TSTP Solution File: SCT193_5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SCT193_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n022.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 : Thu Aug 31 14:23:38 EDT 2023

% Result   : Theorem 0.24s 0.66s
% Output   : Refutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  196
% Syntax   : Number of formulae    :  541 (  49 unt; 123 typ;   0 def)
%            Number of atoms       : 1502 ( 382 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives : 1709 ( 625   ~; 764   |; 191   &)
%                                         (  63 <=>;  66  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  178 ( 105   >;  73   *;   0   +;   0  <<)
%            Number of predicates  :   47 (  45 usr;  34 prp; 0-6 aty)
%            Number of functors    :  108 ( 108 usr;   9 con; 0-7 aty)
%            Number of variables   : 1352 (;1016   !;  37   ?;1352   :)
%                                         ( 299  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

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

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

tff(func_def_1,type,
    arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_2,type,
    arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

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

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

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

tff(func_def_6,type,
    order_215145569der_on: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(fun(product_prod(X0,X0),bool),bool) ) ).

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

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

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

tff(func_def_10,type,
    product_apsnd: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).

tff(func_def_11,type,
    product_curry: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).

tff(func_def_12,type,
    produc1605651328_split: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).

tff(func_def_13,type,
    product_prod_case: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).

tff(func_def_14,type,
    product_prod_rec: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).

tff(func_def_15,type,
    product_scomp: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( fun(X0,product_prod(X1,X2)) * fun(X1,fun(X2,X3)) ) > fun(X0,X3) ) ).

tff(func_def_16,type,
    inv_image: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X1,X0) ) > fun(product_prod(X1,X1),bool) ) ).

tff(func_def_17,type,
    collect: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).

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

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

tff(func_def_20,type,
    fFalse: bool ).

tff(func_def_21,type,
    fTrue: bool ).

tff(func_def_22,type,
    f: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

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

tff(func_def_24,type,
    a: arrow_411405190le_alt ).

tff(func_def_25,type,
    b: arrow_411405190le_alt ).

tff(func_def_26,type,
    i: arrow_159774573e_indi ).

tff(func_def_27,type,
    sK4: arrow_159774573e_indi ).

tff(func_def_28,type,
    sK5: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > arrow_159774573e_indi ).

tff(func_def_29,type,
    sK6: 
      !>[X0: $tType] : X0 ).

tff(func_def_30,type,
    sK7: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_31,type,
    sK8: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_32,type,
    sK9: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_33,type,
    sK10: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_34,type,
    sK11: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_35,type,
    sK12: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_36,type,
    sK13: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_37,type,
    sK14: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_38,type,
    sK15: 
      !>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_39,type,
    sK16: 
      !>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_40,type,
    sK17: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_41,type,
    sK18: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_42,type,
    sK19: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_43,type,
    sK20: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_44,type,
    sK21: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_45,type,
    sK22: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_46,type,
    sK23: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_47,type,
    sK24: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_48,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_49,type,
    sK26: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_50,type,
    sK27: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).

tff(func_def_51,type,
    sK28: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).

tff(func_def_52,type,
    sK29: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_53,type,
    sK30: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).

tff(func_def_54,type,
    sK31: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).

tff(func_def_55,type,
    sK32: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

tff(func_def_56,type,
    sK33: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

tff(func_def_57,type,
    sK34: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

tff(func_def_58,type,
    sK35: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).

tff(func_def_59,type,
    sK36: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).

tff(func_def_60,type,
    sK37: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).

tff(func_def_61,type,
    sK38: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

tff(func_def_62,type,
    sK39: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

tff(func_def_63,type,
    sK40: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

tff(func_def_64,type,
    sK41: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

tff(func_def_65,type,
    sK42: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X0 ) ).

tff(func_def_66,type,
    sK43: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X2 ) ).

tff(func_def_67,type,
    sK44: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).

tff(func_def_68,type,
    sK45: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).

tff(func_def_69,type,
    sK46: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).

tff(func_def_70,type,
    sK47: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).

tff(func_def_71,type,
    sK48: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).

tff(func_def_72,type,
    sK49: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).

tff(func_def_73,type,
    sK50: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).

tff(func_def_74,type,
    sK51: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).

tff(func_def_75,type,
    sK52: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).

tff(func_def_76,type,
    sK53: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).

tff(func_def_77,type,
    sK54: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).

tff(func_def_78,type,
    sK55: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).

tff(func_def_79,type,
    sK56: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).

tff(func_def_80,type,
    sK57: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).

tff(func_def_81,type,
    sK58: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).

tff(func_def_82,type,
    sK59: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).

tff(func_def_83,type,
    sK60: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).

tff(func_def_84,type,
    sK61: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).

tff(func_def_85,type,
    sK62: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).

tff(func_def_86,type,
    sK63: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X2 ) ).

tff(func_def_87,type,
    sK64: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X1 ) ).

tff(func_def_88,type,
    sK65: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).

tff(func_def_89,type,
    sK66: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X3 ) ).

