    ( spl0_36
    | spl0_23
    | spl0_37
    | spl0_35 ),
    inference(avatar_split_clause,[],[f2397,f2636,f2645,f2580,f2640]) ).

thf(f2397,plain,
    ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( $true
      = ( mrel @ mactual @ sK34 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2395]) ).

thf(f2395,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK34 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK34 ) ) ) ),
    inference(beta_eta_normalization,[],[f2394]) ).

thf(f2394,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
        @ sK34 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) ),
    inference(sigma_clausification,[],[f2388]) ).

thf(f2388,plain,
    ( ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2378]) ).

thf(f2643,plain,
    ( spl0_34
    | spl0_35
    | spl0_36
    | spl0_23 ),
    inference(avatar_split_clause,[],[f2396,f2580,f2640,f2636,f2632]) ).

thf(f2396,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( mrel @ mactual @ sK29 )
      = $true )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK34 )
      = $false )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK31 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2395]) ).

thf(f2630,plain,
    ( spl0_21
    | spl0_27
    | spl0_30
    | spl0_33 ),
    inference(avatar_split_clause,[],[f2407,f2627,f2612,f2598,f2572]) ).

thf(f2407,plain,
    ( ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( mrel @ mactual @ sK35 )
      = $true )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK36 ) ) ),
    inference(binary_proxy_clausification,[],[f2405]) ).

thf(f2405,plain,
    ( ( ( mrel @ mactual @ sK35 )
      = $true )
    | ( $false
      = ( ( mrel @ mactual @ sK36 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK36 ) ) )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2404]) ).

thf(f2404,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( mrel @ mactual @ sK35 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
        @ sK36 ) ) ),
    inference(sigma_clausification,[],[f2403]) ).

thf(f2403,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( ( mrel @ mactual @ sK35 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2401]) ).

thf(f2401,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK35 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 ) ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) ) ),
    inference(binary_proxy_clausification,[],[f2399]) ).

thf(f2399,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK30 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK35 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 ) ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2398]) ).

thf(f2398,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK30 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
        @ sK35 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false ) ),
    inference(sigma_clausification,[],[f2374]) ).

thf(f2374,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK30 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2373]) ).

thf(f2625,plain,
    ( spl0_32
    | spl0_27
    | spl0_21
    | spl0_30 ),
    inference(avatar_split_clause,[],[f2406,f2612,f2572,f2598,f2622]) ).

thf(f2406,plain,
    ( ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK36 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( mrel @ mactual @ sK35 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2405]) ).

thf(f2620,plain,
    ( spl0_30
    | spl0_24
    | spl0_31
    | spl0_21 ),
    inference(avatar_split_clause,[],[f2411,f2572,f2617,f2584,f2612]) ).

thf(f2411,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( $true
      = ( mrel @ mactual @ sK37 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2409]) ).

thf(f2409,plain,
    ( ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( ( mrel @ mactual @ sK37 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK37 ) )
      = $false )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2408]) ).

thf(f2408,plain,
    ( ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
        @ sK37 )
      = $false ) ),
    inference(sigma_clausification,[],[f2402]) ).

thf(f2402,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2401]) ).

thf(f2615,plain,
    ( spl0_24
    | spl0_29
    | spl0_30
    | spl0_21 ),
    inference(avatar_split_clause,[],[f2410,f2572,f2612,f2608,f2584]) ).

thf(f2410,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK30 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK37 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2409]) ).

thf(f2606,plain,
    ( spl0_28
    | spl0_21
    | spl0_23
    | spl0_27 ),
    inference(avatar_split_clause,[],[f2417,f2598,f2580,f2572,f2603]) ).

thf(f2417,plain,
    ( ( $true
      = ( mrel @ mactual @ sK38 ) )
    | ( ( mrel @ mactual @ sK35 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2415]) ).

thf(f2415,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK38 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK38 ) ) )
    | ( ( mrel @ mactual @ sK35 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) ) ),
    inference(beta_eta_normalization,[],[f2414]) ).

thf(f2414,plain,
    ( ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
        @ sK38 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( mrel @ mactual @ sK35 )
      = $true ) ),
    inference(sigma_clausification,[],[f2413]) ).

thf(f2413,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( ( mrel @ mactual @ sK35 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2400]) ).

thf(f2400,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK35 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2399]) ).

thf(f2601,plain,
    ( spl0_26
    | spl0_21
    | spl0_27
    | spl0_23 ),
    inference(avatar_split_clause,[],[f2416,f2580,f2598,f2572,f2594]) ).

thf(f2416,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK38 ) )
    | ( ( mrel @ mactual @ sK35 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2415]) ).

thf(f2592,plain,
    ( spl0_25
    | spl0_24
    | spl0_21
    | spl0_23 ),
    inference(avatar_split_clause,[],[f2421,f2580,f2572,f2584,f2589]) ).

thf(f2421,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( ( mrel @ mactual @ sK39 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2419]) ).

thf(f2419,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK39 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK39 ) ) )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2418]) ).

thf(f2418,plain,
    ( ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
        @ sK39 )
      = $false )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false ) ),
    inference(sigma_clausification,[],[f2412]) ).

thf(f2412,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2400]) ).

thf(f2587,plain,
    ( spl0_21
    | spl0_22
    | spl0_23
    | spl0_24 ),
    inference(avatar_split_clause,[],[f2420,f2584,f2580,f2576,f2572]) ).

thf(f2420,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ sK30 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sK35 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sK29 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sK39 ) ) ),
    inference(binary_proxy_clausification,[],[f2419]) ).

thf(f2570,plain,
    ( spl0_19
    | spl0_16
    | spl0_9
    | spl0_20 ),
    inference(avatar_split_clause,[],[f2440,f2566,f2516,f2548,f2561]) ).

thf(f2440,plain,
    ( ( $true
      = ( mrel @ mactual @ sK42 ) )
    | ( $true
      = ( mrel @ mactual @ sK43 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK40 ) ) ),
    inference(binary_proxy_clausification,[],[f2438]) ).

thf(f2438,plain,
    ( ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( ( ( mrel @ mactual @ sK43 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK43 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK42 ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) ) ),
    inference(binary_proxy_clausification,[],[f2436]) ).

thf(f2436,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK42 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) ) )
    | ( ( ( mrel @ mactual @ sK43 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK43 ) )
      = $false )
    | ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK40 ) ) ),
    inference(beta_eta_normalization,[],[f2435]) ).

thf(f2435,plain,
    ( ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
        @ sK43 ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $false
      = ( ( mrel @ mactual @ sK42 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) ) ) ),
    inference(sigma_clausification,[],[f2434]) ).

thf(f2434,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK42 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) ) ) ),
    inference(beta_eta_normalization,[],[f2433]) ).

thf(f2433,plain,
    ( ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
        @ sK42 )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true ) ),
    inference(sigma_clausification,[],[f2432]) ).

thf(f2432,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2430]) ).

thf(f2430,plain,
    ( ( ( ( mrel @ mactual @ sK41 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) ) ),
    inference(beta_eta_normalization,[],[f2429]) ).

thf(f2429,plain,
    ( ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
        @ sK41 )
      = $false ) ),
    inference(sigma_clausification,[],[f2428]) ).

thf(f2428,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2426]) ).

thf(f2426,plain,
    ( ( ( ( mrel @ mactual @ sK40 )
       => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 ) )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f2425]) ).

thf(f2425,plain,
    ( ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
        @ sK40 )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false ) ),
    inference(sigma_clausification,[],[f2424]) ).

thf(f2424,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2423]) ).

thf(f2423,plain,
    ( ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2422]) ).

thf(f2422,plain,
    ( ( $false
      = ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
        & ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ mactual @ Y0 )
             => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f169]) ).

thf(f169,plain,
    ( $false
    = ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
      & ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f168]) ).

thf(f2569,plain,
    ( spl0_20
    | spl0_9
    | spl0_16
    | spl0_18 ),
    inference(avatar_split_clause,[],[f2439,f2556,f2548,f2516,f2566]) ).

thf(f2439,plain,
    ( ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK42 ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK43 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2438]) ).

thf(f2564,plain,
    ( spl0_17
    | spl0_9
    | spl0_19
    | spl0_16 ),
    inference(avatar_split_clause,[],[f2442,f2548,f2561,f2516,f2552]) ).

thf(f2442,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $true
      = ( mrel @ mactual @ sK43 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) ) ),
    inference(binary_proxy_clausification,[],[f2437]) ).

thf(f2437,plain,
    ( ( ( ( mrel @ mactual @ sK43 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK43 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2436]) ).

thf(f2559,plain,
    ( spl0_16
    | spl0_17
    | spl0_18
    | spl0_9 ),
    inference(avatar_split_clause,[],[f2441,f2516,f2556,f2552,f2548]) ).

thf(f2441,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK43 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK42 ) )
    | ( ( mrel @ mactual @ sK41 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK40 ) ) ),
    inference(binary_proxy_clausification,[],[f2437]) ).

thf(f2546,plain,
    ( spl0_8
    | spl0_13
    | spl0_15
    | spl0_9 ),
    inference(avatar_split_clause,[],[f2450,f2516,f2543,f2534,f2512]) ).

thf(f2450,plain,
    ( ( ( mrel @ mactual @ sK45 )
      = $true )
    | ( $true
      = ( mrel @ mactual @ sK44 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) ) ),
    inference(binary_proxy_clausification,[],[f2448]) ).

thf(f2448,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $true
      = ( mrel @ mactual @ sK44 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK45 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK45 ) ) ) ),
    inference(beta_eta_normalization,[],[f2447]) ).

thf(f2447,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $true
      = ( mrel @ mactual @ sK44 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
        @ sK45 )
      = $false ) ),
    inference(sigma_clausification,[],[f2446]) ).

thf(f2446,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $true
      = ( mrel @ mactual @ sK44 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2444]) ).

thf(f2444,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK44 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2443]) ).

thf(f2443,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
        @ sK44 )
      = $false ) ),
    inference(sigma_clausification,[],[f2431]) ).

thf(f2431,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2430]) ).

thf(f2541,plain,
    ( spl0_13
    | spl0_9
    | spl0_14
    | spl0_8 ),
    inference(avatar_split_clause,[],[f2449,f2512,f2538,f2516,f2534]) ).

thf(f2449,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $true
      = ( mrel @ mactual @ sK44 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK45 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2448]) ).

thf(f2532,plain,
    ( spl0_10
    | spl0_8
    | spl0_9
    | spl0_12 ),
    inference(avatar_split_clause,[],[f2454,f2529,f2516,f2512,f2520]) ).

thf(f2454,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( mrel @ mactual @ sK46 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2452]) ).

thf(f2452,plain,
    ( ( ( ( mrel @ mactual @ sK46 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK46 ) )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2451]) ).

thf(f2451,plain,
    ( ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
        @ sK46 )
      = $false )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) ) ),
    inference(sigma_clausification,[],[f2445]) ).

thf(f2445,plain,
    ( ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2444]) ).

thf(f2527,plain,
    ( spl0_8
    | spl0_9
    | spl0_10
    | spl0_11 ),
    inference(avatar_split_clause,[],[f2453,f2524,f2520,f2516,f2512]) ).

thf(f2453,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK41 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK44 ) )
    | ( $true
      = ( mrel @ mactual @ sK40 ) )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK46 ) ) ),
    inference(binary_proxy_clausification,[],[f2452]) ).

thf(f2510,plain,
    ( spl0_6
    | spl0_3
    | spl0_5
    | spl0_7 ),
    inference(avatar_split_clause,[],[f2466,f2504,f2493,f2484,f2498]) ).

thf(f2466,plain,
    ( ( $true
      = ( mrel @ mactual @ sK47 ) )
    | ( ( mrel @ mactual @ sK48 )
      = $true )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( ( mrel @ mactual @ sK49 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2464]) ).

thf(f2464,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $true
      = ( mrel @ mactual @ sK47 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK49 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) ) )
    | ( ( mrel @ mactual @ sK48 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2462]) ).

thf(f2462,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) )
    | ( ( mrel @ mactual @ sK48 )
      = $true )
    | ( $false
      = ( ( mrel @ mactual @ sK49 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) ) )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2460]) ).

thf(f2460,plain,
    ( ( $false
      = ( ( mrel @ mactual @ sK48 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK49 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) ) )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false ) ),
    inference(beta_eta_normalization,[],[f2459]) ).

thf(f2459,plain,
    ( ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
        @ sK49 ) )
    | ( $false
      = ( ( mrel @ mactual @ sK48 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 ) ) )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) ) ),
    inference(sigma_clausification,[],[f2458]) ).

thf(f2458,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK48 )
       => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) ) ),
    inference(beta_eta_normalization,[],[f2457]) ).

thf(f2457,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
        @ sK48 ) ) ),
    inference(sigma_clausification,[],[f2456]) ).

thf(f2456,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) ) ),
    inference(beta_eta_normalization,[],[f2455]) ).

thf(f2455,plain,
    ( ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
        @ sK47 )
      = $false ) ),
    inference(sigma_clausification,[],[f2427]) ).

thf(f2427,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
    | ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) )
      = $false )
    | ( $false
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f2426]) ).

thf(f2509,plain,
    ( spl0_7
    | spl0_2
    | spl0_3
    | spl0_5 ),
    inference(avatar_split_clause,[],[f2465,f2493,f2484,f2480,f2504]) ).

thf(f2465,plain,
    ( ( ( mrel @ mactual @ sK48 )
      = $true )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) )
    | ( $true
      = ( mrel @ mactual @ sK47 ) ) ),
    inference(binary_proxy_clausification,[],[f2464]) ).

thf(f2508,plain,
    ( spl0_6
    | spl0_4
    | spl0_7
    | spl0_3 ),
    inference(avatar_split_clause,[],[f2468,f2484,f2504,f2488,f2498]) ).

thf(f2468,plain,
    ( ( ( mrel @ mactual @ sK49 )
      = $true )
    | ( ( mrel @ mactual @ sK48 )
      = $true )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2463]) ).

thf(f2463,plain,
    ( ( ( mrel @ mactual @ sK48 )
      = $true )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK49 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) ) )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2462]) ).

thf(f2507,plain,
    ( spl0_2
    | spl0_3
    | spl0_7
    | spl0_4 ),
    inference(avatar_split_clause,[],[f2467,f2488,f2504,f2484,f2480]) ).

thf(f2467,plain,
    ( ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 )
      = $false )
    | ( ( mrel @ mactual @ sK48 )
      = $true )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2463]) ).

thf(f2502,plain,
    ( spl0_5
    | spl0_1
    | spl0_6
    | spl0_3 ),
    inference(avatar_split_clause,[],[f2472,f2484,f2498,f2476,f2493]) ).

thf(f2472,plain,
    ( ( $true
      = ( mrel @ mactual @ sK47 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( ( mrel @ mactual @ sK49 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2470]) ).

thf(f2470,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) )
    | ( ( mrel @ mactual @ sK49 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f2461]) ).

thf(f2461,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK49 )
       => ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) ) )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2460]) ).

thf(f2501,plain,
    ( spl0_4
    | spl0_1
    | spl0_3
    | spl0_6 ),
    inference(avatar_split_clause,[],[f2471,f2498,f2484,f2476,f2488]) ).

thf(f2471,plain,
    ( ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 )
      = $false )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false )
    | ( ( mrel @ mactual @ sK49 )
      = $true )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2470]) ).

thf(f2496,plain,
    ( spl0_3
    | spl0_2
    | spl0_5
    | spl0_1 ),
    inference(avatar_split_clause,[],[f2474,f2476,f2493,f2480,f2484]) ).

thf(f2474,plain,
    ( ( $true
      = ( mrel @ mactual @ sK47 ) )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f2469]) ).

thf(f2469,plain,
    ( ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) )
    | ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false )
    | ( $false
      = ( ( mrel @ mactual @ sK47 )
       => ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 ) ) ) ),
    inference(binary_proxy_clausification,[],[f2461]) ).

thf(f2491,plain,
    ( spl0_1
    | spl0_2
    | spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f2473,f2488,f2484,f2480,f2476]) ).

thf(f2473,plain,
    ( ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sK48 )
      = $false )
    | ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sK40 )
      = $false )
    | ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sK47 )
      = $false )
    | ( $false
      = ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sK49 ) ) ),
    inference(binary_proxy_clausification,[],[f2469]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : LCL941^5 : TPTP v8.2.0. Released v8.1.0.
% 0.08/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n003.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   : Mon May 20 03:02:08 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH0_THM_EQU_NAR problem
% 0.15/0.36  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39  % (4826)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.40  % (4827)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.40  % (4829)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.40  % (4828)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.40  % (4830)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.40  % (4832)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.40  % (4831)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.40  % (4833)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.40  % (4829)Instruction limit reached!
% 0.15/0.40  % (4829)------------------------------
% 0.15/0.40  % (4829)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40  % (4829)Termination reason: Unknown
% 0.15/0.40  % (4829)Termination phase: shuffling
% 0.15/0.40  
% 0.15/0.40  % (4829)Memory used [KB]: 1151
% 0.15/0.40  % (4830)Instruction limit reached!
% 0.15/0.40  % (4830)------------------------------
% 0.15/0.40  % (4830)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40  % (4830)Termination reason: Unknown
% 0.15/0.40  % (4830)Termination phase: shuffling
% 0.15/0.40  
% 0.15/0.40  % (4830)Memory used [KB]: 1151
% 0.15/0.40  % (4830)Time elapsed: 0.003 s
% 0.15/0.40  % (4830)Instructions burned: 2 (million)
% 0.15/0.40  % (4830)------------------------------
% 0.15/0.40  % (4830)------------------------------
% 0.15/0.40  % (4829)Time elapsed: 0.003 s
% 0.15/0.40  % (4829)Instructions burned: 2 (million)
% 0.15/0.40  % (4829)------------------------------
% 0.15/0.40  % (4829)------------------------------
% 0.15/0.40  % (4833)Instruction limit reached!
% 0.15/0.40  % (4833)------------------------------
% 0.15/0.40  % (4833)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40  % (4833)Termination reason: Unknown
% 0.15/0.40  % (4833)Termination phase: shuffling
% 0.15/0.40  
% 0.15/0.40  % (4833)Memory used [KB]: 1151
% 0.15/0.40  % (4833)Time elapsed: 0.004 s
% 0.15/0.40  % (4833)Instructions burned: 4 (million)
% 0.15/0.40  % (4833)------------------------------
% 0.15/0.40  % (4833)------------------------------
% 0.15/0.40  % (4827)Instruction limit reached!
% 0.15/0.40  % (4827)------------------------------
% 0.15/0.40  % (4827)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40  % (4827)Termination reason: Unknown
% 0.15/0.40  % (4827)Termination phase: shuffling
% 0.15/0.40  
% 0.15/0.40  % (4827)Memory used [KB]: 1279
% 0.15/0.40  % (4827)Time elapsed: 0.005 s
% 0.15/0.40  % (4827)Instructions burned: 5 (million)
% 0.15/0.40  % (4827)------------------------------
% 0.15/0.40  % (4827)------------------------------
% 0.22/0.40  % (4832)Instruction limit reached!
% 0.22/0.40  % (4832)------------------------------
% 0.22/0.40  % (4832)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (4832)Termination reason: Unknown
% 0.22/0.40  % (4832)Termination phase: shuffling
% 0.22/0.40  
% 0.22/0.40  % (4832)Memory used [KB]: 1279
% 0.22/0.40  % (4832)Time elapsed: 0.011 s
% 0.22/0.40  % (4832)Instructions burned: 18 (million)
% 0.22/0.40  % (4832)------------------------------
% 0.22/0.40  % (4832)------------------------------
% 0.22/0.41  % (4828)Instruction limit reached!
% 0.22/0.41  % (4828)------------------------------
% 0.22/0.41  % (4828)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41  % (4828)Termination reason: Unknown
% 0.22/0.41  % (4828)Termination phase: shuffling
% 0.22/0.41  
% 0.22/0.41  % (4828)Memory used [KB]: 1279
% 0.22/0.41  % (4828)Time elapsed: 0.014 s
% 0.22/0.41  % (4828)Instructions burned: 28 (million)
% 0.22/0.41  % (4828)------------------------------
% 0.22/0.41  % (4828)------------------------------
% 0.22/0.41  % (4834)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.22/0.41  % (4835)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.22/0.41  % (4836)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.41  % (4837)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.22/0.41  % (4836)Instruction limit reached!
% 0.22/0.41  % (4836)------------------------------
% 0.22/0.41  % (4836)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41  % (4836)Termination reason: Unknown
% 0.22/0.41  % (4836)Termination phase: shuffling
% 0.22/0.41  
% 0.22/0.41  % (4836)Memory used [KB]: 1151
% 0.22/0.41  % (4836)Time elapsed: 0.004 s
% 0.22/0.41  % (4836)Instructions burned: 4 (million)
% 0.22/0.41  % (4836)------------------------------
% 0.22/0.41  % (4836)------------------------------
% 0.22/0.42  % (4835)Instruction limit reached!
% 0.22/0.42  % (4835)------------------------------
% 0.22/0.42  % (4835)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (4835)Termination reason: Unknown
% 0.22/0.42  % (4835)Termination phase: shuffling
% 0.22/0.42  
% 0.22/0.42  % (4835)Memory used [KB]: 1151
% 0.22/0.42  % (4835)Time elapsed: 0.009 s
% 0.22/0.42  % (4835)Instructions burned: 17 (million)
% 0.22/0.42  % (4835)------------------------------
% 0.22/0.42  % (4835)------------------------------
% 0.22/0.42  % (4838)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.42  % (4839)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.42  % (4838)Instruction limit reached!
% 0.22/0.42  % (4838)------------------------------
% 0.22/0.42  % (4838)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (4838)Termination reason: Unknown
% 0.22/0.42  % (4838)Termination phase: shuffling
% 0.22/0.42  
% 0.22/0.42  % (4838)Memory used [KB]: 1279
% 0.22/0.42  % (4838)Time elapsed: 0.006 s
% 0.22/0.42  % (4838)Instructions burned: 8 (million)
% 0.22/0.42  % (4838)------------------------------
% 0.22/0.42  % (4838)------------------------------
% 0.22/0.43  % (4834)Instruction limit reached!
% 0.22/0.43  % (4834)------------------------------
% 0.22/0.43  % (4834)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43  % (4834)Termination reason: Unknown
% 0.22/0.43  % (4834)Termination phase: Property scanning
% 0.22/0.43  
% 0.22/0.43  % (4834)Memory used [KB]: 1279
% 0.22/0.43  % (4834)Time elapsed: 0.019 s
% 0.22/0.43  % (4834)Instructions burned: 38 (million)
% 0.22/0.43  % (4834)------------------------------
% 0.22/0.43  % (4834)------------------------------
% 0.22/0.43  % (4839)Instruction limit reached!
% 0.22/0.43  % (4839)------------------------------
% 0.22/0.43  % (4839)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43  % (4839)Termination reason: Unknown
% 0.22/0.43  % (4839)Termination phase: shuffling
% 0.22/0.43  
% 0.22/0.43  % (4839)Memory used [KB]: 1151
% 0.22/0.43  % (4839)Time elapsed: 0.010 s
% 0.22/0.43  % (4839)Instructions burned: 16 (million)
% 0.22/0.43  % (4839)------------------------------
% 0.22/0.43  % (4839)------------------------------
% 0.22/0.43  % (4840)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.43  % (4840)Instruction limit reached!
% 0.22/0.43  % (4840)------------------------------
% 0.22/0.43  % (4840)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43  % (4840)Termination reason: Unknown
% 0.22/0.43  % (4840)Termination phase: shuffling
% 0.22/0.43  
% 0.22/0.43  % (4841)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.43  % (4840)Memory used [KB]: 1151
% 0.22/0.43  % (4840)Time elapsed: 0.004 s
% 0.22/0.43  % (4840)Instructions burned: 4 (million)
% 0.22/0.43  % (4840)------------------------------
% 0.22/0.43  % (4840)------------------------------
% 0.22/0.43  % (4841)Instruction limit reached!
% 0.22/0.43  % (4841)------------------------------
% 0.22/0.43  % (4841)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43  % (4841)Termination reason: Unknown
% 0.22/0.43  % (4841)Termination phase: shuffling
% 0.22/0.43  
% 0.22/0.43  % (4841)Memory used [KB]: 1151
% 0.22/0.43  % (4841)Time elapsed: 0.004 s
% 0.22/0.43  % (4841)Instructions burned: 3 (million)
% 0.22/0.43  % (4841)------------------------------
% 0.22/0.43  % (4841)------------------------------
% 0.22/0.44  % (4842)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.44  % (4831)Refutation not found, incomplete strategy
% 0.22/0.44  % (4831)------------------------------
% 0.22/0.44  % (4831)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44  % (4831)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44  
% 0.22/0.44  
% 0.22/0.44  % (4831)Memory used [KB]: 5884
% 0.22/0.44  % (4831)Time elapsed: 0.048 s
% 0.22/0.44  % (4831)Instructions burned: 98 (million)
% 0.22/0.44  % (4831)------------------------------
% 0.22/0.44  % (4831)------------------------------
% 0.22/0.44  % (4842)Instruction limit reached!
% 0.22/0.44  % (4842)------------------------------
% 0.22/0.44  % (4842)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44  % (4842)Termination reason: Unknown
% 0.22/0.44  % (4842)Termination phase: shuffling
% 0.22/0.44  
% 0.22/0.44  % (4842)Memory used [KB]: 1151
% 0.22/0.44  % (4842)Time elapsed: 0.006 s
% 0.22/0.44  % (4842)Instructions burned: 8 (million)
% 0.22/0.44  % (4842)------------------------------
% 0.22/0.44  % (4842)------------------------------
% 0.22/0.44  % (4843)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.44  % (4843)Instruction limit reached!
% 0.22/0.44  % (4843)------------------------------
% 0.22/0.44  % (4843)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44  % (4843)Termination reason: Unknown
% 0.22/0.44  % (4843)Termination phase: shuffling
% 0.22/0.44  
% 0.22/0.44  % (4843)Memory used [KB]: 1151
% 0.22/0.44  % (4843)Time elapsed: 0.004 s
% 0.22/0.44  % (4843)Instructions burned: 4 (million)
% 0.22/0.44  % (4843)------------------------------
% 0.22/0.44  % (4843)------------------------------
% 0.22/0.45  % (4847)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.45  % (4848)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.45  % (4845)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.46  % (4847)Instruction limit reached!
% 0.22/0.46  % (4847)------------------------------
% 0.22/0.46  % (4847)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46  % (4847)Termination reason: Unknown
% 0.22/0.46  % (4847)Termination phase: shuffling
% 0.22/0.46  
% 0.22/0.46  % (4847)Memory used [KB]: 1279
% 0.22/0.46  % (4847)Time elapsed: 0.010 s
% 0.22/0.46  % (4847)Instructions burned: 19 (million)
% 0.22/0.46  % (4847)------------------------------
% 0.22/0.46  % (4847)------------------------------
% 0.22/0.46  % (4849)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.46  % (4850)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.46  % (4845)Instruction limit reached!
% 0.22/0.46  % (4845)------------------------------
% 0.22/0.46  % (4845)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46  % (4845)Termination reason: Unknown
% 0.22/0.46  % (4845)Termination phase: shuffling
% 0.22/0.46  
% 0.22/0.46  % (4845)Memory used [KB]: 1151
% 0.22/0.46  % (4845)Time elapsed: 0.005 s
% 0.22/0.46  % (4845)Instructions burned: 4 (million)
% 0.22/0.46  % (4845)------------------------------
% 0.22/0.46  % (4845)------------------------------
% 0.22/0.46  % (4849)Instruction limit reached!
% 0.22/0.46  % (4849)------------------------------
% 0.22/0.46  % (4849)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46  % (4849)Termination reason: Unknown
% 0.22/0.46  % (4849)Termination phase: shuffling
% 0.22/0.46  
% 0.22/0.46  % (4849)Memory used [KB]: 1151
% 0.22/0.46  % (4849)Time elapsed: 0.005 s
% 0.22/0.46  % (4849)Instructions burned: 7 (million)
% 0.22/0.46  % (4851)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.46  % (4849)------------------------------
% 0.22/0.46  % (4849)------------------------------
% 0.22/0.47  % (4826)Instruction limit reached!
% 0.22/0.47  % (4826)------------------------------
% 0.22/0.47  % (4826)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47  % (4826)Termination reason: Unknown
% 0.22/0.47  % (4826)Termination phase: Saturation
% 0.22/0.47  
% 0.22/0.47  % (4826)Memory used [KB]: 6268
% 0.22/0.47  % (4826)Time elapsed: 0.075 s
% 0.22/0.47  % (4826)Instructions burned: 184 (million)
% 0.22/0.47  % (4826)------------------------------
% 0.22/0.47  % (4826)------------------------------
% 0.22/0.47  % (4851)Instruction limit reached!
% 0.22/0.47  % (4851)------------------------------
% 0.22/0.47  % (4851)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47  % (4851)Termination reason: Unknown
% 0.22/0.47  % (4851)Termination phase: shuffling
% 0.22/0.47  
% 0.22/0.47  % (4851)Memory used [KB]: 1279
% 0.22/0.47  % (4851)Time elapsed: 0.013 s
% 0.22/0.47  % (4851)Instructions burned: 22 (million)
% 0.22/0.47  % (4851)------------------------------
% 0.22/0.47  % (4851)------------------------------
% 0.22/0.47  % (4852)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.47  % (4854)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.48  % (4852)Instruction limit reached!
% 0.22/0.48  % (4852)------------------------------
% 0.22/0.48  % (4852)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48  % (4852)Termination reason: Unknown
% 0.22/0.48  % (4852)Termination phase: shuffling
% 0.22/0.48  
% 0.22/0.48  % (4852)Memory used [KB]: 1151
% 0.22/0.48  % (4852)Time elapsed: 0.005 s
% 0.22/0.48  % (4852)Instructions burned: 5 (million)
% 0.22/0.48  % (4852)------------------------------
% 0.22/0.48  % (4852)------------------------------
% 0.22/0.48  % (4853)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.48  % (4853)Instruction limit reached!
% 0.22/0.48  % (4853)------------------------------
% 0.22/0.48  % (4853)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48  % (4853)Termination reason: Unknown
% 0.22/0.48  % (4853)Termination phase: shuffling
% 0.22/0.48  
% 0.22/0.48  % (4853)Memory used [KB]: 1279
% 0.22/0.48  % (4853)Time elapsed: 0.008 s
% 0.22/0.48  % (4853)Instructions burned: 7 (million)
% 0.22/0.48  % (4853)------------------------------
% 0.22/0.48  % (4853)------------------------------
% 0.22/0.49  % (4855)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.22/0.50  % (4863)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.22/0.51  % (4864)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.22/0.51  % (4865)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.22/0.51  % (4863)Instruction limit reached!
% 0.22/0.51  % (4863)------------------------------
% 0.22/0.51  % (4863)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51  % (4863)Termination reason: Unknown
% 0.22/0.51  % (4863)Termination phase: Property scanning
% 0.22/0.51  
% 0.22/0.51  % (4863)Memory used [KB]: 1279
% 0.22/0.51  % (4863)Time elapsed: 0.017 s
% 0.22/0.51  % (4863)Instructions burned: 19 (million)
% 0.22/0.51  % (4863)------------------------------
% 0.22/0.51  % (4863)------------------------------
% 0.22/0.52  % (4865)Instruction limit reached!
% 0.22/0.52  % (4865)------------------------------
% 0.22/0.52  % (4865)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52  % (4865)Termination reason: Unknown
% 0.22/0.52  % (4865)Termination phase: shuffling
% 0.22/0.52  
% 0.22/0.52  % (4865)Memory used [KB]: 1151
% 0.22/0.52  % (4865)Time elapsed: 0.013 s
% 0.22/0.52  % (4865)Instructions burned: 18 (million)
% 0.22/0.52  % (4865)------------------------------
% 0.22/0.52  % (4865)------------------------------
% 0.22/0.52  % (4850)Refutation not found, incomplete strategy
% 0.22/0.52  % (4850)------------------------------
% 0.22/0.52  % (4850)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52  % (4850)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.52  
% 0.22/0.52  
% 0.22/0.52  % (4850)Memory used [KB]: 5884
% 0.22/0.52  % (4850)Time elapsed: 0.065 s
% 0.22/0.52  % (4850)Instructions burned: 97 (million)
% 0.22/0.52  % (4850)------------------------------
% 0.22/0.52  % (4850)------------------------------
% 0.22/0.53  % (4866)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.53  % (4866)Instruction limit reached!
% 0.22/0.53  % (4866)------------------------------
% 0.22/0.53  % (4866)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53  % (4866)Termination reason: Unknown
% 0.22/0.53  % (4866)Termination phase: shuffling