tff(func_def_90,type,
    sK67: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X2 ) ).

tff(func_def_91,type,
    sK68: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X1 ) ).

tff(func_def_92,type,
    sK69: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X0 ) ).

tff(func_def_93,type,
    sK70: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).

tff(func_def_94,type,
    sK71: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).

tff(func_def_95,type,
    sK72: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).

tff(func_def_96,type,
    sK73: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).

tff(func_def_97,type,
    sK74: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).

tff(func_def_98,type,
    sK75: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).

tff(func_def_99,type,
    sK76: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X5 ) ).

tff(func_def_100,type,
    sK77: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X4 ) ).

tff(func_def_101,type,
    sK78: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X3 ) ).

tff(func_def_102,type,
    sK79: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X2 ) ).

tff(func_def_103,type,
    sK80: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X1 ) ).

tff(func_def_104,type,
    sK81: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X0 ) ).

tff(func_def_105,type,
    sK82: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

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

tff(pred_def_2,type,
    in_rel: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).

tff(pred_def_3,type,
    inv_imagep: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).

tff(pred_def_4,type,
    irrefl: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).

tff(pred_def_5,type,
    total_on: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).

tff(pred_def_6,type,
    trans: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).

tff(pred_def_7,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_8,type,
    pp: bool > $o ).

tff(pred_def_9,type,
    sP0: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_10,type,
    sP1: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).

tff(pred_def_11,type,
    sP2: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_12,type,
    sP3: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).

tff(f3604,plain,
    $false,
    inference(avatar_sat_refutation,[],[f697,f699,f701,f703,f714,f722,f818,f865,f1063,f1110,f1118,f1182,f1192,f1345,f1394,f1399,f1409,f1605,f1756,f1844,f1941,f1998,f2055,f2116,f2173,f2481,f2513,f2979,f2982,f2997,f2999,f3020,f3022,f3519,f3575,f3577]) ).

tff(f3577,plain,
    ( ~ spl83_4
    | ~ spl83_5
    | ~ spl83_21 ),
    inference(avatar_contradiction_clause,[],[f3576]) ).

tff(f3576,plain,
    ( $false
    | ~ spl83_4
    | ~ spl83_5
    | ~ spl83_21 ),
    inference(subsumption_resolution,[],[f3523,f716]) ).

tff(f716,plain,
    ( ! [X1: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X1),f(p))
    | ~ spl83_5 ),
    inference(resolution,[],[f713,f379]) ).

tff(f379,plain,
    ! [X0: $tType,X3: X0,X1: fun(product_prod(X0,X0),bool)] :
      ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
      | ~ irrefl(X0,X1) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f265,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( irrefl(X0,X1)
        | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK11(X0,X1)),X1) )
      & ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
        | ~ irrefl(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f263,f264]) ).

tff(f264,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
     => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK11(X0,X1)),X1) ),
    introduced(choice_axiom,[]) ).

tff(f263,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( irrefl(X0,X1)
        | ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
      & ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
        | ~ irrefl(X0,X1) ) ),
    inference(rectify,[],[f262]) ).

tff(f262,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( irrefl(X0,X1)
        | ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
      & ( ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
        | ~ irrefl(X0,X1) ) ),
    inference(nnf_transformation,[],[f111]) ).

tff(f111,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( irrefl(X0,X1)
    <=> ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
      ( irrefl(X0,X5)
    <=> ! [X6: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X6),X5) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_0_irrefl__def) ).

tff(f713,plain,
    ( irrefl(arrow_411405190le_alt,f(p))
    | ~ spl83_5 ),
    inference(avatar_component_clause,[],[f711]) ).

tff(f711,plain,
    ( spl83_5
  <=> irrefl(arrow_411405190le_alt,f(p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_5])]) ).

tff(f3523,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),b),f(p))
    | ~ spl83_4
    | ~ spl83_21 ),
    inference(resolution,[],[f1842,f896]) ).

tff(f896,plain,
    ( ! [X56: arrow_411405190le_alt] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X56),a),f(p))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X56),b),f(p)) )
    | ~ spl83_4 ),
    inference(subsumption_resolution,[],[f668,f696]) ).

tff(f696,plain,
    ( trans(arrow_411405190le_alt,f(p))
    | ~ spl83_4 ),
    inference(avatar_component_clause,[],[f694]) ).

tff(f694,plain,
    ( spl83_4
  <=> trans(arrow_411405190le_alt,f(p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_4])]) ).

tff(f668,plain,
    ! [X56: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X56),b),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X56),a),f(p))
      | ~ trans(arrow_411405190le_alt,f(p)) ),
    inference(resolution,[],[f351,f478]) ).

tff(f478,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: fun(product_prod(X0,X0),bool)] :
      ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
      | ~ trans(X0,X4) ),
    inference(cnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
      ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
      | ~ trans(X0,X4) ),
    inference(flattening,[],[f218]) ).

tff(f218,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
      ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
      | ~ trans(X0,X4) ),
    inference(ennf_transformation,[],[f140]) ).