% 0.22/0.53  
% 0.22/0.53  % (4866)Memory used [KB]: 1151
% 0.22/0.53  % (4866)Time elapsed: 0.002 s
% 0.22/0.53  % (4866)Instructions burned: 3 (million)
% 0.22/0.53  % (4866)------------------------------
% 0.22/0.53  % (4866)------------------------------
% 0.22/0.54  % (4868)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.22/0.54  % (4867)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.22/0.55  % (4867)Instruction limit reached!
% 0.22/0.55  % (4867)------------------------------
% 0.22/0.55  % (4867)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55  % (4867)Termination reason: Unknown
% 0.22/0.55  % (4867)Termination phase: shuffling
% 0.22/0.55  
% 0.22/0.55  % (4867)Memory used [KB]: 1151
% 0.22/0.55  % (4867)Time elapsed: 0.014 s
% 0.22/0.55  % (4867)Instructions burned: 31 (million)
% 0.22/0.55  % (4867)------------------------------
% 0.22/0.55  % (4867)------------------------------
% 0.22/0.56  % (4869)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.22/0.57  % (4871)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.57  % (4871)Instruction limit reached!
% 0.22/0.57  % (4871)------------------------------
% 0.22/0.57  % (4871)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.57  % (4871)Termination reason: Unknown
% 0.22/0.57  % (4871)Termination phase: shuffling
% 0.22/0.57  
% 0.22/0.57  % (4871)Memory used [KB]: 1151
% 0.22/0.57  % (4871)Time elapsed: 0.003 s
% 0.22/0.57  % (4871)Instructions burned: 6 (million)
% 0.22/0.57  % (4871)------------------------------
% 0.22/0.57  % (4871)------------------------------
% 1.67/0.59  % (4868)Instruction limit reached!
% 1.67/0.59  % (4868)------------------------------
% 1.67/0.59  % (4868)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.67/0.59  % (4868)Termination reason: Unknown
% 1.67/0.59  % (4868)Termination phase: Property scanning
% 1.67/0.59  
% 1.67/0.59  % (4868)Memory used [KB]: 1279
% 1.67/0.59  % (4868)Time elapsed: 0.054 s
% 1.67/0.59  % (4868)Instructions burned: 127 (million)
% 1.67/0.59  % (4868)------------------------------
% 1.67/0.59  % (4868)------------------------------
% 1.67/0.60  % (4874)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2997ds/20Mi)
% 1.67/0.60  % (4869)Instruction limit reached!
% 1.67/0.60  % (4869)------------------------------
% 1.67/0.60  % (4869)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.67/0.60  % (4869)Termination reason: Unknown
% 1.67/0.60  % (4869)Termination phase: Saturation
% 1.67/0.60  
% 1.67/0.60  % (4869)Memory used [KB]: 5884
% 1.67/0.60  % (4869)Time elapsed: 0.045 s
% 1.67/0.60  % (4869)Instructions burned: 101 (million)
% 1.67/0.60  % (4869)------------------------------
% 1.67/0.60  % (4869)------------------------------
% 1.84/0.61  % (4874)Instruction limit reached!
% 1.84/0.61  % (4874)------------------------------
% 1.84/0.61  % (4874)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.84/0.61  % (4874)Termination reason: Unknown
% 1.84/0.61  % (4874)Termination phase: shuffling
% 1.84/0.61  
% 1.84/0.61  % (4874)Memory used [KB]: 1279
% 1.84/0.61  % (4874)Time elapsed: 0.010 s
% 1.84/0.61  % (4874)Instructions burned: 20 (million)
% 1.84/0.61  % (4874)------------------------------
% 1.84/0.61  % (4874)------------------------------
% 1.84/0.61  % (4875)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 1.84/0.62  % (4855)Refutation not found, incomplete strategy
% 1.84/0.62  % (4855)------------------------------
% 1.84/0.62  % (4855)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.84/0.62  % (4855)Termination reason: Refutation not found, incomplete strategy
% 1.84/0.62  
% 1.84/0.62  
% 1.84/0.62  % (4855)Memory used [KB]: 8443
% 1.84/0.62  % (4855)Time elapsed: 0.127 s
% 1.84/0.62  % (4855)Instructions burned: 242 (million)
% 1.84/0.62  % (4855)------------------------------
% 1.84/0.62  % (4855)------------------------------
% 1.84/0.62  % (4877)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 1.84/0.63  % (4878)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.84/0.63  % (4879)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2997ds/448Mi)
% 1.99/0.65  % (4875)Instruction limit reached!
% 1.99/0.65  % (4875)------------------------------
% 1.99/0.65  % (4875)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.65  % (4875)Termination reason: Unknown
% 1.99/0.65  % (4875)Termination phase: Function definition elimination
% 1.99/0.65  
% 1.99/0.65  % (4875)Memory used [KB]: 1279
% 1.99/0.65  % (4875)Time elapsed: 0.037 s
% 1.99/0.65  % (4875)Instructions burned: 87 (million)
% 1.99/0.65  % (4875)------------------------------
% 1.99/0.65  % (4875)------------------------------
% 1.99/0.65  % (4878)Instruction limit reached!
% 1.99/0.65  % (4878)------------------------------
% 1.99/0.65  % (4878)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.65  % (4878)Termination reason: Unknown
% 1.99/0.65  % (4878)Termination phase: Property scanning
% 1.99/0.65  
% 1.99/0.65  % (4878)Memory used [KB]: 1279
% 1.99/0.65  % (4878)Time elapsed: 0.019 s
% 1.99/0.65  % (4878)Instructions burned: 39 (million)
% 1.99/0.65  % (4878)------------------------------
% 1.99/0.65  % (4878)------------------------------
% 1.99/0.65  % (4854)Instruction limit reached!
% 1.99/0.65  % (4854)------------------------------
% 1.99/0.65  % (4854)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.65  % (4854)Termination reason: Unknown
% 1.99/0.65  % (4854)Termination phase: Saturation
% 1.99/0.65  
% 1.99/0.65  % (4854)Memory used [KB]: 6908
% 1.99/0.65  % (4854)Time elapsed: 0.174 s
% 1.99/0.65  % (4854)Instructions burned: 378 (million)
% 1.99/0.65  % (4854)------------------------------
% 1.99/0.65  % (4854)------------------------------
% 1.99/0.66  % (4877)Instruction limit reached!
% 1.99/0.66  % (4877)------------------------------
% 1.99/0.66  % (4877)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.66  % (4877)Termination reason: Unknown
% 1.99/0.66  % (4877)Termination phase: Property scanning
% 1.99/0.66  
% 1.99/0.66  % (4877)Memory used [KB]: 1279
% 1.99/0.66  % (4877)Time elapsed: 0.046 s
% 1.99/0.66  % (4877)Instructions burned: 108 (million)
% 1.99/0.66  % (4877)------------------------------
% 1.99/0.66  % (4877)------------------------------
% 1.99/0.66  % (4881)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2997ds/98Mi)
% 1.99/0.67  % (4882)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2997ds/507Mi)
% 1.99/0.67  % (4880)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2997ds/46Mi)
% 1.99/0.68  % (4883)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2997ds/149Mi)
% 1.99/0.69  % (4880)Instruction limit reached!
% 1.99/0.69  % (4880)------------------------------
% 1.99/0.69  % (4880)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.69  % (4880)Termination reason: Unknown
% 1.99/0.69  % (4880)Termination phase: shuffling
% 1.99/0.69  
% 1.99/0.69  % (4880)Memory used [KB]: 1279
% 1.99/0.69  % (4880)Time elapsed: 0.020 s
% 1.99/0.69  % (4880)Instructions burned: 46 (million)
% 1.99/0.69  % (4880)------------------------------
% 1.99/0.69  % (4880)------------------------------
% 1.99/0.70  % (4881)Instruction limit reached!
% 1.99/0.70  % (4881)------------------------------
% 1.99/0.70  % (4881)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.70  % (4881)Termination reason: Unknown
% 1.99/0.70  % (4881)Termination phase: Saturation
% 1.99/0.70  
% 1.99/0.70  % (4881)Memory used [KB]: 1407
% 1.99/0.70  % (4881)Time elapsed: 0.043 s
% 1.99/0.70  % (4881)Instructions burned: 98 (million)
% 1.99/0.70  % (4881)------------------------------
% 1.99/0.70  % (4881)------------------------------
% 1.99/0.71  % (4884)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2996ds/39Mi)
% 1.99/0.72  % (4884)Instruction limit reached!
% 1.99/0.72  % (4884)------------------------------
% 1.99/0.72  % (4884)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.72  % (4884)Termination reason: Unknown
% 1.99/0.72  % (4884)Termination phase: shuffling
% 1.99/0.72  
% 1.99/0.72  % (4884)Memory used [KB]: 1279
% 1.99/0.72  % (4884)Time elapsed: 0.017 s
% 1.99/0.72  % (4884)Instructions burned: 39 (million)
% 1.99/0.72  % (4884)------------------------------
% 1.99/0.72  % (4884)------------------------------
% 1.99/0.72  % (4885)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2996ds/6Mi)
% 1.99/0.72  % (4885)Instruction limit reached!
% 1.99/0.72  % (4885)------------------------------
% 1.99/0.72  % (4885)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.99/0.72  % (4885)Termination reason: Unknown
% 1.99/0.72  % (4885)Termination phase: shuffling
% 1.99/0.72  
% 1.99/0.72  % (4885)Memory used [KB]: 1279
% 1.99/0.72  % (4885)Time elapsed: 0.004 s
% 1.99/0.72  % (4885)Instructions burned: 6 (million)
% 1.99/0.72  % (4885)------------------------------
% 1.99/0.72  % (4885)------------------------------
% 2.57/0.74  % (4886)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on theBenchmark for (2996ds/1087Mi)
% 2.57/0.74  % (4887)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2996ds/47Mi)
% 2.57/0.74  % (4883)Instruction limit reached!
% 2.57/0.74  % (4883)------------------------------
% 2.57/0.74  % (4883)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.57/0.74  % (4883)Termination reason: Unknown
% 2.57/0.74  % (4883)Termination phase: Saturation
% 2.57/0.74  
% 2.57/0.74  % (4883)Memory used [KB]: 6140
% 2.57/0.74  % (4883)Time elapsed: 0.064 s
% 2.57/0.74  % (4883)Instructions burned: 150 (million)
% 2.57/0.74  % (4883)------------------------------
% 2.57/0.74  % (4883)------------------------------
% 2.57/0.76  % (4887)Instruction limit reached!
% 2.57/0.76  % (4887)------------------------------
% 2.57/0.76  % (4887)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.57/0.76  % (4887)Termination reason: Unknown
% 2.57/0.76  % (4887)Termination phase: shuffling
% 2.57/0.76  
% 2.57/0.76  % (4887)Memory used [KB]: 1279
% 2.57/0.76  % (4887)Time elapsed: 0.020 s
% 2.57/0.76  % (4887)Instructions burned: 49 (million)
% 2.57/0.76  % (4887)------------------------------
% 2.57/0.76  % (4887)------------------------------
% 2.57/0.77  % (4888)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on theBenchmark for (2996ds/44Mi)
% 2.57/0.78  % (4889)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on theBenchmark for (2996ds/432Mi)
% 2.86/0.79  % (4848)Instruction limit reached!
% 2.86/0.79  % (4848)------------------------------
% 2.86/0.79  % (4848)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.79  % (4848)Termination reason: Unknown
% 2.86/0.79  % (4848)Termination phase: Saturation
% 2.86/0.79  
% 2.86/0.79  % (4848)Memory used [KB]: 8315
% 2.86/0.79  % (4848)Time elapsed: 0.352 s
% 2.86/0.79  % (4848)Instructions burned: 711 (million)
% 2.86/0.79  % (4848)------------------------------
% 2.86/0.79  % (4848)------------------------------
% 2.86/0.80  % (4888)Instruction limit reached!
% 2.86/0.80  % (4888)------------------------------
% 2.86/0.80  % (4888)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.80  % (4888)Termination reason: Unknown
% 2.86/0.80  % (4888)Termination phase: Property scanning
% 2.86/0.80  
% 2.86/0.80  % (4888)Memory used [KB]: 1279
% 2.86/0.80  % (4888)Time elapsed: 0.019 s
% 2.86/0.80  % (4888)Instructions burned: 45 (million)
% 2.86/0.80  % (4888)------------------------------
% 2.86/0.80  % (4888)------------------------------
% 2.86/0.80  % (4890)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2995ds/62Mi)
% 2.86/0.82  % (4886)Refutation not found, incomplete strategy
% 2.86/0.82  % (4886)------------------------------
% 2.86/0.82  % (4886)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.82  % (4886)Termination reason: Refutation not found, incomplete strategy
% 2.86/0.82  
% 2.86/0.82  
% 2.86/0.82  % (4886)Memory used [KB]: 8059
% 2.86/0.82  % (4886)Time elapsed: 0.081 s
% 2.86/0.82  % (4886)Instructions burned: 169 (million)
% 2.86/0.82  % (4886)------------------------------
% 2.86/0.82  % (4886)------------------------------
% 2.86/0.82  % (4891)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2995ds/31Mi)
% 2.86/0.83  % (4879)Instruction limit reached!
% 2.86/0.83  % (4879)------------------------------
% 2.86/0.83  % (4879)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.83  % (4879)Termination reason: Unknown
% 2.86/0.83  % (4879)Termination phase: Saturation
% 2.86/0.83  
% 2.86/0.83  % (4879)Memory used [KB]: 7419
% 2.86/0.83  % (4879)Time elapsed: 0.202 s
% 2.86/0.83  % (4879)Instructions burned: 448 (million)
% 2.86/0.83  % (4879)------------------------------
% 2.86/0.83  % (4879)------------------------------
% 2.86/0.83  % (4837)Instruction limit reached!
% 2.86/0.83  % (4837)------------------------------
% 2.86/0.83  % (4837)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.83  % (4837)Termination reason: Unknown
% 2.86/0.83  % (4837)Termination phase: Saturation
% 2.86/0.83  
% 2.86/0.83  % (4837)Memory used [KB]: 8315
% 2.86/0.83  % (4837)Time elapsed: 0.417 s
% 2.86/0.83  % (4837)Instructions burned: 1041 (million)
% 2.86/0.83  % (4837)------------------------------
% 2.86/0.83  % (4837)------------------------------
% 2.86/0.83  % (4890)Instruction limit reached!
% 2.86/0.83  % (4890)------------------------------
% 2.86/0.83  % (4890)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.83  % (4890)Termination reason: Unknown
% 2.86/0.83  % (4890)Termination phase: Property scanning
% 2.86/0.83  
% 2.86/0.83  % (4890)Memory used [KB]: 1279
% 2.86/0.83  % (4890)Time elapsed: 0.029 s
% 2.86/0.83  % (4890)Instructions burned: 63 (million)
% 2.86/0.83  % (4890)------------------------------
% 2.86/0.83  % (4890)------------------------------
% 2.86/0.83  % (4891)Instruction limit reached!
% 2.86/0.83  % (4891)------------------------------
% 2.86/0.83  % (4891)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.83  % (4891)Termination reason: Unknown
% 2.86/0.83  % (4891)Termination phase: shuffling
% 2.86/0.83  
% 2.86/0.83  % (4891)Memory used [KB]: 1279
% 2.86/0.83  % (4891)Time elapsed: 0.014 s
% 2.86/0.83  % (4891)Instructions burned: 32 (million)
% 2.86/0.83  % (4891)------------------------------
% 2.86/0.83  % (4891)------------------------------
% 2.86/0.84  % (4892)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2995ds/96Mi)
% 2.86/0.84  % (4893)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on theBenchmark for (2995ds/453Mi)
% 2.86/0.84  % (4894)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2995ds/71Mi)
% 2.86/0.85  % (4896)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2995ds/11Mi)
% 2.86/0.85  % (4896)Instruction limit reached!
% 2.86/0.85  % (4896)------------------------------
% 2.86/0.85  % (4896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.85  % (4896)Termination reason: Unknown
% 2.86/0.85  % (4896)Termination phase: shuffling
% 2.86/0.85  
% 2.86/0.85  % (4896)Memory used [KB]: 1279
% 2.86/0.85  % (4896)Time elapsed: 0.007 s
% 2.86/0.85  % (4896)Instructions burned: 11 (million)
% 2.86/0.85  % (4896)------------------------------
% 2.86/0.85  % (4896)------------------------------
% 3.40/0.86  % (4892)Instruction limit reached!
% 3.40/0.86  % (4892)------------------------------
% 3.40/0.86  % (4892)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.40/0.86  % (4892)Termination reason: Unknown
% 3.40/0.86  % (4892)Termination phase: Property scanning
% 3.40/0.86  
% 3.40/0.86  % (4892)Memory used [KB]: 1279
% 3.40/0.86  % (4892)Time elapsed: 0.025 s
% 3.40/0.86  % (4892)Instructions burned: 97 (million)
% 3.40/0.86  % (4892)------------------------------
% 3.40/0.86  % (4892)------------------------------
% 3.40/0.86  % (4895)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2995ds/83Mi)
% 3.44/0.87  % (4898)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2995ds/6Mi)
% 3.44/0.87  % (4898)Instruction limit reached!
% 3.44/0.87  % (4898)------------------------------
% 3.44/0.87  % (4898)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.44/0.87  % (4898)Termination reason: Unknown
% 3.44/0.87  % (4898)Termination phase: shuffling
% 3.44/0.87  
% 3.44/0.87  % (4898)Memory used [KB]: 1151
% 3.44/0.87  % (4898)Time elapsed: 0.003 s
% 3.44/0.87  % (4898)Instructions burned: 6 (million)
% 3.44/0.87  % (4898)------------------------------
% 3.44/0.87  % (4898)------------------------------
% 3.44/0.87  % (4897)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on theBenchmark for (2995ds/41Mi)
% 3.44/0.87  % (4894)Instruction limit reached!
% 3.44/0.87  % (4894)------------------------------
% 3.44/0.87  % (4894)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.44/0.87  % (4894)Termination reason: Unknown
% 3.44/0.87  % (4894)Termination phase: Preprocessing 3
% 3.44/0.87  
% 3.44/0.87  % (4894)Memory used [KB]: 1279
% 3.44/0.87  % (4894)Time elapsed: 0.030 s
% 3.44/0.87  % (4894)Instructions burned: 71 (million)
% 3.44/0.87  % (4894)------------------------------
% 3.44/0.87  % (4894)------------------------------
% 3.44/0.88  % (4899)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2995ds/150Mi)
% 3.44/0.88  % (4882)Instruction limit reached!
% 3.44/0.88  % (4882)------------------------------
% 3.44/0.88  % (4882)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.44/0.88  % (4882)Termination reason: Unknown
% 3.44/0.88  % (4882)Termination phase: Saturation
% 3.44/0.88  
% 3.44/0.88  % (4882)Memory used [KB]: 7419
% 3.44/0.88  % (4882)Time elapsed: 0.216 s
% 3.44/0.88  % (4882)Instructions burned: 508 (million)
% 3.44/0.88  % (4882)------------------------------
% 3.44/0.88  % (4882)------------------------------
% 3.44/0.89  % (4897)Instruction limit reached!
% 3.44/0.89  % (4897)------------------------------
% 3.44/0.89  % (4897)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.44/0.89  % (4897)Termination reason: Unknown
% 3.44/0.89  % (4897)Termination phase: Function definition elimination
% 3.44/0.89  
% 3.44/0.89  % (4897)Memory used [KB]: 1279
% 3.44/0.89  % (4897)Time elapsed: 0.019 s
% 3.44/0.89  % (4897)Instructions burned: 41 (million)
% 3.44/0.89  % (4897)------------------------------
% 3.44/0.89  % (4897)------------------------------
% 3.44/0.89  % (4900)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on theBenchmark for (2995ds/343Mi)
% 3.44/0.90  % (4895)Instruction limit reached!
% 3.44/0.90  % (4895)------------------------------
% 3.44/0.90  % (4895)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.44/0.90  % (4895)Termination reason: Unknown
% 3.44/0.90  % (4895)Termination phase: Property scanning
% 3.44/0.90  
% 3.44/0.90  % (4895)Memory used [KB]: 1279
% 3.44/0.90  % (4895)Time elapsed: 0.033 s
% 3.44/0.90  % (4895)Instructions burned: 83 (million)
% 3.44/0.90  % (4895)------------------------------
% 3.44/0.90  % (4895)------------------------------
% 3.44/0.90  % (4901)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on theBenchmark for (2994ds/109Mi)
% 3.44/0.90  % (4902)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on theBenchmark for (2994ds/253Mi)
% 3.84/0.91  % (4864)Instruction limit reached!
% 3.84/0.91  % (4864)------------------------------
% 3.84/0.91  % (4864)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.91  % (4864)Termination reason: Unknown
% 3.84/0.91  % (4864)Termination phase: Saturation
% 3.84/0.91  
% 3.84/0.91  % (4864)Memory used [KB]: 9210
% 3.84/0.91  % (4864)Time elapsed: 0.401 s
% 3.84/0.91  % (4864)Instructions burned: 880 (million)
% 3.84/0.91  % (4864)------------------------------
% 3.84/0.91  % (4864)------------------------------
% 3.84/0.91  % (4903)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2994ds/140Mi)
% 3.84/0.92  % (4904)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on theBenchmark for (2994ds/614Mi)
% 3.84/0.93  % (4899)Instruction limit reached!
% 3.84/0.93  % (4899)------------------------------
% 3.84/0.93  % (4899)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.84/0.93  % (4899)Termination reason: Unknown
% 3.84/0.93  % (4899)Termination phase: Saturation
% 3.84/0.93  
% 3.84/0.93  % (4899)Memory used [KB]: 6012
% 3.84/0.93  % (4899)Time elapsed: 0.037 s
% 3.84/0.93  % (4899)Instructions burned: 153 (million)
% 3.84/0.93  % (4899)------------------------------
% 3.84/0.93  % (4899)------------------------------
% 3.84/0.93  % (4905)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on theBenchmark for (2994ds/202Mi)
% 3.89/0.94  % (4901)Instruction limit reached!
% 3.89/0.94  % (4901)------------------------------
% 3.89/0.94  % (4901)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/0.94  % (4901)Termination reason: Unknown
% 3.89/0.94  % (4901)Termination phase: Property scanning
% 3.89/0.94  
% 3.89/0.94  % (4901)Memory used [KB]: 1279
% 3.89/0.94  % (4901)Time elapsed: 0.046 s
% 3.89/0.94  % (4901)Instructions burned: 109 (million)
% 3.89/0.94  % (4901)------------------------------
% 3.89/0.94  % (4901)------------------------------
% 3.89/0.96  % (4902)Refutation not found, incomplete strategy
% 3.89/0.96  % (4902)------------------------------
% 3.89/0.96  % (4902)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/0.96  % (4902)Termination reason: Refutation not found, incomplete strategy
% 3.89/0.96  
% 3.89/0.96  
% 3.89/0.96  % (4902)Memory used [KB]: 7803
% 3.89/0.96  % (4902)Time elapsed: 0.059 s
% 3.89/0.96  % (4902)Instructions burned: 136 (million)
% 3.89/0.96  % (4902)------------------------------
% 3.89/0.96  % (4902)------------------------------
% 3.89/0.96  % (4889)Instruction limit reached!
% 3.89/0.96  % (4889)------------------------------
% 3.89/0.96  % (4889)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/0.96  % (4889)Termination reason: Unknown
% 3.89/0.96  % (4889)Termination phase: Saturation
% 3.89/0.96  
% 3.89/0.96  % (4889)Memory used [KB]: 3198
% 3.89/0.96  % (4889)Time elapsed: 0.185 s
% 3.89/0.96  % (4889)Instructions burned: 432 (million)
% 3.89/0.96  % (4889)------------------------------
% 3.89/0.96  % (4889)------------------------------
% 3.89/0.96  % (4903)Instruction limit reached!
% 3.89/0.96  % (4903)------------------------------
% 3.89/0.96  % (4903)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/0.96  % (4903)Termination reason: Unknown
% 3.89/0.96  % (4903)Termination phase: Saturation
% 3.89/0.96  
% 3.89/0.96  % (4903)Memory used [KB]: 6012
% 3.89/0.96  % (4903)Time elapsed: 0.053 s
% 3.89/0.96  % (4903)Instructions burned: 141 (million)
% 3.89/0.96  % (4903)------------------------------
% 3.89/0.96  % (4903)------------------------------
% 3.89/0.96  % (4906)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on theBenchmark for (2994ds/339Mi)
% 3.89/0.97  % (4900)Refutation not found, incomplete strategy
% 3.89/0.97  % (4900)------------------------------
% 3.89/0.97  % (4900)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/0.97  % (4900)Termination reason: Refutation not found, incomplete strategy
% 3.89/0.97  
% 3.89/0.97  
% 3.89/0.97  % (4900)Memory used [KB]: 7931
% 3.89/0.97  % (4900)Time elapsed: 0.108 s
% 3.89/0.97  % (4900)Instructions burned: 173 (million)
% 3.89/0.97  % (4900)------------------------------
% 3.89/0.97  % (4900)------------------------------
% 3.89/0.97  % (4907)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on theBenchmark for (2994ds/283Mi)
% 3.89/0.97  % (4908)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on theBenchmark for (2994ds/134Mi)
% 3.89/0.98  % (4910)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on theBenchmark for (2994ds/192Mi)
% 3.89/0.99  % (4909)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on theBenchmark for (2994ds/298Mi)
% 3.89/1.00  % (4905)Instruction limit reached!
% 3.89/1.00  % (4905)------------------------------
% 3.89/1.00  % (4905)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/1.00  % (4905)Termination reason: Unknown
% 3.89/1.00  % (4905)Termination phase: Saturation
% 3.89/1.00  
% 3.89/1.00  % (4905)Memory used [KB]: 9722
% 3.89/1.00  % (4905)Time elapsed: 0.069 s
% 3.89/1.00  % (4905)Instructions burned: 203 (million)
% 3.89/1.00  % (4905)------------------------------
% 3.89/1.00  % (4905)------------------------------
% 3.89/1.01  % (4893)Instruction limit reached!
% 3.89/1.01  % (4893)------------------------------
% 3.89/1.01  % (4893)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/1.01  % (4893)Termination reason: Unknown
% 3.89/1.01  % (4893)Termination phase: Saturation
% 3.89/1.01  
% 3.89/1.01  % (4893)Memory used [KB]: 6908
% 3.89/1.01  % (4893)Time elapsed: 0.174 s
% 3.89/1.01  % (4893)Instructions burned: 455 (million)
% 3.89/1.01  % (4893)------------------------------
% 3.89/1.01  % (4893)------------------------------
% 3.89/1.02  % (4908)Instruction limit reached!
% 3.89/1.02  % (4908)------------------------------
% 3.89/1.02  % (4908)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.89/1.02  % (4908)Termination reason: Unknown
% 3.89/1.02  % (4908)Termination phase: Saturation
% 3.89/1.02  
% 3.89/1.02  % (4908)Memory used [KB]: 5884
% 3.89/1.02  % (4908)Time elapsed: 0.052 s
% 3.89/1.02  % (4908)Instructions burned: 134 (million)
% 3.89/1.02  % (4908)------------------------------
% 3.89/1.02  % (4908)------------------------------
% 4.70/1.03  % (4906)Refutation not found, incomplete strategy
% 4.70/1.03  % (4906)------------------------------
% 4.70/1.03  % (4906)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.70/1.03  % (4906)Termination reason: Refutation not found, incomplete strategy
% 4.70/1.03  
% 4.70/1.03  
% 4.70/1.03  % (4906)Memory used [KB]: 8059
% 4.70/1.03  % (4906)Time elapsed: 0.075 s
% 4.70/1.03  % (4906)Instructions burned: 190 (million)
% 4.70/1.03  % (4906)------------------------------
% 4.70/1.03  % (4906)------------------------------
% 4.70/1.03  % (4911)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on theBenchmark for (2993ds/258Mi)
% 4.70/1.04  % (4913)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on theBenchmark for (2993ds/231Mi)
% 4.70/1.04  % (4912)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on theBenchmark for (2993ds/90Mi)
% 4.70/1.05  % (4914)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on theBenchmark for (2993ds/458Mi)
% 4.70/1.05  % (4910)Instruction limit reached!
% 4.70/1.05  % (4910)------------------------------
% 4.70/1.05  % (4910)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.70/1.05  % (4910)Termination reason: Unknown
% 4.70/1.05  % (4910)Termination phase: Saturation
% 4.70/1.05  
% 4.70/1.05  % (4910)Memory used [KB]: 1918
% 4.70/1.05  % (4910)Time elapsed: 0.071 s
% 4.70/1.05  % (4910)Instructions burned: 192 (million)
% 4.70/1.05  % (4910)------------------------------
% 4.70/1.05  % (4910)------------------------------
% 4.70/1.07  % (4915)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2993ds/31Mi)
% 4.70/1.07  % (4912)Instruction limit reached!
% 4.70/1.07  % (4912)------------------------------
% 4.70/1.07  % (4912)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.70/1.07  % (4912)Termination reason: Unknown
% 4.70/1.07  % (4912)Termination phase: Function definition elimination
% 4.70/1.07  
% 4.70/1.07  % (4912)Memory used [KB]: 1279
% 4.70/1.07  % (4912)Time elapsed: 0.023 s
% 4.70/1.07  % (4912)Instructions burned: 93 (million)
% 4.70/1.07  % (4912)------------------------------
% 4.70/1.07  % (4912)------------------------------
% 4.70/1.08  % (4916)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on theBenchmark for (2993ds/297Mi)
% 4.70/1.08  % (4915)Instruction limit reached!
% 4.70/1.08  % (4915)------------------------------
% 4.70/1.08  % (4915)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.70/1.08  % (4915)Termination reason: Unknown
% 4.70/1.08  % (4915)Termination phase: shuffling
% 4.70/1.08  
% 4.70/1.08  % (4915)Memory used [KB]: 1279
% 4.70/1.08  % (4915)Time elapsed: 0.013 s
% 4.70/1.08  % (4915)Instructions burned: 32 (million)
% 4.70/1.08  % (4915)------------------------------
% 4.70/1.08  % (4915)------------------------------
% 4.70/1.08  % (4907)Instruction limit reached!
% 4.70/1.08  % (4907)------------------------------
% 4.70/1.08  % (4907)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.70/1.08  % (4907)Termination reason: Unknown
% 4.70/1.08  % (4907)Termination phase: Saturation
% 4.70/1.08  
% 4.70/1.08  % (4907)Memory used [KB]: 6908
% 4.70/1.08  % (4907)Time elapsed: 0.110 s
% 4.70/1.08  % (4907)Instructions burned: 284 (million)
% 4.70/1.08  % (4907)------------------------------
% 4.70/1.08  % (4907)------------------------------
% 5.01/1.09  % (4918)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on theBenchmark for (2992ds/182Mi)
% 5.01/1.10  % (4909)Instruction limit reached!
% 5.01/1.10  % (4909)------------------------------
% 5.01/1.10  % (4909)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.01/1.10  % (4909)Termination reason: Unknown
% 5.01/1.10  % (4909)Termination phase: Saturation
% 5.01/1.10  
% 5.01/1.10  % (4909)Memory used [KB]: 6780
% 5.01/1.10  % (4909)Time elapsed: 0.108 s
% 5.01/1.10  % (4909)Instructions burned: 298 (million)
% 5.01/1.10  % (4909)------------------------------
% 5.01/1.10  % (4909)------------------------------
% 5.01/1.11  % (4917)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on theBenchmark for (2992ds/987Mi)
% 5.01/1.11  % (4913)Instruction limit reached!
% 5.01/1.11  % (4913)------------------------------
% 5.01/1.11  % (4913)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.01/1.11  % (4913)Termination reason: Unknown
% 5.01/1.11  % (4913)Termination phase: Saturation
% 5.01/1.11  
% 5.01/1.11  % (4913)Memory used [KB]: 6524
% 5.01/1.11  % (4913)Time elapsed: 0.079 s
% 5.01/1.11  % (4913)Instructions burned: 231 (million)
% 5.01/1.11  % (4913)------------------------------
% 5.01/1.11  % (4913)------------------------------
% 5.01/1.11  % (4919)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on theBenchmark for (2992ds/182Mi)
% 5.01/1.12  % (4911)Instruction limit reached!
% 5.01/1.12  % (4911)------------------------------
% 5.01/1.12  % (4911)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.01/1.12  % (4911)Termination reason: Unknown
% 5.01/1.12  % (4911)Termination phase: Saturation
% 5.01/1.12  
% 5.01/1.12  % (4911)Memory used [KB]: 2174
% 5.01/1.12  % (4911)Time elapsed: 0.094 s
% 5.01/1.12  % (4911)Instructions burned: 259 (million)
% 5.01/1.12  % (4911)------------------------------
% 5.01/1.12  % (4911)------------------------------
% 5.01/1.13  % (4920)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on theBenchmark for (2992ds/154Mi)
% 5.01/1.14  % (4921)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on theBenchmark for (2992ds/79Mi)
% 5.01/1.16  % (4918)Instruction limit reached!
% 5.01/1.16  % (4918)------------------------------
% 5.01/1.16  % (4918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.01/1.16  % (4918)Termination reason: Unknown
% 5.01/1.16  % (4918)Termination phase: Saturation
% 5.01/1.16  
% 5.01/1.16  % (4918)Memory used [KB]: 6140
% 5.01/1.16  % (4918)Time elapsed: 0.072 s
% 5.01/1.16  % (4918)Instructions burned: 182 (million)
% 5.01/1.16  % (4918)------------------------------
% 5.01/1.16  % (4918)------------------------------
% 5.01/1.16  % (4904)Instruction limit reached!
% 5.01/1.16  % (4904)------------------------------
% 5.01/1.16  % (4904)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.01/1.16  % (4904)Termination reason: Unknown
% 5.01/1.16  % (4904)Termination phase: Saturation
% 5.01/1.16  
% 5.01/1.16  % (4904)Memory used [KB]: 7419
% 5.01/1.16  % (4904)Time elapsed: 0.243 s
% 5.01/1.16  % (4904)Instructions burned: 614 (million)
% 5.01/1.16  % (4904)------------------------------
% 5.01/1.16  % (4904)------------------------------
% 5.01/1.17  % (4921)Instruction limit reached!
% 5.01/1.17  % (4921)------------------------------
% 5.01/1.17  % (4921)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.01/1.17  % (4921)Termination reason: Unknown
% 5.01/1.17  % (4921)Termination phase: Property scanning
% 5.01/1.17  
% 5.01/1.17  % (4921)Memory used [KB]: 1279
% 5.01/1.17  % (4921)Time elapsed: 0.032 s
% 5.01/1.17  % (4921)Instructions burned: 81 (million)
% 5.01/1.17  % (4921)------------------------------
% 5.01/1.17  % (4921)------------------------------
% 6.11/1.18  % (4922)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on theBenchmark for (2992ds/216Mi)
% 6.11/1.18  % (4923)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on theBenchmark for (2992ds/114Mi)
% 6.11/1.18  % (4924)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on theBenchmark for (2992ds/922Mi)
% 6.11/1.18  % (4920)Instruction limit reached!
% 6.11/1.18  % (4920)------------------------------
% 6.11/1.18  % (4920)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.11/1.18  % (4920)Termination reason: Unknown
% 6.11/1.18  % (4920)Termination phase: Saturation
% 6.11/1.18  
% 6.11/1.18  % (4920)Memory used [KB]: 1791
% 6.11/1.18  % (4920)Time elapsed: 0.059 s
% 6.11/1.18  % (4920)Instructions burned: 155 (million)
% 6.11/1.18  % (4920)------------------------------
% 6.11/1.18  % (4920)------------------------------
% 6.11/1.19  % (4916)Instruction limit reached!
% 6.11/1.19  % (4916)------------------------------
% 6.11/1.19  % (4916)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.11/1.19  % (4916)Termination reason: Unknown
% 6.11/1.19  % (4916)Termination phase: Saturation
% 6.11/1.19  
% 6.11/1.19  % (4916)Memory used [KB]: 7675