tff(f140,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X4)
     => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
       => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
         => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4) ) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X0: $tType,X20: X0,X14: X0,X15: X0,X5: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X5)
     => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X15),X14),X5)
       => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X14),X20),X5)
         => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X15),X20),X5) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_8_transD) ).

tff(f351,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),f(p)),
    inference(cnf_transformation,[],[f91]) ).

tff(f91,axiom,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),f(p)),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_2) ).

tff(f1842,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
    | ~ spl83_21 ),
    inference(avatar_component_clause,[],[f1841]) ).

tff(f1841,plain,
    ( spl83_21
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_21])]) ).

tff(f3575,plain,
    ( ~ spl83_4
    | ~ spl83_5
    | ~ spl83_21 ),
    inference(avatar_contradiction_clause,[],[f3574]) ).

tff(f3574,plain,
    ( $false
    | ~ spl83_4
    | ~ spl83_5
    | ~ spl83_21 ),
    inference(subsumption_resolution,[],[f3520,f716]) ).

tff(f3520,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),a),f(p))
    | ~ spl83_4
    | ~ spl83_21 ),
    inference(resolution,[],[f1842,f897]) ).

tff(f897,plain,
    ( ! [X55: arrow_411405190le_alt] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),X55),f(p))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X55),f(p)) )
    | ~ spl83_4 ),
    inference(subsumption_resolution,[],[f667,f696]) ).

tff(f667,plain,
    ! [X55: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X55),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),X55),f(p))
      | ~ trans(arrow_411405190le_alt,f(p)) ),
    inference(resolution,[],[f351,f478]) ).

tff(f3519,plain,
    ( spl83_21
    | spl83_8
    | ~ spl83_16 ),
    inference(avatar_split_clause,[],[f2583,f1391,f815,f1841]) ).

tff(f815,plain,
    ( spl83_8
  <=> ( a = b ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_8])]) ).

tff(f1391,plain,
    ( spl83_16
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_16])]) ).

tff(f2583,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
    | spl83_8
    | ~ spl83_16 ),
    inference(subsumption_resolution,[],[f2549,f816]) ).

tff(f816,plain,
    ( ( a != b )
    | spl83_8 ),
    inference(avatar_component_clause,[],[f815]) ).

tff(f2549,plain,
    ( ( a = b )
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
    | ~ spl83_16 ),
    inference(resolution,[],[f736,f1393]) ).

tff(f1393,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
    | ~ spl83_16 ),
    inference(avatar_component_clause,[],[f1391]) ).

tff(f736,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
      | ( X0 = X1 )
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),f(p)) ),
    inference(subsumption_resolution,[],[f735,f355]) ).

tff(f355,plain,
    ! [X0: arrow_159774573e_indi] : trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
    inference(cnf_transformation,[],[f97]) ).

tff(f97,plain,
    ! [X0: arrow_159774573e_indi] :
      ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
      & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
      & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X52: arrow_159774573e_indi] :
      ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52))
      & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52))
      & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52)) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_1) ).

tff(f735,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
      | ( X0 = X1 )
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),f(p))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK5(p))) ),
    inference(subsumption_resolution,[],[f730,f357]) ).

tff(f357,plain,
    ! [X0: arrow_159774573e_indi] : total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
    inference(cnf_transformation,[],[f97]) ).

tff(f730,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
      | ( X0 = X1 )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK5(p)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),f(p))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK5(p))) ),
    inference(resolution,[],[f358,f356]) ).

tff(f356,plain,
    ! [X0: arrow_159774573e_indi] : irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
    inference(cnf_transformation,[],[f97]) ).

tff(f358,plain,
    ! [X2: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: arrow_411405190le_alt] :
      ( ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
      | ( X1 = X2 )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(X0))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0))) ),
    inference(cnf_transformation,[],[f255]) ).

tff(f255,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X1 = X2 ) )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
      | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f253,f254]) ).

tff(f254,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ? [X3: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3)) )
     => ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
        | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
        | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f253,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X1 = X2 ) )
      | ? [X3: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3)) ) ),
    inference(rectify,[],[f183]) ).

tff(f183,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X2 = X3 ) )
      | ? [X1: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
    inference(flattening,[],[f182]) ).

tff(f182,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X2 = X3 ) )
      | ? [X1: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
    inference(ennf_transformation,[],[f98]) ).

tff(f98,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: arrow_159774573e_indi] :
          ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) )
     => ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
          ( ( X2 != X3 )
         => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
           => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X0)) ) ) ),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X57: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X28: arrow_159774573e_indi] :
          ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,X28))
          & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,X28))
          & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,X28)) )
     => ! [X58: arrow_411405190le_alt,X59: arrow_411405190le_alt] :
          ( ( X58 != X59 )
         => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X58),X59),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,i))
           => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X58),X59),f(X57)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_0) ).

tff(f3022,plain,
    spl83_31,
    inference(avatar_contradiction_clause,[],[f3021]) ).