% 6.11/1.19  % (4916)Time elapsed: 0.113 s
% 6.11/1.19  % (4916)Instructions burned: 299 (million)
% 6.11/1.19  % (4916)------------------------------
% 6.11/1.19  % (4916)------------------------------
% 6.11/1.19  % (4919)Instruction limit reached!
% 6.11/1.19  % (4919)------------------------------
% 6.11/1.19  % (4919)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.11/1.19  % (4919)Termination reason: Unknown
% 6.11/1.19  % (4919)Termination phase: Saturation
% 6.11/1.19  
% 6.11/1.19  % (4919)Memory used [KB]: 6524
% 6.11/1.19  % (4919)Time elapsed: 0.077 s
% 6.11/1.19  % (4919)Instructions burned: 184 (million)
% 6.11/1.19  % (4919)------------------------------
% 6.11/1.19  % (4919)------------------------------
% 6.11/1.20  % (4926)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on theBenchmark for (2991ds/164Mi)
% 6.11/1.20  % (4925)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on theBenchmark for (2991ds/182Mi)
% 6.11/1.21  % (4927)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on theBenchmark for (2991ds/50Mi)
% 6.24/1.22  % (4923)Instruction limit reached!
% 6.24/1.22  % (4923)------------------------------
% 6.24/1.22  % (4923)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.24/1.22  % (4923)Termination reason: Unknown
% 6.24/1.22  % (4923)Termination phase: Property scanning
% 6.24/1.22  
% 6.24/1.22  % (4923)Memory used [KB]: 1279
% 6.24/1.22  % (4923)Time elapsed: 0.044 s
% 6.24/1.22  % (4923)Instructions burned: 114 (million)
% 6.24/1.22  % (4923)------------------------------
% 6.24/1.22  % (4923)------------------------------
% 6.24/1.22  % (4914)Instruction limit reached!
% 6.24/1.22  % (4914)------------------------------
% 6.24/1.22  % (4914)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.24/1.22  % (4914)Termination reason: Unknown
% 6.24/1.22  % (4914)Termination phase: Saturation
% 6.24/1.22  
% 6.24/1.22  % (4914)Memory used [KB]: 7036
% 6.24/1.22  % (4914)Time elapsed: 0.172 s
% 6.24/1.22  % (4914)Instructions burned: 458 (million)
% 6.24/1.22  % (4914)------------------------------
% 6.24/1.22  % (4914)------------------------------
% 6.24/1.23  % (4927)Instruction limit reached!
% 6.24/1.23  % (4927)------------------------------
% 6.24/1.23  % (4927)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.24/1.23  % (4927)Termination reason: Unknown
% 6.24/1.23  % (4927)Termination phase: Function definition elimination
% 6.24/1.23  
% 6.24/1.23  % (4927)Memory used [KB]: 1279
% 6.24/1.23  % (4927)Time elapsed: 0.022 s
% 6.24/1.23  % (4927)Instructions burned: 51 (million)
% 6.24/1.23  % (4927)------------------------------
% 6.24/1.23  % (4927)------------------------------
% 6.24/1.23  % (4928)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on theBenchmark for (2991ds/368Mi)
% 6.24/1.23  % (4929)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on theBenchmark for (2991ds/1021Mi)
% 6.35/1.24  % (4926)Refutation not found, incomplete strategy
% 6.35/1.24  % (4926)------------------------------
% 6.35/1.24  % (4926)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.35/1.24  % (4926)Termination reason: Refutation not found, incomplete strategy
% 6.35/1.24  
% 6.35/1.24  
% 6.35/1.24  % (4926)Memory used [KB]: 3454
% 6.35/1.24  % (4926)Time elapsed: 0.039 s
% 6.35/1.24  % (4926)Instructions burned: 132 (million)
% 6.35/1.24  % (4926)------------------------------
% 6.35/1.24  % (4926)------------------------------
% 6.35/1.24  % (4930)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on theBenchmark for (2991ds/267Mi)
% 6.35/1.24  % (4931)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on theBenchmark for (2991ds/204Mi)
% 6.35/1.26  % (4922)Instruction limit reached!
% 6.35/1.26  % (4922)------------------------------
% 6.35/1.26  % (4922)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.35/1.26  % (4922)Termination reason: Unknown
% 6.35/1.26  % (4922)Termination phase: Saturation
% 6.35/1.26  
% 6.35/1.26  % (4922)Memory used [KB]: 7036
% 6.35/1.26  % (4922)Time elapsed: 0.088 s
% 6.35/1.26  % (4922)Instructions burned: 218 (million)
% 6.35/1.26  % (4922)------------------------------
% 6.35/1.26  % (4922)------------------------------
% 6.35/1.26  % (4925)Instruction limit reached!
% 6.35/1.26  % (4925)------------------------------
% 6.35/1.26  % (4925)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.35/1.26  % (4925)Termination reason: Unknown
% 6.35/1.26  % (4925)Termination phase: Saturation
% 6.35/1.26  
% 6.35/1.26  % (4925)Memory used [KB]: 6524
% 6.35/1.26  % (4925)Time elapsed: 0.068 s
% 6.35/1.26  % (4925)Instructions burned: 184 (million)
% 6.35/1.26  % (4925)------------------------------
% 6.35/1.26  % (4925)------------------------------
% 6.35/1.28  % (4933)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on theBenchmark for (2991ds/53Mi)
% 6.35/1.28  % (4932)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2991ds/26Mi)
% 6.35/1.29  % (4931)Instruction limit reached!
% 6.35/1.29  % (4931)------------------------------
% 6.35/1.29  % (4931)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.35/1.29  % (4931)Termination reason: Unknown
% 6.35/1.29  % (4931)Termination phase: Saturation
% 6.35/1.29  
% 6.35/1.29  % (4931)Memory used [KB]: 6140
% 6.35/1.29  % (4931)Time elapsed: 0.045 s
% 6.35/1.29  % (4931)Instructions burned: 206 (million)
% 6.35/1.29  % (4931)------------------------------
% 6.35/1.29  % (4931)------------------------------
% 6.35/1.29  % (4932)Instruction limit reached!
% 6.35/1.29  % (4932)------------------------------
% 6.35/1.29  % (4932)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.35/1.29  % (4932)Termination reason: Unknown
% 6.35/1.29  % (4932)Termination phase: Property scanning
% 6.35/1.29  
% 6.35/1.29  % (4932)Memory used [KB]: 1279
% 6.35/1.29  % (4932)Time elapsed: 0.013 s
% 6.35/1.29  % (4932)Instructions burned: 27 (million)
% 6.35/1.29  % (4932)------------------------------
% 6.35/1.29  % (4932)------------------------------
% 6.35/1.30  % (4934)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on theBenchmark for (2990ds/4436Mi)
% 6.35/1.30  % (4924)Refutation not found, incomplete strategy
% 6.35/1.30  % (4924)------------------------------
% 6.35/1.30  % (4924)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.35/1.30  % (4924)Termination reason: Refutation not found, incomplete strategy
% 6.35/1.30  
% 6.35/1.30  
% 6.35/1.30  % (4924)Memory used [KB]: 8699
% 6.35/1.30  % (4924)Time elapsed: 0.120 s
% 6.35/1.30  % (4924)Instructions burned: 321 (million)
% 6.35/1.30  % (4924)------------------------------
% 6.35/1.30  % (4924)------------------------------
% 6.35/1.30  % (4933)Instruction limit reached!
% 6.35/1.30  % (4933)------------------------------
% 6.35/1.30  % (4933)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.35/1.30  % (4933)Termination reason: Unknown
% 6.35/1.30  % (4933)Termination phase: Property scanning
% 6.35/1.30  
% 6.35/1.30  % (4933)Memory used [KB]: 1279
% 6.35/1.30  % (4933)Time elapsed: 0.022 s
% 6.35/1.30  % (4933)Instructions burned: 53 (million)
% 6.35/1.30  % (4933)------------------------------
% 6.35/1.30  % (4933)------------------------------
% 6.35/1.31  % (4936)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on theBenchmark for (2990ds/408Mi)
% 6.35/1.31  % (4935)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on theBenchmark for (2990ds/1539Mi)
% 6.35/1.31  % (4937)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on theBenchmark for (2990ds/5205Mi)
% 6.90/1.34  % (4930)Instruction limit reached!
% 6.90/1.34  % (4930)------------------------------
% 6.90/1.34  % (4930)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.90/1.34  % (4930)Termination reason: Unknown
% 6.90/1.34  % (4930)Termination phase: Saturation
% 6.90/1.34  
% 6.90/1.34  % (4930)Memory used [KB]: 6908
% 6.90/1.34  % (4930)Time elapsed: 0.102 s
% 6.90/1.34  % (4930)Instructions burned: 269 (million)
% 6.90/1.34  % (4930)------------------------------
% 6.90/1.34  % (4930)------------------------------
% 6.90/1.34  % (4934)Refutation not found, incomplete strategy
% 6.90/1.34  % (4934)------------------------------
% 6.90/1.34  % (4934)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.90/1.34  % (4934)Termination reason: Refutation not found, incomplete strategy
% 6.90/1.34  
% 6.90/1.34  
% 6.90/1.34  % (4934)Memory used [KB]: 8059
% 6.90/1.34  % (4934)Time elapsed: 0.048 s
% 6.90/1.34  % (4934)Instructions burned: 168 (million)
% 6.90/1.34  % (4934)------------------------------
% 6.90/1.34  % (4934)------------------------------
% 6.90/1.35  % (4938)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on theBenchmark for (2990ds/1913Mi)
% 6.90/1.36  % (4939)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on theBenchmark for (2990ds/4350Mi)
% 7.12/1.38  % (4928)Instruction limit reached!
% 7.12/1.38  % (4928)------------------------------
% 7.12/1.38  % (4928)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.12/1.38  % (4928)Termination reason: Unknown
% 7.12/1.38  % (4928)Termination phase: Saturation
% 7.12/1.38  
% 7.12/1.38  % (4928)Memory used [KB]: 6908
% 7.12/1.38  % (4928)Time elapsed: 0.147 s
% 7.12/1.38  % (4928)Instructions burned: 368 (million)
% 7.12/1.38  % (4928)------------------------------
% 7.12/1.38  % (4928)------------------------------
% 7.12/1.39  % (4940)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on theBenchmark for (2990ds/68Mi)
% 7.12/1.42  % (4940)Instruction limit reached!
% 7.12/1.42  % (4940)------------------------------
% 7.12/1.42  % (4940)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.12/1.42  % (4940)Termination reason: Unknown
% 7.12/1.42  % (4940)Termination phase: Property scanning
% 7.12/1.42  
% 7.12/1.42  % (4940)Memory used [KB]: 1279
% 7.12/1.42  % (4940)Time elapsed: 0.027 s
% 7.12/1.42  % (4940)Instructions burned: 69 (million)
% 7.12/1.42  % (4940)------------------------------
% 7.12/1.42  % (4940)------------------------------
% 7.12/1.43  % (4938)Refutation not found, incomplete strategy
% 7.12/1.43  % (4938)------------------------------
% 7.12/1.43  % (4938)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.12/1.43  % (4938)Termination reason: Refutation not found, incomplete strategy
% 7.12/1.43  
% 7.12/1.43  
% 7.12/1.43  % (4938)Memory used [KB]: 2942
% 7.12/1.43  % (4938)Time elapsed: 0.102 s
% 7.12/1.43  % (4938)Instructions burned: 193 (million)
% 7.12/1.43  % (4938)------------------------------
% 7.12/1.43  % (4938)------------------------------
% 7.12/1.44  % (4942)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2989ds/31Mi)
% 7.12/1.45  % (4941)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on theBenchmark for (2989ds/358Mi)
% 7.12/1.45  % (4942)Instruction limit reached!
% 7.12/1.45  % (4942)------------------------------
% 7.12/1.45  % (4942)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.12/1.45  % (4942)Termination reason: Unknown
% 7.12/1.45  % (4942)Termination phase: shuffling
% 7.12/1.45  
% 7.12/1.45  % (4942)Memory used [KB]: 1279
% 7.12/1.45  % (4942)Time elapsed: 0.013 s
% 7.12/1.45  % (4942)Instructions burned: 33 (million)
% 7.12/1.45  % (4942)------------------------------
% 7.12/1.45  % (4942)------------------------------
% 7.52/1.47  % (4943)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on theBenchmark for (2989ds/279Mi)
% 7.54/1.48  % (4936)Instruction limit reached!
% 7.54/1.48  % (4936)------------------------------
% 7.54/1.48  % (4936)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.54/1.48  % (4936)Termination reason: Unknown
% 7.54/1.48  % (4936)Termination phase: Saturation
% 7.54/1.48  
% 7.54/1.48  % (4936)Memory used [KB]: 6908
% 7.54/1.48  % (4936)Time elapsed: 0.195 s
% 7.54/1.48  % (4936)Instructions burned: 408 (million)
% 7.54/1.48  % (4936)------------------------------
% 7.54/1.48  % (4936)------------------------------
% 7.54/1.50  % (4939)Refutation not found, incomplete strategy
% 7.54/1.50  % (4939)------------------------------
% 7.54/1.50  % (4939)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.54/1.50  % (4939)Termination reason: Refutation not found, incomplete strategy
% 7.54/1.50  
% 7.54/1.50  
% 7.54/1.50  % (4939)Memory used [KB]: 7675
% 7.54/1.50  % (4939)Time elapsed: 0.168 s
% 7.54/1.50  % (4939)Instructions burned: 541 (million)
% 7.54/1.50  % (4939)------------------------------
% 7.54/1.50  % (4939)------------------------------
% 7.54/1.50  % (4944)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on theBenchmark for (2988ds/258Mi)
% 7.91/1.52  % (4945)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2988ds/26Mi)
% 7.91/1.52  % (4941)Refutation not found, incomplete strategy
% 7.91/1.52  % (4941)------------------------------
% 7.91/1.52  % (4941)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.91/1.52  % (4941)Termination reason: Refutation not found, incomplete strategy
% 7.91/1.52  
% 7.91/1.52  
% 7.91/1.52  % (4941)Memory used [KB]: 7931
% 7.91/1.52  % (4941)Time elapsed: 0.113 s
% 7.91/1.52  % (4941)Instructions burned: 180 (million)
% 7.91/1.52  % (4941)------------------------------
% 7.91/1.52  % (4941)------------------------------
% 7.91/1.52  % (4917)Instruction limit reached!
% 7.91/1.52  % (4917)------------------------------
% 7.91/1.52  % (4917)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.91/1.52  % (4917)Termination reason: Unknown
% 7.91/1.52  % (4917)Termination phase: Saturation
% 7.91/1.52  
% 7.91/1.52  % (4917)Memory used [KB]: 8699
% 7.91/1.52  % (4917)Time elapsed: 0.448 s
% 7.91/1.52  % (4917)Instructions burned: 988 (million)
% 7.91/1.52  % (4917)------------------------------
% 7.91/1.52  % (4917)------------------------------
% 7.91/1.53  % (4945)Instruction limit reached!
% 7.91/1.53  % (4945)------------------------------
% 7.91/1.53  % (4945)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.91/1.53  % (4945)Termination reason: Unknown
% 7.91/1.53  % (4945)Termination phase: Preprocessing 1
% 7.91/1.53  
% 7.91/1.53  % (4945)Memory used [KB]: 1279
% 7.91/1.53  % (4945)Time elapsed: 0.013 s
% 7.91/1.53  % (4945)Instructions burned: 27 (million)
% 7.91/1.53  % (4945)------------------------------
% 7.91/1.53  % (4945)------------------------------
% 8.03/1.54  % (4947)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on theBenchmark for (2988ds/373Mi)
% 8.03/1.54  % (4948)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on theBenchmark for (2988ds/253Mi)
% 8.03/1.54  % (4946)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on theBenchmark for (2988ds/995Mi)
% 8.03/1.59  % (4943)Instruction limit reached!
% 8.03/1.59  % (4943)------------------------------
% 8.03/1.59  % (4943)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.03/1.59  % (4943)Termination reason: Unknown
% 8.03/1.59  % (4943)Termination phase: Saturation
% 8.03/1.59  
% 8.03/1.59  % (4943)Memory used [KB]: 7803
% 8.03/1.59  % (4943)Time elapsed: 0.145 s
% 8.03/1.59  % (4943)Instructions burned: 280 (million)
% 8.03/1.59  % (4943)------------------------------
% 8.03/1.59  % (4943)------------------------------
% 8.03/1.61  % (4949)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on theBenchmark for (2987ds/832Mi)
% 8.03/1.61  % (4944)Instruction limit reached!
% 8.03/1.61  % (4944)------------------------------
% 8.03/1.61  % (4944)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.03/1.61  % (4944)Termination reason: Unknown
% 8.03/1.61  % (4944)Termination phase: Saturation
% 8.03/1.61  
% 8.03/1.61  % (4944)Memory used [KB]: 8187
% 8.03/1.61  % (4944)Time elapsed: 0.118 s
% 8.03/1.61  % (4944)Instructions burned: 260 (million)
% 8.03/1.61  % (4944)------------------------------
% 8.03/1.61  % (4944)------------------------------
% 8.25/1.62  % (4950)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on theBenchmark for (2987ds/668Mi)
% 8.25/1.63  % (4948)Instruction limit reached!
% 8.25/1.63  % (4948)------------------------------
% 8.25/1.63  % (4948)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.25/1.63  % (4948)Termination reason: Unknown
% 8.25/1.63  % (4948)Termination phase: Saturation
% 8.25/1.63  
% 8.25/1.63  % (4948)Memory used [KB]: 6908
% 8.25/1.63  % (4948)Time elapsed: 0.095 s
% 8.25/1.63  % (4948)Instructions burned: 255 (million)
% 8.25/1.63  % (4948)------------------------------
% 8.25/1.63  % (4948)------------------------------
% 8.25/1.65  % (4951)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on theBenchmark for (2987ds/40Mi)
% 8.25/1.66  % (4949)Refutation not found, incomplete strategy
% 8.25/1.66  % (4949)------------------------------
% 8.25/1.66  % (4949)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.25/1.66  % (4949)Termination reason: Refutation not found, incomplete strategy
% 8.25/1.66  
% 8.25/1.66  
% 8.25/1.66  % (4949)Memory used [KB]: 6012
% 8.25/1.66  % (4949)Time elapsed: 0.065 s
% 8.25/1.66  % (4949)Instructions burned: 111 (million)
% 8.25/1.66  % (4949)------------------------------
% 8.25/1.66  % (4949)------------------------------
% 8.25/1.66  % (4951)Instruction limit reached!
% 8.25/1.66  % (4951)------------------------------
% 8.25/1.66  % (4951)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.25/1.66  % (4951)Termination reason: Unknown
% 8.25/1.66  % (4951)Termination phase: Property scanning
% 8.25/1.66  
% 8.25/1.66  % (4951)Memory used [KB]: 1279
% 8.25/1.66  % (4951)Time elapsed: 0.018 s
% 8.25/1.66  % (4951)Instructions burned: 41 (million)
% 8.25/1.66  % (4951)------------------------------
% 8.25/1.66  % (4951)------------------------------
% 8.25/1.67  % (4929)Instruction limit reached!
% 8.25/1.67  % (4929)------------------------------
% 8.25/1.67  % (4929)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.25/1.67  % (4929)Termination reason: Unknown
% 8.25/1.67  % (4929)Termination phase: Saturation
% 8.25/1.67  
% 8.25/1.67  % (4929)Memory used [KB]: 9594
% 8.25/1.67  % (4929)Time elapsed: 0.435 s
% 8.25/1.67  % (4929)Instructions burned: 1022 (million)
% 8.25/1.67  % (4929)------------------------------
% 8.25/1.67  % (4929)------------------------------
% 8.25/1.68  % (4953)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on theBenchmark for (2987ds/187Mi)
% 8.25/1.68  % (4954)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on theBenchmark for (2987ds/371Mi)
% 9.95/1.69  % (4947)Instruction limit reached!
% 9.95/1.69  % (4947)------------------------------
% 9.95/1.69  % (4947)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 9.95/1.69  % (4947)Termination reason: Unknown
% 9.95/1.69  % (4947)Termination phase: Saturation
% 9.95/1.69  
% 9.95/1.69  % (4947)Memory used [KB]: 6780
% 9.95/1.69  % (4947)Time elapsed: 0.152 s
% 9.95/1.69  % (4947)Instructions burned: 373 (million)
% 9.95/1.69  % (4947)------------------------------
% 9.95/1.69  % (4947)------------------------------
% 9.95/1.69  % (4952)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on theBenchmark for (2987ds/294Mi)
% 9.95/1.70  % (4955)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on theBenchmark for (2986ds/1827Mi)
% 9.95/1.75  % (4953)Instruction limit reached!
% 9.95/1.75  % (4953)------------------------------
% 9.95/1.75  % (4953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 9.95/1.75  % (4953)Termination reason: Unknown
% 9.95/1.75  % (4953)Termination phase: Saturation
% 9.95/1.75  
% 9.95/1.75  % (4953)Memory used [KB]: 6140
% 9.95/1.75  % (4953)Time elapsed: 0.075 s
% 9.95/1.75  % (4953)Instructions burned: 189 (million)
% 9.95/1.75  % (4953)------------------------------
% 9.95/1.75  % (4953)------------------------------
% 9.95/1.75  % (4954)Refutation not found, incomplete strategy
% 9.95/1.75  % (4954)------------------------------
% 9.95/1.75  % (4954)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 9.95/1.75  % (4954)Termination reason: Refutation not found, incomplete strategy
% 9.95/1.75  
% 9.95/1.75  
% 9.95/1.75  % (4954)Memory used [KB]: 8187
% 9.95/1.75  % (4954)Time elapsed: 0.074 s
% 9.95/1.75  % (4954)Instructions burned: 171 (million)
% 9.95/1.75  % (4954)------------------------------
% 9.95/1.75  % (4954)------------------------------
% 9.95/1.76  % (4952)Instruction limit reached!
% 9.95/1.76  % (4952)------------------------------
% 9.95/1.76  % (4952)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 9.95/1.76  % (4952)Termination reason: Unknown
% 9.95/1.76  % (4952)Termination phase: Saturation
% 9.95/1.76  
% 9.95/1.76  % (4952)Memory used [KB]: 7291
% 9.95/1.76  % (4952)Time elapsed: 0.072 s
% 9.95/1.76  % (4952)Instructions burned: 296 (million)
% 9.95/1.76  % (4952)------------------------------
% 9.95/1.76  % (4952)------------------------------
% 9.95/1.76  % (4956)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on theBenchmark for (2986ds/70Mi)
% 10.54/1.77  % (4958)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on theBenchmark for (2986ds/932Mi)
% 10.54/1.77  % (4957)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on theBenchmark for (2986ds/316Mi)
% 10.62/1.79  % (4956)Instruction limit reached!
% 10.62/1.79  % (4956)------------------------------
% 10.62/1.79  % (4956)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.62/1.79  % (4956)Termination reason: Unknown
% 10.62/1.79  % (4956)Termination phase: Property scanning
% 10.62/1.79  
% 10.62/1.79  % (4956)Memory used [KB]: 1279
% 10.62/1.79  % (4956)Time elapsed: 0.030 s
% 10.62/1.79  % (4956)Instructions burned: 72 (million)
% 10.62/1.79  % (4956)------------------------------
% 10.62/1.79  % (4956)------------------------------
% 10.62/1.81  % (4959)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on theBenchmark for (2985ds/4714Mi)
% 10.79/1.89  % (4950)Instruction limit reached!
% 10.79/1.89  % (4950)------------------------------
% 10.79/1.89  % (4950)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.79/1.89  % (4950)Termination reason: Unknown
% 10.79/1.89  % (4950)Termination phase: Saturation
% 10.79/1.89  
% 10.79/1.89  % (4950)Memory used [KB]: 12920
% 10.79/1.89  % (4950)Time elapsed: 0.268 s
% 10.79/1.89  % (4950)Instructions burned: 669 (million)
% 10.79/1.89  % (4950)------------------------------
% 10.79/1.89  % (4950)------------------------------
% 10.79/1.89  % (4957)Instruction limit reached!
% 10.79/1.89  % (4957)------------------------------
% 10.79/1.89  % (4957)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.79/1.89  % (4957)Termination reason: Unknown
% 10.79/1.89  % (4957)Termination phase: Saturation
% 10.79/1.89  
% 10.79/1.89  % (4957)Memory used [KB]: 7036
% 10.79/1.89  % (4957)Time elapsed: 0.121 s
% 10.79/1.89  % (4957)Instructions burned: 316 (million)
% 10.79/1.89  % (4957)------------------------------
% 10.79/1.89  % (4957)------------------------------
% 11.23/1.91  % (4961)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on theBenchmark for (2984ds/770Mi)
% 11.23/1.92  % (4960)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on theBenchmark for (2984ds/8250Mi)
% 11.23/1.94  % (4946)Instruction limit reached!
% 11.23/1.94  % (4946)------------------------------
% 11.23/1.94  % (4946)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.23/1.94  % (4946)Termination reason: Unknown
% 11.23/1.94  % (4946)Termination phase: Saturation
% 11.23/1.94  
% 11.23/1.94  % (4946)Memory used [KB]: 8699
% 11.23/1.94  % (4946)Time elapsed: 0.403 s
% 11.23/1.94  % (4946)Instructions burned: 997 (million)
% 11.23/1.94  % (4946)------------------------------
% 11.23/1.94  % (4946)------------------------------
% 11.23/1.95  % (4962)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on theBenchmark for (2984ds/794Mi)
% 11.44/1.99  % (4935)Instruction limit reached!
% 11.44/1.99  % (4935)------------------------------
% 11.44/1.99  % (4935)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.44/1.99  % (4935)Termination reason: Unknown
% 11.44/1.99  % (4935)Termination phase: Saturation
% 11.44/1.99  
% 11.44/1.99  % (4935)Memory used [KB]: 10106
% 11.44/1.99  % (4935)Time elapsed: 0.709 s
% 11.44/1.99  % (4935)Instructions burned: 1539 (million)
% 11.44/1.99  % (4935)------------------------------
% 11.44/1.99  % (4935)------------------------------
% 11.44/2.01  % (4961)Refutation not found, incomplete strategy
% 11.44/2.01  % (4961)------------------------------
% 11.44/2.01  % (4961)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.44/2.01  % (4961)Termination reason: Refutation not found, incomplete strategy
% 11.44/2.01  
% 11.44/2.01  
% 11.44/2.01  % (4961)Memory used [KB]: 8187
% 11.44/2.01  % (4961)Time elapsed: 0.100 s
% 11.44/2.01  % (4961)Instructions burned: 231 (million)
% 11.44/2.01  % (4961)------------------------------
% 11.44/2.01  % (4961)------------------------------
% 11.44/2.01  % (4963)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on theBenchmark for (2983ds/464Mi)
% 11.44/2.03  % (4964)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on theBenchmark for (2983ds/1376Mi)
% 11.44/2.05  % (4959)Refutation not found, incomplete strategy
% 11.44/2.05  % (4959)------------------------------
% 11.44/2.05  % (4959)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.44/2.05  % (4959)Termination reason: Refutation not found, incomplete strategy
% 11.44/2.05  
% 11.44/2.05  
% 11.44/2.05  % (4959)Memory used [KB]: 7675
% 11.44/2.05  % (4959)Time elapsed: 0.246 s
% 11.44/2.05  % (4959)Instructions burned: 601 (million)
% 11.44/2.05  % (4959)------------------------------
% 11.44/2.05  % (4959)------------------------------
% 11.44/2.07  % (4965)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on theBenchmark for (2983ds/906Mi)
% 11.92/2.08  % (4958)Instruction limit reached!
% 11.92/2.08  % (4958)------------------------------
% 11.92/2.08  % (4958)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.92/2.08  % (4958)Termination reason: Unknown
% 11.92/2.08  % (4958)Termination phase: Saturation
% 11.92/2.08  
% 11.92/2.08  % (4958)Memory used [KB]: 7547
% 11.92/2.08  % (4958)Time elapsed: 0.319 s
% 11.92/2.08  % (4958)Instructions burned: 934 (million)
% 11.92/2.08  % (4958)------------------------------
% 11.92/2.08  % (4958)------------------------------
% 12.23/2.10  % (4966)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on theBenchmark for (2982ds/434Mi)
% 12.26/2.19  % (4963)Instruction limit reached!
% 12.26/2.19  % (4963)------------------------------
% 12.26/2.19  % (4963)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.26/2.19  % (4963)Termination reason: Unknown
% 12.26/2.19  % (4963)Termination phase: Saturation
% 12.26/2.19  
% 12.26/2.19  % (4963)Memory used [KB]: 6524
% 12.26/2.19  % (4963)Time elapsed: 0.187 s
% 12.26/2.19  % (4963)Instructions burned: 464 (million)
% 12.26/2.19  % (4963)------------------------------
% 12.26/2.19  % (4963)------------------------------
% 12.26/2.21  % (4967)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on theBenchmark for (2981ds/865Mi)
% 13.97/2.22  % (4966)Refutation not found, incomplete strategy
% 13.97/2.22  % (4966)------------------------------
% 13.97/2.22  % (4966)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.97/2.22  % (4966)Termination reason: Refutation not found, incomplete strategy
% 13.97/2.22  
% 13.97/2.22  
% 13.97/2.22  % (4966)Memory used [KB]: 6652
% 13.97/2.22  % (4966)Time elapsed: 0.134 s
% 13.97/2.22  % (4966)Instructions burned: 338 (million)
% 13.97/2.22  % (4966)------------------------------
% 13.97/2.22  % (4966)------------------------------
% 13.97/2.23  % (4968)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on theBenchmark for (2981ds/593Mi)
% 13.97/2.29  % (4962)Instruction limit reached!
% 13.97/2.29  % (4962)------------------------------
% 13.97/2.29  % (4962)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.97/2.29  % (4962)Termination reason: Unknown
% 13.97/2.29  % (4962)Termination phase: Saturation
% 13.97/2.29  
% 13.97/2.29  % (4962)Memory used [KB]: 4477
% 13.97/2.29  % (4962)Time elapsed: 0.337 s
% 13.97/2.29  % (4962)Instructions burned: 794 (million)
% 13.97/2.29  % (4962)------------------------------
% 13.97/2.29  % (4962)------------------------------
% 13.97/2.29  % (4967)Refutation not found, incomplete strategy
% 13.97/2.29  % (4967)------------------------------
% 13.97/2.29  % (4967)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.97/2.29  % (4967)Termination reason: Refutation not found, incomplete strategy
% 13.97/2.29  
% 13.97/2.29  
% 13.97/2.29  % (4967)Memory used [KB]: 8571
% 13.97/2.29  % (4967)Time elapsed: 0.102 s
% 13.97/2.29  % (4967)Instructions burned: 234 (million)
% 13.97/2.29  % (4967)------------------------------
% 13.97/2.29  % (4967)------------------------------
% 14.54/2.29  % (4969)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on theBenchmark for (2980ds/443Mi)
% 14.54/2.30  % (4970)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on theBenchmark for (2980ds/594Mi)
% 15.10/2.41  % (4969)Instruction limit reached!
% 15.10/2.41  % (4969)------------------------------
% 15.10/2.41  % (4969)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.10/2.41  % (4969)Termination reason: Unknown
% 15.10/2.41  % (4969)Termination phase: Saturation
% 15.10/2.41  
% 15.10/2.41  % (4969)Memory used [KB]: 7036
% 15.10/2.41  % (4969)Time elapsed: 0.118 s
% 15.10/2.41  % (4969)Instructions burned: 444 (million)
% 15.10/2.41  % (4969)------------------------------
% 15.10/2.41  % (4969)------------------------------
% 15.10/2.43  % (4971)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on theBenchmark for (2979ds/327Mi)
% 15.10/2.45  % (4965)Instruction limit reached!
% 15.10/2.45  % (4965)------------------------------
% 15.10/2.45  % (4965)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.10/2.45  % (4965)Termination reason: Unknown
% 15.10/2.45  % (4965)Termination phase: Saturation
% 15.10/2.45  
% 15.10/2.45  % (4965)Memory used [KB]: 9338
% 15.10/2.45  % (4965)Time elapsed: 0.388 s
% 15.10/2.45  % (4965)Instructions burned: 906 (million)
% 15.10/2.45  % (4965)------------------------------
% 15.10/2.45  % (4965)------------------------------
% 15.10/2.47  % (4968)Instruction limit reached!
% 15.10/2.47  % (4968)------------------------------
% 15.10/2.47  % (4968)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.10/2.47  % (4968)Termination reason: Unknown
% 15.10/2.47  % (4968)Termination phase: Saturation
% 15.10/2.47  
% 15.10/2.47  % (4968)Memory used [KB]: 7547
% 15.10/2.47  % (4968)Time elapsed: 0.240 s
% 15.10/2.47  % (4968)Instructions burned: 593 (million)
% 15.10/2.47  % (4968)------------------------------
% 15.10/2.47  % (4968)------------------------------
% 15.10/2.47  % (4972)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on theBenchmark for (2979ds/5411Mi)
% 15.10/2.48  % (4973)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on theBenchmark for (2979ds/1762Mi)
% 15.10/2.49  % (4955)Instruction limit reached!
% 15.10/2.49  % (4955)------------------------------
% 15.10/2.49  % (4955)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.10/2.49  % (4955)Termination reason: Unknown
% 15.10/2.49  % (4955)Termination phase: Saturation
% 15.10/2.49  
% 15.10/2.49  % (4955)Memory used [KB]: 9210
% 15.10/2.49  % (4955)Time elapsed: 0.792 s
% 15.10/2.49  % (4955)Instructions burned: 1828 (million)
% 15.10/2.49  % (4955)------------------------------
% 15.10/2.49  % (4955)------------------------------
% 15.92/2.51  % (4974)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on theBenchmark for (2978ds/96Mi)
% 15.92/2.52  % (4972)Refutation not found, incomplete strategy
% 15.92/2.52  % (4972)------------------------------
% 15.92/2.52  % (4972)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.92/2.52  % (4972)Termination reason: Refutation not found, incomplete strategy
% 15.92/2.52  
% 15.92/2.52  
% 15.92/2.52  % (4972)Memory used [KB]: 5884
% 15.92/2.52  % (4972)Time elapsed: 0.071 s
% 15.92/2.52  % (4972)Instructions burned: 99 (million)
% 15.92/2.52  % (4972)------------------------------
% 15.92/2.52  % (4972)------------------------------
% 15.92/2.53  % (4970)Instruction limit reached!
% 15.92/2.53  % (4970)------------------------------
% 15.92/2.53  % (4970)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.92/2.53  % (4970)Termination reason: Unknown
% 15.92/2.53  % (4970)Termination phase: Saturation
% 15.92/2.53  
% 15.92/2.53  % (4970)Memory used [KB]: 7931
% 15.92/2.53  % (4970)Time elapsed: 0.226 s
% 15.92/2.53  % (4970)Instructions burned: 594 (million)
% 15.92/2.53  % (4970)------------------------------
% 15.92/2.53  % (4970)------------------------------
% 15.92/2.54  % (4975)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on theBenchmark for (2978ds/503Mi)
% 15.92/2.54  % (4976)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on theBenchmark for (2978ds/90Mi)
% 15.92/2.54  % (4974)Instruction limit reached!
% 15.92/2.54  % (4974)------------------------------
% 15.92/2.54  % (4974)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.92/2.54  % (4974)Termination reason: Unknown
% 15.92/2.54  % (4974)Termination phase: Saturation
% 15.92/2.54  
% 15.92/2.54  % (4974)Memory used [KB]: 5884
% 15.92/2.54  % (4974)Time elapsed: 0.039 s
% 15.92/2.54  % (4974)Instructions burned: 96 (million)
% 15.92/2.54  % (4974)------------------------------
% 15.92/2.54  % (4974)------------------------------
% 15.92/2.56  % (4977)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on theBenchmark for (2978ds/593Mi)
% 15.92/2.57  % (4971)Instruction limit reached!