tff(f3021,plain,
    ( $false
    | spl83_31 ),
    inference(subsumption_resolution,[],[f3016,f369]) ).

tff(f369,plain,
    ! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,plain,
    ! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X0: $tType,X7: X0] : member(X0,X7,top_top(fun(X0,bool))),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_2_UNIV__I) ).

tff(f3016,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK16(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),sK15(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
    | spl83_31 ),
    inference(resolution,[],[f2971,f396]) ).

tff(f396,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
      ( total_on(X0,X2,X1)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK16(X0,X1,X2)),sK15(X0,X1,X2)),X1) ),
    inference(cnf_transformation,[],[f275]) ).

tff(f275,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( ( total_on(X0,X2,X1)
        | ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK16(X0,X1,X2)),sK15(X0,X1,X2)),X1)
          & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),sK16(X0,X1,X2)),X1)
          & ( sK15(X0,X1,X2) != sK16(X0,X1,X2) )
          & member(X0,sK16(X0,X1,X2),X2)
          & member(X0,sK15(X0,X1,X2),X2) ) )
      & ( ! [X5: X0] :
            ( ! [X6: X0] :
                ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
                | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
                | ( X5 = X6 )
                | ~ member(X0,X6,X2) )
            | ~ member(X0,X5,X2) )
        | ~ total_on(X0,X2,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f272,f274,f273]) ).

tff(f273,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( ? [X3: X0] :
          ( ? [X4: X0] :
              ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
              & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
              & ( X3 != X4 )
              & member(X0,X4,X2) )
          & member(X0,X3,X2) )
     => ( ? [X4: X0] :
            ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),sK15(X0,X1,X2)),X1)
            & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),X4),X1)
            & ( sK15(X0,X1,X2) != X4 )
            & member(X0,X4,X2) )
        & member(X0,sK15(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

tff(f274,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( ? [X4: X0] :
          ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),sK15(X0,X1,X2)),X1)
          & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),X4),X1)
          & ( sK15(X0,X1,X2) != X4 )
          & member(X0,X4,X2) )
     => ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK16(X0,X1,X2)),sK15(X0,X1,X2)),X1)
        & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),sK16(X0,X1,X2)),X1)
        & ( sK15(X0,X1,X2) != sK16(X0,X1,X2) )
        & member(X0,sK16(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

tff(f272,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( ( total_on(X0,X2,X1)
        | ? [X3: X0] :
            ( ? [X4: X0] :
                ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
                & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
                & ( X3 != X4 )
                & member(X0,X4,X2) )
            & member(X0,X3,X2) ) )
      & ( ! [X5: X0] :
            ( ! [X6: X0] :
                ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
                | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
                | ( X5 = X6 )
                | ~ member(X0,X6,X2) )
            | ~ member(X0,X5,X2) )
        | ~ total_on(X0,X2,X1) ) ),
    inference(rectify,[],[f271]) ).

tff(f271,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( ( total_on(X0,X2,X1)
        | ? [X3: X0] :
            ( ? [X4: X0] :
                ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
                & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
                & ( X3 != X4 )
                & member(X0,X4,X2) )
            & member(X0,X3,X2) ) )
      & ( ! [X3: X0] :
            ( ! [X4: X0] :
                ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
                | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
                | ( X3 = X4 )
                | ~ member(X0,X4,X2) )
            | ~ member(X0,X3,X2) )
        | ~ total_on(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f202]) ).

tff(f202,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( total_on(X0,X2,X1)
    <=> ! [X3: X0] :
          ( ! [X4: X0] :
              ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
              | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
              | ( X3 = X4 )
              | ~ member(X0,X4,X2) )
          | ~ member(X0,X3,X2) ) ),
    inference(flattening,[],[f201]) ).

tff(f201,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( total_on(X0,X2,X1)
    <=> ! [X3: X0] :
          ( ! [X4: X0] :
              ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
              | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
              | ( X3 = X4 )
              | ~ member(X0,X4,X2) )
          | ~ member(X0,X3,X2) ) ),
    inference(ennf_transformation,[],[f118]) ).

tff(f118,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( total_on(X0,X2,X1)
    <=> ! [X3: X0] :
          ( member(X0,X3,X2)
         => ! [X4: X0] :
              ( member(X0,X4,X2)
             => ( ( X3 != X4 )
               => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
                  | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1) ) ) ) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X0: $tType,X5: fun(product_prod(X0,X0),bool),X16: fun(X0,bool)] :
      ( total_on(X0,X16,X5)
    <=> ! [X6: X0] :
          ( member(X0,X6,X16)
         => ! [X17: X0] :
              ( member(X0,X17,X16)
             => ( ( X6 != X17 )
               => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X17),X6),X5)
                  | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X17),X5) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_6_total__on__def) ).

tff(f2971,plain,
    ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
    | spl83_31 ),
    inference(avatar_component_clause,[],[f2969]) ).

tff(f2969,plain,
    ( spl83_31
  <=> total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_31])]) ).