% 15.92/2.57  % (4971)------------------------------
% 15.92/2.57  % (4971)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.92/2.57  % (4971)Termination reason: Unknown
% 15.92/2.57  % (4971)Termination phase: Saturation
% 15.92/2.57  
% 15.92/2.57  % (4971)Memory used [KB]: 7036
% 15.92/2.57  % (4971)Time elapsed: 0.146 s
% 15.92/2.57  % (4971)Instructions burned: 328 (million)
% 15.92/2.57  % (4971)------------------------------
% 15.92/2.57  % (4971)------------------------------
% 15.92/2.57  % (4976)Instruction limit reached!
% 15.92/2.57  % (4976)------------------------------
% 15.92/2.57  % (4976)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.92/2.57  % (4976)Termination reason: Unknown
% 15.92/2.57  % (4976)Termination phase: Function definition elimination
% 15.92/2.57  
% 15.92/2.57  % (4976)Memory used [KB]: 1279
% 15.92/2.57  % (4976)Time elapsed: 0.023 s
% 15.92/2.57  % (4976)Instructions burned: 94 (million)
% 15.92/2.57  % (4976)------------------------------
% 15.92/2.57  % (4976)------------------------------
% 15.92/2.58  % (4979)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on theBenchmark for (2978ds/569Mi)
% 15.92/2.59  % (4978)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on theBenchmark for (2978ds/1512Mi)
% 16.67/2.60  % (4964)Instruction limit reached!
% 16.67/2.60  % (4964)------------------------------
% 16.67/2.60  % (4964)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.67/2.60  % (4964)Termination reason: Unknown
% 16.67/2.60  % (4964)Termination phase: Saturation
% 16.67/2.60  
% 16.67/2.60  % (4964)Memory used [KB]: 9850
% 16.67/2.60  % (4964)Time elapsed: 0.599 s
% 16.67/2.60  % (4964)Instructions burned: 1376 (million)
% 16.67/2.60  % (4964)------------------------------
% 16.67/2.60  % (4964)------------------------------
% 16.67/2.62  % (4980)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on theBenchmark for (2977ds/501Mi)
% 16.67/2.63  % (4978)Refutation not found, incomplete strategy
% 16.67/2.63  % (4978)------------------------------
% 16.67/2.63  % (4978)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.67/2.63  % (4978)Termination reason: Refutation not found, incomplete strategy
% 16.67/2.63  
% 16.67/2.63  
% 16.67/2.63  % (4978)Memory used [KB]: 6012
% 16.67/2.63  % (4978)Time elapsed: 0.047 s
% 16.67/2.63  % (4978)Instructions burned: 117 (million)
% 16.67/2.63  % (4978)------------------------------
% 16.67/2.63  % (4978)------------------------------
% 16.67/2.64  % (4981)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on theBenchmark for (2977ds/562Mi)
% 16.95/2.70  % (4980)Refutation not found, incomplete strategy
% 16.95/2.70  % (4980)------------------------------
% 16.95/2.70  % (4980)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.95/2.70  % (4980)Termination reason: Refutation not found, incomplete strategy
% 16.95/2.70  
% 16.95/2.70  
% 16.95/2.70  % (4980)Memory used [KB]: 6908
% 16.95/2.70  % (4980)Time elapsed: 0.107 s
% 16.95/2.70  % (4980)Instructions burned: 315 (million)
% 16.95/2.70  % (4980)------------------------------
% 16.95/2.70  % (4980)------------------------------
% 16.95/2.71  % (4982)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on theBenchmark for (2976ds/406Mi)
% 17.83/2.72  % (4975)Refutation not found, incomplete strategy
% 17.83/2.72  % (4975)------------------------------
% 17.83/2.72  % (4975)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.83/2.72  % (4975)Termination reason: Refutation not found, incomplete strategy
% 17.83/2.72  
% 17.83/2.72  
% 17.83/2.72  % (4975)Memory used [KB]: 8699
% 17.83/2.72  % (4975)Time elapsed: 0.190 s
% 17.83/2.72  % (4975)Instructions burned: 435 (million)
% 17.83/2.72  % (4975)------------------------------
% 17.83/2.72  % (4975)------------------------------
% 17.83/2.74  % (4983)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on theBenchmark for (2976ds/582Mi)
% 17.83/2.78  % (4979)Instruction limit reached!
% 17.83/2.78  % (4979)------------------------------
% 17.83/2.78  % (4979)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.83/2.78  % (4979)Termination reason: Unknown
% 17.83/2.78  % (4979)Termination phase: Saturation
% 17.83/2.78  
% 17.83/2.78  % (4979)Memory used [KB]: 7931
% 17.83/2.78  % (4979)Time elapsed: 0.170 s
% 17.83/2.78  % (4979)Instructions burned: 570 (million)
% 17.83/2.78  % (4979)------------------------------
% 17.83/2.78  % (4979)------------------------------
% 17.83/2.79  % (4984)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on theBenchmark for (2976ds/456Mi)
% 17.83/2.80  % (4977)Instruction limit reached!
% 17.83/2.80  % (4977)------------------------------
% 17.83/2.80  % (4977)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.83/2.80  % (4977)Termination reason: Unknown
% 17.83/2.80  % (4977)Termination phase: Saturation
% 17.83/2.80  
% 17.83/2.80  % (4977)Memory used [KB]: 7419
% 17.83/2.80  % (4977)Time elapsed: 0.233 s
% 17.83/2.80  % (4977)Instructions burned: 595 (million)
% 17.83/2.80  % (4977)------------------------------
% 17.83/2.80  % (4977)------------------------------
% 17.83/2.81  % (4985)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on theBenchmark for (2975ds/393Mi)
% 18.49/2.87  % (4981)Instruction limit reached!
% 18.49/2.87  % (4981)------------------------------
% 18.49/2.87  % (4981)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.49/2.87  % (4981)Termination reason: Unknown
% 18.49/2.87  % (4981)Termination phase: Saturation
% 18.49/2.87  
% 18.49/2.87  % (4981)Memory used [KB]: 6908
% 18.49/2.87  % (4981)Time elapsed: 0.250 s
% 18.49/2.87  % (4981)Instructions burned: 562 (million)
% 18.49/2.87  % (4981)------------------------------
% 18.49/2.87  % (4981)------------------------------
% 18.49/2.88  % (4982)Instruction limit reached!
% 18.49/2.88  % (4982)------------------------------
% 18.49/2.88  % (4982)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.49/2.88  % (4982)Termination reason: Unknown
% 18.49/2.88  % (4982)Termination phase: Saturation
% 18.49/2.88  
% 18.49/2.88  % (4982)Memory used [KB]: 8187
% 18.49/2.88  % (4982)Time elapsed: 0.176 s
% 18.49/2.88  % (4982)Instructions burned: 408 (million)
% 18.49/2.88  % (4982)------------------------------
% 18.49/2.88  % (4982)------------------------------
% 18.49/2.89  % (4986)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on theBenchmark for (2975ds/1335Mi)
% 18.49/2.91  % (4987)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on theBenchmark for (2974ds/3373Mi)
% 18.90/2.92  % (4983)Instruction limit reached!
% 18.90/2.92  % (4983)------------------------------
% 18.90/2.92  % (4983)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.90/2.92  % (4983)Termination reason: Unknown
% 18.90/2.92  % (4983)Termination phase: Saturation
% 18.90/2.92  
% 18.90/2.92  % (4983)Memory used [KB]: 7931
% 18.90/2.92  % (4983)Time elapsed: 0.181 s
% 18.90/2.92  % (4983)Instructions burned: 582 (million)
% 18.90/2.92  % (4983)------------------------------
% 18.90/2.92  % (4983)------------------------------
% 18.90/2.93  % (4988)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on theBenchmark for (2974ds/474Mi)
% 18.90/2.94  % (4985)Instruction limit reached!
% 18.90/2.94  % (4985)------------------------------
% 18.90/2.94  % (4985)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.90/2.94  % (4985)Termination reason: Unknown
% 18.90/2.94  % (4985)Termination phase: Saturation
% 18.90/2.94  
% 18.90/2.94  % (4985)Memory used [KB]: 7036
% 18.90/2.94  % (4985)Time elapsed: 0.114 s
% 18.90/2.94  % (4985)Instructions burned: 394 (million)
% 18.90/2.94  % (4985)------------------------------
% 18.90/2.94  % (4985)------------------------------
% 18.90/2.95  % (4986)Refutation not found, incomplete strategy
% 18.90/2.95  % (4986)------------------------------
% 18.90/2.95  % (4986)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.90/2.95  % (4986)Termination reason: Refutation not found, incomplete strategy
% 18.90/2.95  
% 18.90/2.95  
% 18.90/2.95  % (4986)Memory used [KB]: 8059
% 18.90/2.95  % (4986)Time elapsed: 0.088 s
% 18.90/2.95  % (4986)Instructions burned: 136 (million)
% 18.90/2.95  % (4986)------------------------------
% 18.90/2.95  % (4986)------------------------------
% 18.90/2.96  % (4989)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on theBenchmark for (2974ds/157Mi)
% 18.90/2.96  % (4990)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on theBenchmark for (2974ds/590Mi)
% 18.90/2.97  % (4984)Instruction limit reached!
% 18.90/2.97  % (4984)------------------------------
% 18.90/2.97  % (4984)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.90/2.97  % (4984)Termination reason: Unknown
% 18.90/2.97  % (4984)Termination phase: Saturation
% 18.90/2.97  
% 18.90/2.97  % (4984)Memory used [KB]: 7291
% 18.90/2.97  % (4984)Time elapsed: 0.177 s
% 18.90/2.97  % (4984)Instructions burned: 457 (million)
% 18.90/2.97  % (4984)------------------------------
% 18.90/2.97  % (4984)------------------------------
% 19.71/2.99  % (4991)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on theBenchmark for (2973ds/104Mi)
% 19.71/3.02  % (4989)Instruction limit reached!
% 19.71/3.02  % (4989)------------------------------
% 19.71/3.02  % (4989)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.71/3.02  % (4989)Termination reason: Unknown
% 19.71/3.02  % (4989)Termination phase: Saturation
% 19.71/3.02  
% 19.71/3.02  % (4989)Memory used [KB]: 6396
% 19.71/3.02  % (4989)Time elapsed: 0.061 s
% 19.71/3.02  % (4989)Instructions burned: 159 (million)
% 19.71/3.02  % (4989)------------------------------
% 19.71/3.02  % (4989)------------------------------
% 19.71/3.03  % (4991)Instruction limit reached!
% 19.71/3.03  % (4991)------------------------------
% 19.71/3.03  % (4991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.71/3.03  % (4991)Termination reason: Unknown
% 19.71/3.03  % (4991)Termination phase: Property scanning
% 19.71/3.03  
% 19.71/3.03  % (4991)Memory used [KB]: 1279
% 19.71/3.03  % (4991)Time elapsed: 0.026 s
% 19.71/3.03  % (4991)Instructions burned: 108 (million)
% 19.71/3.03  % (4991)------------------------------
% 19.71/3.03  % (4991)------------------------------
% 19.71/3.03  % (4992)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on theBenchmark for (2973ds/414Mi)
% 19.71/3.03  % (4993)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on theBenchmark for (2973ds/715Mi)
% 20.21/3.13  % (4988)Instruction limit reached!
% 20.21/3.13  % (4988)------------------------------
% 20.21/3.13  % (4988)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.21/3.13  % (4988)Termination reason: Unknown
% 20.21/3.13  % (4988)Termination phase: Saturation
% 20.21/3.13  
% 20.21/3.13  % (4988)Memory used [KB]: 7803
% 20.21/3.13  % (4988)Time elapsed: 0.200 s
% 20.21/3.13  % (4988)Instructions burned: 476 (million)
% 20.21/3.13  % (4988)------------------------------
% 20.21/3.13  % (4988)------------------------------
% 20.21/3.15  % (4994)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on theBenchmark for (2972ds/961Mi)
% 20.21/3.19  % (4992)Instruction limit reached!
% 20.21/3.19  % (4992)------------------------------
% 20.21/3.19  % (4992)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.21/3.19  % (4992)Termination reason: Unknown
% 20.21/3.19  % (4992)Termination phase: Saturation
% 20.21/3.19  
% 20.21/3.19  % (4992)Memory used [KB]: 6908
% 20.21/3.19  % (4992)Time elapsed: 0.155 s
% 20.21/3.19  % (4992)Instructions burned: 414 (million)
% 20.21/3.19  % (4992)------------------------------
% 20.21/3.19  % (4992)------------------------------
% 20.21/3.20  % (4995)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on theBenchmark for (2971ds/1213Mi)
% 20.85/3.21  % (4990)Instruction limit reached!
% 20.85/3.21  % (4990)------------------------------
% 20.85/3.21  % (4990)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.85/3.21  % (4990)Termination reason: Unknown
% 20.85/3.21  % (4990)Termination phase: Saturation
% 20.85/3.21  
% 20.85/3.21  % (4990)Memory used [KB]: 8059
% 20.85/3.21  % (4990)Time elapsed: 0.252 s
% 20.85/3.21  % (4990)Instructions burned: 592 (million)
% 20.85/3.21  % (4990)------------------------------
% 20.85/3.21  % (4990)------------------------------
% 20.85/3.23  % (4996)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on theBenchmark for (2971ds/1979Mi)
% 20.85/3.23  % (4993)Instruction limit reached!
% 20.85/3.23  % (4993)------------------------------
% 20.85/3.23  % (4993)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.85/3.23  % (4993)Termination reason: Unknown
% 20.85/3.23  % (4993)Termination phase: Saturation
% 20.85/3.23  
% 20.85/3.23  % (4993)Memory used [KB]: 3837
% 20.85/3.23  % (4993)Time elapsed: 0.197 s
% 20.85/3.23  % (4993)Instructions burned: 718 (million)
% 20.85/3.23  % (4993)------------------------------
% 20.85/3.23  % (4993)------------------------------
% 20.85/3.24  % (4997)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on theBenchmark for (2971ds/481Mi)
% 20.85/3.25  % (4973)Instruction limit reached!
% 20.85/3.25  % (4973)------------------------------
% 20.85/3.25  % (4973)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.85/3.25  % (4973)Termination reason: Unknown
% 20.85/3.25  % (4973)Termination phase: Saturation
% 20.85/3.25  
% 20.85/3.25  % (4973)Memory used [KB]: 8827
% 20.85/3.25  % (4973)Time elapsed: 0.772 s
% 20.85/3.25  % (4973)Instructions burned: 1763 (million)
% 20.85/3.25  % (4973)------------------------------
% 20.85/3.25  % (4973)------------------------------
% 20.85/3.27  % (4994)Refutation not found, incomplete strategy
% 20.85/3.27  % (4994)------------------------------
% 20.85/3.27  % (4994)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.85/3.27  % (4994)Termination reason: Refutation not found, incomplete strategy
% 20.85/3.27  
% 20.85/3.27  
% 20.85/3.27  % (4994)Memory used [KB]: 6652
% 20.85/3.27  % (4994)Time elapsed: 0.135 s
% 20.85/3.27  % (4994)Instructions burned: 303 (million)
% 20.85/3.27  % (4994)------------------------------
% 20.85/3.27  % (4994)------------------------------
% 20.85/3.28  % (4998)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on theBenchmark for (2971ds/783Mi)
% 20.85/3.28  % (4999)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on theBenchmark for (2971ds/432Mi)
% 21.80/3.39  % (4997)Instruction limit reached!
% 21.80/3.39  % (4997)------------------------------
% 21.80/3.39  % (4997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.80/3.39  % (4997)Termination reason: Unknown
% 21.80/3.39  % (4997)Termination phase: Saturation
% 21.80/3.39  
% 21.80/3.39  % (4997)Memory used [KB]: 7675
% 21.80/3.39  % (4997)Time elapsed: 0.159 s
% 21.80/3.39  % (4997)Instructions burned: 481 (million)
% 21.80/3.39  % (4997)------------------------------
% 21.80/3.39  % (4997)------------------------------
% 21.80/3.40  % (5000)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on theBenchmark for (2969ds/1670Mi)
% 23.30/3.46  % (4999)Instruction limit reached!
% 23.30/3.46  % (4999)------------------------------
% 23.30/3.46  % (4999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.30/3.46  % (4999)Termination reason: Unknown
% 23.30/3.46  % (4999)Termination phase: Saturation
% 23.30/3.46  
% 23.30/3.46  % (4999)Memory used [KB]: 8443
% 23.30/3.46  % (4999)Time elapsed: 0.184 s
% 23.30/3.46  % (4999)Instructions burned: 432 (million)
% 23.30/3.46  % (4999)------------------------------
% 23.30/3.46  % (4999)------------------------------
% 23.30/3.48  % (5001)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on theBenchmark for (2969ds/90Mi)
% 23.30/3.51  % (4937)Instruction limit reached!
% 23.30/3.51  % (4937)------------------------------
% 23.30/3.51  % (4937)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.30/3.51  % (4937)Termination reason: Unknown
% 23.30/3.51  % (4937)Termination phase: Saturation
% 23.30/3.51  
% 23.30/3.51  % (4937)Memory used [KB]: 11129
% 23.30/3.51  % (4937)Time elapsed: 2.218 s
% 23.30/3.51  % (4937)Instructions burned: 5206 (million)
% 23.30/3.51  % (4937)------------------------------
% 23.30/3.51  % (4937)------------------------------
% 23.75/3.51  % (5001)Instruction limit reached!
% 23.75/3.51  % (5001)------------------------------
% 23.75/3.51  % (5001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.75/3.51  % (5001)Termination reason: Unknown
% 23.75/3.51  % (5001)Termination phase: Function definition elimination
% 23.75/3.51  
% 23.75/3.51  % (5001)Memory used [KB]: 1279
% 23.75/3.51  % (5001)Time elapsed: 0.036 s
% 23.75/3.51  % (5001)Instructions burned: 92 (million)
% 23.75/3.51  % (5001)------------------------------
% 23.75/3.51  % (5001)------------------------------