tff(f3020,plain,
    spl83_31,
    inference(avatar_contradiction_clause,[],[f3019]) ).

tff(f3019,plain,
    ( $false
    | spl83_31 ),
    inference(subsumption_resolution,[],[f3015,f369]) ).

tff(f3015,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK15(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),sK16(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
    | spl83_31 ),
    inference(resolution,[],[f2971,f395]) ).

tff(f395,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
      ( total_on(X0,X2,X1)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),sK16(X0,X1,X2)),X1) ),
    inference(cnf_transformation,[],[f275]) ).

tff(f2999,plain,
    spl83_30,
    inference(avatar_contradiction_clause,[],[f2998]) ).

tff(f2998,plain,
    ( $false
    | spl83_30 ),
    inference(subsumption_resolution,[],[f2993,f369]) ).

tff(f2993,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK12(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),sK14(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
    | spl83_30 ),
    inference(resolution,[],[f2967,f384]) ).

tff(f384,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK14(X0,X1)),X1) ),
    inference(cnf_transformation,[],[f269]) ).

tff(f269,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( trans(X0,X1)
        | ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK14(X0,X1)),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK14(X0,X1)),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK13(X0,X1)),X1) ) )
      & ( ! [X5: X0,X6: X0,X7: X0] :
            ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
            | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
            | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1) )
        | ~ trans(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f267,f268]) ).

tff(f268,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ? [X2: X0,X3: X0,X4: X0] :
          ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
     => ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK14(X0,X1)),X1)
        & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK14(X0,X1)),X1)
        & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK13(X0,X1)),X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f267,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( trans(X0,X1)
        | ? [X2: X0,X3: X0,X4: X0] :
            ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
            & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
            & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) )
      & ( ! [X5: X0,X6: X0,X7: X0] :
            ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
            | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
            | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1) )
        | ~ trans(X0,X1) ) ),
    inference(rectify,[],[f266]) ).

tff(f266,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( trans(X0,X1)
        | ? [X2: X0,X3: X0,X4: X0] :
            ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
            & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
            & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) )
      & ( ! [X2: X0,X3: X0,X4: X0] :
            ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
            | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
            | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
        | ~ trans(X0,X1) ) ),
    inference(nnf_transformation,[],[f192]) ).

tff(f192,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
    <=> ! [X2: X0,X3: X0,X4: X0] :
          ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
          | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
          | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
    inference(flattening,[],[f191]) ).

tff(f191,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
    <=> ! [X2: X0,X3: X0,X4: X0] :
          ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
          | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
          | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
    inference(ennf_transformation,[],[f112]) ).

tff(f112,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
    <=> ! [X2: X0,X3: X0,X4: X0] :
          ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1)
         => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
           => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1) ) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X5)
    <=> ! [X6: X0,X18: X0,X19: X0] :
          ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X18),X5)
         => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X18),X19),X5)
           => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X19),X5) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_7_trans__def) ).

tff(f2967,plain,
    ( ~ trans(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
    | spl83_30 ),
    inference(avatar_component_clause,[],[f2965]) ).

tff(f2965,plain,
    ( spl83_30
  <=> trans(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_30])]) ).

tff(f2997,plain,
    spl83_30,
    inference(avatar_contradiction_clause,[],[f2996]) ).

tff(f2996,plain,
    ( $false
    | spl83_30 ),
    inference(subsumption_resolution,[],[f2990,f369]) ).

tff(f2990,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK8(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),sK10(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
    | spl83_30 ),
    inference(resolution,[],[f2967,f378]) ).

tff(f378,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK10(X0,X1)),X1) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f261,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
      | ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK10(X0,X1)),X1)
        & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK9(X0,X1)),sK10(X0,X1)),X1)
        & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK9(X0,X1)),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f190,f260]) ).

tff(f260,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ? [X2: X0,X3: X0,X4: X0] :
          ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
     => ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK10(X0,X1)),X1)
        & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK9(X0,X1)),sK10(X0,X1)),X1)
        & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK9(X0,X1)),X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f190,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
      | ? [X2: X0,X3: X0,X4: X0] :
          ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
    inference(flattening,[],[f189]) ).

tff(f189,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
      | ? [X2: X0,X3: X0,X4: X0] :
          ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
          & member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
    inference(ennf_transformation,[],[f110]) ).

tff(f110,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ! [X2: X0,X3: X0,X4: X0] :
          ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1)
         => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
           => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1) ) )
     => trans(X0,X1) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
      ( ! [X28: X0,X29: X0,X30: X0] :
          ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X28),X29),X5)
         => ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X29),X30),X5)
           => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X28),X30),X5) ) )
     => trans(X0,X5) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_15_transI) ).

tff(f2982,plain,
    spl83_29,
    inference(avatar_contradiction_clause,[],[f2981]) ).

tff(f2981,plain,
    ( $false
    | spl83_29 ),
    inference(subsumption_resolution,[],[f2980,f360]) ).

tff(f360,plain,
    top(bool),
    inference(cnf_transformation,[],[f83]) ).

tff(f83,axiom,
    top(bool),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',arity_HOL_Obool___Orderings_Otop) ).

tff(f2980,plain,
    ( ~ top(bool)
    | spl83_29 ),
    inference(resolution,[],[f2963,f371]) ).

tff(f371,plain,
    ! [X1: $tType,X0: $tType] :
      ( top(fun(X0,X1))
      | ~ top(X1) ),
    inference(cnf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: $tType,X1: $tType] :
      ( top(fun(X0,X1))
      | ~ top(X1) ),
    inference(ennf_transformation,[],[f105]) ).

tff(f105,plain,
    ! [X0: $tType,X1: $tType] :
      ( top(X1)
     => top(fun(X0,X1)) ),
    inference(rectify,[],[f82]) ).

tff(f82,axiom,
    ! [X53: $tType,X54: $tType] :
      ( top(X54)
     => top(fun(X53,X54)) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',arity_fun___Orderings_Otop) ).

tff(f2963,plain,
    ( ~ top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))
    | spl83_29 ),
    inference(avatar_component_clause,[],[f2961]) ).

tff(f2961,plain,
    ( spl83_29
  <=> top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_29])]) ).

tff(f2979,plain,
    ( ~ spl83_29
    | ~ spl83_30
    | ~ spl83_31
    | spl83_32
    | ~ spl83_33 ),
    inference(avatar_split_clause,[],[f734,f2976,f2973,f2969,f2965,f2961]) ).

tff(f2973,plain,
    ( spl83_32
  <=> ! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
        ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),i))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X4),f(top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))))
        | ( X3 = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_32])]) ).

tff(f2976,plain,
    ( spl83_33
  <=> irrefl(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_33])]) ).

tff(f734,plain,
    ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ~ irrefl(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),i))
      | ( X3 = X4 )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X4),f(top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))))
      | ~ trans(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
      | ~ top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ),
    inference(superposition,[],[f358,f372]) ).

tff(f372,plain,
    ! [X1: $tType,X0: $tType,X2: X0] :
      ( ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
      | ~ top(X1) ),
    inference(cnf_transformation,[],[f185]) ).

tff(f185,plain,
    ! [X0: $tType,X1: $tType] :
      ( ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
      | ~ top(X1) ),
    inference(ennf_transformation,[],[f106]) ).

tff(f106,plain,
    ! [X0: $tType,X1: $tType] :
      ( top(X1)
     => ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X1: $tType,X0: $tType] :
      ( top(X0)
     => ! [X7: X1] : ( aa(X1,X0,top_top(fun(X1,X0)),X7) = top_top(X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_10_top__apply) ).

tff(f2513,plain,
    ( spl83_8
    | spl83_28 ),
    inference(avatar_split_clause,[],[f648,f2511,f815]) ).

tff(f2511,plain,
    ( spl83_28
  <=> ! [X30: arrow_411405190le_alt,X31: arrow_411405190le_alt] :
        ( sP2(f(p),b,a,X30,X31)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X31),b),f(p))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X31),f(p)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_28])]) ).

tff(f648,plain,
    ! [X31: arrow_411405190le_alt,X30: arrow_411405190le_alt] :
      ( sP2(f(p),b,a,X30,X31)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X31),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X31),b),f(p))
      | ( a = b ) ),
    inference(resolution,[],[f351,f476]) ).

tff(f476,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f314,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP2(X0,X1,X2,X3,X4)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
              & ( X1 != X3 ) )
            | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
              & ( X2 != X4 )
              & ( X1 = X3 ) ) )
          & ( X2 != X3 ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
          & ( X2 = X3 ) )
        | ( X1 = X2 ) )
      & ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
                | ( X1 = X3 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
                | ( X2 = X4 )
                | ( X1 != X3 ) ) )
            | ( X2 = X3 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
            | ( X2 != X3 ) )
          & ( X1 != X2 ) )
        | ~ sP2(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f313]) ).

tff(f313,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP2(X2,X0,X1,X3,X4)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
              & ( X0 != X3 ) )
            | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
              & ( X1 != X4 )
              & ( X0 = X3 ) ) )
          & ( X1 != X3 ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
          & ( X1 = X3 ) )
        | ( X0 = X1 ) )
      & ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
                | ( X0 = X3 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
                | ( X1 = X4 )
                | ( X0 != X3 ) ) )
            | ( X1 = X3 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
            | ( X1 != X3 ) )
          & ( X0 != X1 ) )
        | ~ sP2(X2,X0,X1,X3,X4) ) ),
    inference(flattening,[],[f312]) ).

tff(f312,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP2(X2,X0,X1,X3,X4)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
              & ( X0 != X3 ) )
            | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
              & ( X1 != X4 )
              & ( X0 = X3 ) ) )
          & ( X1 != X3 ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
          & ( X1 = X3 ) )
        | ( X0 = X1 ) )
      & ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
                | ( X0 = X3 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
                | ( X1 = X4 )
                | ( X0 != X3 ) ) )
            | ( X1 = X3 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
            | ( X1 != X3 ) )
          & ( X0 != X1 ) )
        | ~ sP2(X2,X0,X1,X3,X4) ) ),
    inference(nnf_transformation,[],[f248]) ).