% 23.75/3.53  % (5002)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on theBenchmark for (2968ds/346Mi)
% 23.75/3.53  % (5003)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on theBenchmark for (2968ds/401Mi)
% 24.08/3.58  % (4998)Refutation not found, incomplete strategy
% 24.08/3.58  % (4998)------------------------------
% 24.08/3.58  % (4998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.08/3.58  % (4998)Termination reason: Refutation not found, incomplete strategy
% 24.08/3.58  
% 24.08/3.58  
% 24.08/3.58  % (4998)Memory used [KB]: 8443
% 24.08/3.58  % (4998)Time elapsed: 0.311 s
% 24.08/3.58  % (4998)Instructions burned: 646 (million)
% 24.08/3.58  % (4998)------------------------------
% 24.08/3.58  % (4998)------------------------------
% 24.08/3.60  % (5004)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on theBenchmark for (2967ds/6454Mi)
% 24.46/3.66  % (5002)Instruction limit reached!
% 24.46/3.66  % (5002)------------------------------
% 24.46/3.66  % (5002)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.46/3.66  % (5002)Termination reason: Unknown
% 24.46/3.66  % (5002)Termination phase: Saturation
% 24.46/3.66  
% 24.46/3.66  % (5002)Memory used [KB]: 7036
% 24.46/3.66  % (5002)Time elapsed: 0.137 s
% 24.46/3.66  % (5002)Instructions burned: 348 (million)
% 24.46/3.66  % (5002)------------------------------
% 24.46/3.66  % (5002)------------------------------
% 24.46/3.67  % (5005)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on theBenchmark for (2967ds/283Mi)
% 24.74/3.69  % (5003)Instruction limit reached!
% 24.74/3.69  % (5003)------------------------------
% 24.74/3.69  % (5003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.74/3.69  % (5003)Termination reason: Unknown
% 24.74/3.69  % (5003)Termination phase: Saturation
% 24.74/3.69  
% 24.74/3.69  % (5003)Memory used [KB]: 7164
% 24.74/3.69  % (5003)Time elapsed: 0.164 s
% 24.74/3.69  % (5003)Instructions burned: 402 (million)
% 24.74/3.69  % (5003)------------------------------
% 24.74/3.69  % (5003)------------------------------
% 24.74/3.70  % (5006)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on theBenchmark for (2966ds/865Mi)
% 25.09/3.73  % (4995)Instruction limit reached!
% 25.09/3.73  % (4995)------------------------------
% 25.09/3.73  % (4995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.09/3.73  % (4995)Termination reason: Unknown
% 25.09/3.73  % (4995)Termination phase: Saturation
% 25.09/3.73  
% 25.09/3.73  % (4995)Memory used [KB]: 9210
% 25.09/3.73  % (4995)Time elapsed: 0.534 s
% 25.09/3.73  % (4995)Instructions burned: 1214 (million)
% 25.09/3.73  % (4995)------------------------------
% 25.09/3.73  % (4995)------------------------------
% 25.15/3.75  % (5007)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on theBenchmark for (2966ds/4528Mi)
% 25.15/3.78  % (5005)Instruction limit reached!
% 25.15/3.78  % (5005)------------------------------
% 25.15/3.78  % (5005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.15/3.78  % (5005)Termination reason: Unknown
% 25.15/3.78  % (5005)Termination phase: Saturation
% 25.15/3.78  
% 25.15/3.78  % (5005)Memory used [KB]: 6524
% 25.15/3.78  % (5005)Time elapsed: 0.109 s
% 25.15/3.78  % (5005)Instructions burned: 283 (million)
% 25.15/3.78  % (5005)------------------------------
% 25.15/3.78  % (5005)------------------------------
% 25.15/3.79  % (5008)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on theBenchmark for (2965ds/1001Mi)
% 25.15/3.80  % (5007)Refutation not found, incomplete strategy
% 25.15/3.80  % (5007)------------------------------
% 25.15/3.80  % (5007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.15/3.80  % (5007)Termination reason: Refutation not found, incomplete strategy
% 25.15/3.80  
% 25.15/3.80  
% 25.15/3.80  % (5007)Memory used [KB]: 3198
% 25.15/3.80  % (5007)Time elapsed: 0.056 s
% 25.15/3.80  % (5007)Instructions burned: 135 (million)
% 25.15/3.80  % (5007)------------------------------
% 25.15/3.80  % (5007)------------------------------
% 25.55/3.81  % (5009)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on theBenchmark for (2965ds/102Mi)
% 25.55/3.86  % (5009)Instruction limit reached!
% 25.55/3.86  % (5009)------------------------------
% 25.55/3.86  % (5009)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.55/3.86  % (5009)Termination reason: Unknown
% 25.55/3.86  % (5009)Termination phase: Saturation
% 25.55/3.86  
% 25.55/3.86  % (5009)Memory used [KB]: 6012
% 25.55/3.86  % (5009)Time elapsed: 0.042 s
% 25.55/3.86  % (5009)Instructions burned: 103 (million)
% 25.55/3.86  % (5009)------------------------------
% 25.55/3.86  % (5009)------------------------------
% 25.77/3.87  % (5010)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on theBenchmark for (2965ds/952Mi)
% 27.23/4.00  % (5000)Refutation not found, non-redundant clauses discarded% (5000)------------------------------
% 27.23/4.00  % (5000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.23/4.00  % (5000)Termination reason: Refutation not found, non-redundant clauses discarded
% 27.23/4.00  
% 27.23/4.00  % (5000)Memory used [KB]: 9083
% 27.23/4.00  % (5000)Time elapsed: 0.599 s
% 27.23/4.00  % (5000)Instructions burned: 1660 (million)
% 27.23/4.00  % (5000)------------------------------
% 27.23/4.00  % (5000)------------------------------
% 27.57/4.01  % (5011)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on theBenchmark for (2963ds/578Mi)
% 27.89/4.06  % (5006)Instruction limit reached!
% 27.89/4.06  % (5006)------------------------------
% 27.89/4.06  % (5006)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.89/4.06  % (5006)Termination reason: Unknown
% 27.89/4.06  % (5006)Termination phase: Saturation
% 27.89/4.06  
% 27.89/4.06  % (5006)Memory used [KB]: 7931
% 27.89/4.06  % (5006)Time elapsed: 0.365 s
% 27.89/4.06  % (5006)Instructions burned: 866 (million)
% 27.89/4.06  % (5006)------------------------------
% 27.89/4.06  % (5006)------------------------------
% 27.89/4.07  % (5012)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on theBenchmark for (2963ds/643Mi)
% 27.89/4.11  % (4996)Instruction limit reached!
% 27.89/4.11  % (4996)------------------------------
% 27.89/4.11  % (4996)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.89/4.11  % (4996)Termination reason: Unknown
% 27.89/4.11  % (4996)Termination phase: Saturation
% 27.89/4.11  
% 27.89/4.11  % (4996)Memory used [KB]: 10490
% 27.89/4.11  % (4996)Time elapsed: 0.882 s
% 27.89/4.11  % (4996)Instructions burned: 1980 (million)
% 27.89/4.11  % (4996)------------------------------
% 27.89/4.11  % (4996)------------------------------
% 27.89/4.13  % (5013)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on theBenchmark for (2962ds/865Mi)
% 28.63/4.22  % (5008)Instruction limit reached!
% 28.63/4.22  % (5008)------------------------------
% 28.63/4.22  % (5008)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.63/4.22  % (5008)Termination reason: Unknown
% 28.63/4.22  % (5008)Termination phase: Saturation
% 28.63/4.22  
% 28.63/4.22  % (5008)Memory used [KB]: 9978
% 28.63/4.22  % (5008)Time elapsed: 0.425 s
% 28.63/4.22  % (5008)Instructions burned: 1001 (million)
% 28.63/4.22  % (5008)------------------------------
% 28.63/4.22  % (5008)------------------------------
% 28.63/4.23  % (5012)Instruction limit reached!
% 28.63/4.23  % (5012)------------------------------
% 28.63/4.23  % (5012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.63/4.23  % (5012)Termination reason: Unknown
% 28.63/4.23  % (5012)Termination phase: Saturation
% 28.63/4.23  
% 28.63/4.23  % (5012)Memory used [KB]: 8059
% 28.63/4.23  % (5012)Time elapsed: 0.156 s
% 28.63/4.23  % (5012)Instructions burned: 644 (million)
% 28.63/4.23  % (5012)------------------------------
% 28.63/4.23  % (5012)------------------------------
% 28.63/4.23  % (5014)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on theBenchmark for (2961ds/1174Mi)
% 28.63/4.24  % (5015)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on theBenchmark for (2961ds/644Mi)
% 28.63/4.24  % (5011)Instruction limit reached!
% 28.63/4.24  % (5011)------------------------------
% 28.63/4.24  % (5011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.63/4.24  % (5011)Termination reason: Unknown
% 28.63/4.24  % (5011)Termination phase: Saturation
% 28.63/4.24  
% 28.63/4.24  % (5011)Memory used [KB]: 8699
% 28.63/4.24  % (5011)Time elapsed: 0.233 s
% 28.63/4.24  % (5011)Instructions burned: 580 (million)
% 28.63/4.24  % (5011)------------------------------
% 28.63/4.24  % (5011)------------------------------
% 29.35/4.26  % (5016)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on theBenchmark for (2961ds/1201Mi)
% 29.35/4.27  % (5010)Instruction limit reached!
% 29.35/4.27  % (5010)------------------------------
% 29.35/4.27  % (5010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.35/4.27  % (5010)Termination reason: Unknown
% 29.35/4.27  % (5010)Termination phase: Saturation
% 29.35/4.27  
% 29.35/4.27  % (5010)Memory used [KB]: 9466
% 29.35/4.27  % (5010)Time elapsed: 0.402 s
% 29.35/4.27  % (5010)Instructions burned: 953 (million)
% 29.35/4.27  % (5010)------------------------------
% 29.35/4.27  % (5010)------------------------------
% 29.35/4.29  % (5017)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on theBenchmark for (2961ds/1046Mi)
% 29.68/4.40  % (4987)Instruction limit reached!
% 29.68/4.40  % (4987)------------------------------
% 29.68/4.40  % (4987)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.68/4.41  % (4987)Termination reason: Unknown
% 29.68/4.41  % (4987)Termination phase: Saturation
% 29.68/4.41  
% 29.68/4.41  % (4987)Memory used [KB]: 13816
% 29.68/4.41  % (4987)Time elapsed: 1.515 s
% 29.68/4.41  % (4987)Instructions burned: 3374 (million)
% 29.68/4.41  % (4987)------------------------------
% 29.68/4.41  % (4987)------------------------------
% 29.68/4.43  % (5018)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on theBenchmark for (2959ds/222Mi)
% 29.92/4.45  % (5015)Instruction limit reached!
% 29.92/4.45  % (5015)------------------------------
% 29.92/4.45  % (5015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.92/4.45  % (5015)Termination reason: Unknown
% 29.92/4.45  % (5015)Termination phase: Saturation
% 29.92/4.45  
% 29.92/4.45  % (5015)Memory used [KB]: 7803
% 29.92/4.45  % (5015)Time elapsed: 0.201 s
% 29.92/4.45  % (5015)Instructions burned: 644 (million)
% 29.92/4.45  % (5015)------------------------------
% 29.92/4.45  % (5015)------------------------------
% 29.92/4.47  % (5019)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on theBenchmark for (2959ds/68Mi)
% 29.92/4.47  % (5013)Instruction limit reached!
% 29.92/4.47  % (5013)------------------------------
% 29.92/4.47  % (5013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.92/4.48  % (5013)Termination reason: Unknown
% 29.92/4.48  % (5013)Termination phase: Saturation
% 29.92/4.48  
% 29.92/4.48  % (5013)Memory used [KB]: 7547
% 29.92/4.48  % (5013)Time elapsed: 0.369 s
% 29.92/4.48  % (5013)Instructions burned: 866 (million)
% 29.92/4.48  % (5013)------------------------------
% 29.92/4.48  % (5013)------------------------------
% 29.92/4.48  % (5018)Instruction limit reached!
% 29.92/4.48  % (5018)------------------------------
% 29.92/4.48  % (5018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.92/4.48  % (5018)Termination reason: Unknown
% 29.92/4.48  % (5018)Termination phase: Saturation
% 29.92/4.48  
% 29.92/4.48  % (5018)Memory used [KB]: 6652
% 29.92/4.48  % (5018)Time elapsed: 0.053 s
% 29.92/4.48  % (5018)Instructions burned: 224 (million)
% 29.92/4.48  % (5018)------------------------------
% 29.92/4.48  % (5018)------------------------------
% 30.59/4.49  % (5021)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on theBenchmark for (2959ds/360Mi)
% 30.59/4.49  % (5020)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on theBenchmark for (2959ds/454Mi)
% 30.59/4.49  % (5019)Instruction limit reached!
% 30.59/4.49  % (5019)------------------------------
% 30.59/4.49  % (5019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 30.59/4.50  % (5019)Termination reason: Unknown
% 30.59/4.50  % (5019)Termination phase: Property scanning
% 30.59/4.50  
% 30.59/4.50  % (5019)Memory used [KB]: 1279
% 30.59/4.50  % (5019)Time elapsed: 0.027 s
% 30.59/4.50  % (5019)Instructions burned: 69 (million)
% 30.59/4.50  % (5019)------------------------------
% 30.59/4.50  % (5019)------------------------------
% 30.59/4.51  % (5022)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on theBenchmark for (2958ds/157Mi)
% 30.59/4.56  % (5022)Instruction limit reached!
% 30.59/4.56  % (5022)------------------------------
% 30.59/4.56  % (5022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 30.59/4.56  % (5022)Termination reason: Unknown
% 30.59/4.56  % (5022)Termination phase: Saturation
% 30.59/4.56  
% 30.59/4.56  % (5022)Memory used [KB]: 6396
% 30.59/4.56  % (5022)Time elapsed: 0.047 s
% 30.59/4.56  % (5022)Instructions burned: 157 (million)
% 30.59/4.56  % (5022)------------------------------
% 30.59/4.56  % (5022)------------------------------
% 31.89/4.57  % (5023)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on theBenchmark for (2958ds/5061Mi)
% 31.89/4.58  % (5021)Instruction limit reached!
% 31.89/4.58  % (5021)------------------------------
% 31.89/4.58  % (5021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.89/4.58  % (5021)Termination reason: Unknown
% 31.89/4.58  % (5021)Termination phase: Saturation
% 31.89/4.58  
% 31.89/4.58  % (5021)Memory used [KB]: 6908
% 31.89/4.58  % (5021)Time elapsed: 0.088 s
% 31.89/4.58  % (5021)Instructions burned: 362 (million)
% 31.89/4.58  % (5021)------------------------------
% 31.89/4.58  % (5021)------------------------------
% 31.89/4.59  % (5024)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on theBenchmark for (2957ds/2401Mi)
% 32.23/4.65  % (5014)First to succeed.
% 32.40/4.67  % (5020)Instruction limit reached!
% 32.40/4.67  % (5020)------------------------------
% 32.40/4.67  % (5020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 32.40/4.67  % (5020)Termination reason: Unknown
% 32.40/4.67  % (5020)Termination phase: Saturation
% 32.40/4.67  
% 32.40/4.67  % (5020)Memory used [KB]: 12665
% 32.40/4.67  % (5020)Time elapsed: 0.178 s
% 32.40/4.67  % (5020)Instructions burned: 454 (million)
% 32.40/4.67  % (5020)------------------------------
% 32.40/4.67  % (5020)------------------------------
% 32.40/4.69  % (5025)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on theBenchmark for (2957ds/5798Mi)
% 32.79/4.75  % (5017)Instruction limit reached!
% 32.79/4.75  % (5017)------------------------------
% 32.79/4.75  % (5017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 32.79/4.75  % (5017)Termination reason: Unknown
% 32.79/4.75  % (5017)Termination phase: Saturation
% 32.79/4.75  
% 32.79/4.75  % (5017)Memory used [KB]: 8443
% 32.79/4.75  % (5017)Time elapsed: 0.425 s
% 32.79/4.75  % (5017)Instructions burned: 1047 (million)
% 32.79/4.75  % (5017)------------------------------
% 32.79/4.75  % (5017)------------------------------
% 32.79/4.76  % (5026)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on theBenchmark for (2956ds/346Mi)
% 33.00/4.81  % (5016)Instruction limit reached!
% 33.00/4.81  % (5016)------------------------------
% 33.00/4.81  % (5016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 33.00/4.81  % (5016)Termination reason: Unknown
% 33.00/4.81  % (5016)Termination phase: Saturation
% 33.00/4.81  
% 33.00/4.81  % (5016)Memory used [KB]: 11641
% 33.00/4.81  % (5016)Time elapsed: 0.553 s
% 33.00/4.81  % (5016)Instructions burned: 1202 (million)
% 33.00/4.81  % (5016)------------------------------
% 33.00/4.81  % (5016)------------------------------
% 33.00/4.82  % (5027)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on theBenchmark for (2955ds/1321Mi)
% 33.27/4.86  % (5014)Refutation found. Thanks to Tanya!
% 33.27/4.86  % SZS status Theorem for theBenchmark
% 33.27/4.86  % SZS output start Proof for theBenchmark
% See solution above
% 33.36/4.89  % (5014)------------------------------
% 33.36/4.89  % (5014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 33.36/4.89  % (5014)Termination reason: Refutation
% 33.36/4.89  
% 33.36/4.89  % (5014)Memory used [KB]: 9850
% 33.36/4.89  % (5014)Time elapsed: 0.628 s
% 33.36/4.89  % (5014)Instructions burned: 923 (million)
% 33.36/4.89  % (5014)------------------------------
% 33.36/4.89  % (5014)------------------------------
% 33.36/4.89  % (4825)Success in time 4.523 s
% 33.36/4.89  % Vampire---4.8 exiting
%------------------------------------------------------------------------------