tff(f248,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X2,X0,X1,X3,X4)
    <=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
              | ( X0 = X3 ) )
            & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
              | ( X1 = X4 )
              | ( X0 != X3 ) ) )
          | ( X1 = X3 ) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
          | ( X1 != X3 ) )
        & ( X0 != X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

tff(f2481,plain,
    ( spl83_8
    | spl83_27 ),
    inference(avatar_split_clause,[],[f640,f2479,f815]) ).

tff(f2479,plain,
    ( spl83_27
  <=> ! [X14: arrow_411405190le_alt,X15: arrow_411405190le_alt] :
        ( sP0(f(p),b,a,X14,X15)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X15),f(p))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X15),b),f(p)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_27])]) ).

tff(f640,plain,
    ! [X14: arrow_411405190le_alt,X15: arrow_411405190le_alt] :
      ( sP0(f(p),b,a,X14,X15)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X15),b),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X15),f(p))
      | ( a = b ) ),
    inference(resolution,[],[f351,f455]) ).

tff(f455,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f309,plain,
    ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( ( sP0(X0,X1,X2,X3,X4)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
              & ( X2 != X3 ) )
            | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
              & ( X1 != X4 )
              & ( X2 = X3 ) ) )
          & ( X1 != X3 ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
          & ( X1 = X3 ) )
        | ( X1 = X2 ) )
      & ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
                | ( X2 = X3 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
                | ( X1 = X4 )
                | ( X2 != X3 ) ) )
            | ( X1 = X3 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
            | ( X1 != X3 ) )
          & ( X1 != X2 ) )
        | ~ sP0(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f308]) ).

tff(f308,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( sP0(X2,X0,X1,X4,X3)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
              & ( X1 != X4 ) )
            | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
              & ( X0 != X3 )
              & ( X1 = X4 ) ) )
          & ( X0 != X4 ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
          & ( X0 = X4 ) )
        | ( X0 = X1 ) )
      & ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
                | ( X1 = X4 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
                | ( X0 = X3 )
                | ( X1 != X4 ) ) )
            | ( X0 = X4 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
            | ( X0 != X4 ) )
          & ( X0 != X1 ) )
        | ~ sP0(X2,X0,X1,X4,X3) ) ),
    inference(flattening,[],[f307]) ).

tff(f307,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( sP0(X2,X0,X1,X4,X3)
        | ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
              & ( X1 != X4 ) )
            | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
              & ( X0 != X3 )
              & ( X1 = X4 ) ) )
          & ( X0 != X4 ) )
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
          & ( X0 = X4 ) )
        | ( X0 = X1 ) )
      & ( ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
                | ( X1 = X4 ) )
              & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
                | ( X0 = X3 )
                | ( X1 != X4 ) ) )
            | ( X0 = X4 ) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
            | ( X0 != X4 ) )
          & ( X0 != X1 ) )
        | ~ sP0(X2,X0,X1,X4,X3) ) ),
    inference(nnf_transformation,[],[f245]) ).

tff(f245,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( sP0(X2,X0,X1,X4,X3)
    <=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
              | ( X1 = X4 ) )
            & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
              | ( X0 = X3 )
              | ( X1 != X4 ) ) )
          | ( X0 = X4 ) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
          | ( X0 != X4 ) )
        & ( X0 != X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f2173,plain,
    ( spl83_26
    | spl83_8 ),
    inference(avatar_split_clause,[],[f612,f815,f2171]) ).

tff(f2171,plain,
    ( spl83_26
  <=> ! [X14: $tType,X17: fun(product_prod(X14,X14),bool),X16: X14,X15: X14] : ~ member(product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),fun(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14))),product_Pair(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),a),X15)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),b),X16)),lex_prod(arrow_411405190le_alt,X14,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X17)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_26])]) ).

tff(f612,plain,
    ! [X14: $tType,X16: X14,X17: fun(product_prod(X14,X14),bool),X15: X14] :
      ( ( a = b )
      | ~ member(product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),fun(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14))),product_Pair(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),a),X15)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),b),X16)),lex_prod(arrow_411405190le_alt,X14,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X17)) ),
    inference(resolution,[],[f350,f526]) ).

tff(f526,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
      ( ( X5 = X7 )
      | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
      | ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f347,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
      ( ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
        | ( ( ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
            | ( X5 != X7 ) )
          & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) )
      & ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
          & ( X5 = X7 ) )
        | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
        | ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
    inference(flattening,[],[f346]) ).

tff(f346,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
      ( ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
        | ( ( ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
            | ( X5 != X7 ) )
          & ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) )
      & ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
          & ( X5 = X7 ) )
        | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
        | ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
    inference(nnf_transformation,[],[f179]) ).

tff(f179,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
      ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
    <=> ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
          & ( X5 = X7 ) )
        | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X0: $tType,X1: $tType,X47: fun(product_prod(X1,X1),bool),X5: fun(product_prod(X0,X0),bool),X12: X1,X13: X0,X14: X1,X15: X0] :
      ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X15),X14)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X13),X12)),lex_prod(X0,X1,X5,X47))
    <=> ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X14),X12),X47)
          & ( X13 = X15 ) )
        | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X15),X13),X5) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_56_in__lex__prod) ).

tff(f350,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
    inference(cnf_transformation,[],[f95]) ).

tff(f95,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
    inference(flattening,[],[f94]) ).

tff(f94,negated_conjecture,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
    inference(negated_conjecture,[],[f93]) ).

tff(f93,conjecture,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_4) ).

tff(f2116,plain,
    ( spl83_8
    | spl83_25 ),
    inference(avatar_split_clause,[],[f646,f2114,f815]) ).

tff(f2114,plain,
    ( spl83_25
  <=> ! [X27: arrow_411405190le_alt,X26: arrow_411405190le_alt] :
        ( sP2(f(p),b,a,X26,X27)
        | ( a = X26 )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X27),f(p)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_25])]) ).

tff(f646,plain,
    ! [X26: arrow_411405190le_alt,X27: arrow_411405190le_alt] :
      ( sP2(f(p),b,a,X26,X27)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X27),f(p))
      | ( a = X26 )
      | ( a = b ) ),
    inference(resolution,[],[f351,f475]) ).

tff(f475,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f2055,plain,
    ( spl83_8
    | spl83_24 ),
    inference(avatar_split_clause,[],[f644,f2053,f815]) ).

tff(f2053,plain,
    ( spl83_24
  <=> ! [X22: arrow_411405190le_alt,X23: arrow_411405190le_alt] :
        ( sP2(f(p),b,a,X22,X23)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X23),b),f(p))
        | ( b = X22 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_24])]) ).

tff(f644,plain,
    ! [X22: arrow_411405190le_alt,X23: arrow_411405190le_alt] :
      ( sP2(f(p),b,a,X22,X23)
      | ( b = X22 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X23),b),f(p))
      | ( a = b ) ),
    inference(resolution,[],[f351,f472]) ).

tff(f472,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X1 = X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f1998,plain,
    ( spl83_8
    | spl83_23 ),
    inference(avatar_split_clause,[],[f638,f1996,f815]) ).

tff(f1996,plain,
    ( spl83_23
  <=> ! [X11: arrow_411405190le_alt,X10: arrow_411405190le_alt] :
        ( sP0(f(p),b,a,X10,X11)
        | ( b = X10 )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X11),b),f(p)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_23])]) ).

tff(f638,plain,
    ! [X10: arrow_411405190le_alt,X11: arrow_411405190le_alt] :
      ( sP0(f(p),b,a,X10,X11)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X11),b),f(p))
      | ( b = X10 )
      | ( a = b ) ),
    inference(resolution,[],[f351,f454]) ).

tff(f454,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f1941,plain,
    ( spl83_8
    | spl83_22 ),
    inference(avatar_split_clause,[],[f636,f1939,f815]) ).

tff(f1939,plain,
    ( spl83_22
  <=> ! [X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
        ( sP0(f(p),b,a,X6,X7)
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X7),f(p))
        | ( a = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_22])]) ).

tff(f636,plain,
    ! [X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
      ( sP0(f(p),b,a,X6,X7)
      | ( a = X6 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X7),f(p))
      | ( a = b ) ),
    inference(resolution,[],[f351,f451]) ).

tff(f451,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X2 = X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f1844,plain,
    ( ~ spl83_20
    | ~ spl83_21 ),
    inference(avatar_split_clause,[],[f629,f1841,f1837]) ).

tff(f1837,plain,
    ( spl83_20
  <=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f(p),arrow_1985332922le_Lin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_20])]) ).

tff(f629,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
    | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f(p),arrow_1985332922le_Lin) ),
    inference(resolution,[],[f351,f390]) ).

tff(f390,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(flattening,[],[f199]) ).

tff(f199,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f117]) ).

tff(f117,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
     => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
       => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) ) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X14: arrow_411405190le_alt,X15: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X22,arrow_1985332922le_Lin)
     => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X15),X14),X22)
       => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X14),X15),X22) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_24_Lin__irrefl) ).

tff(f1756,plain,
    ( spl83_8
    | spl83_19 ),
    inference(avatar_split_clause,[],[f634,f1754,f815]) ).

tff(f1754,plain,
    ( spl83_19
  <=> ! [X3: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_276188178_mkbot(f(p),X3))
        | ( b = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_19])]) ).

tff(f634,plain,
    ! [X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_276188178_mkbot(f(p),X3))
      | ( a = b )
      | ( b = X3 ) ),
    inference(resolution,[],[f351,f433]) ).

tff(f433,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
      | ( X2 = X3 )
      | ( X0 = X2 ) ),
    inference(cnf_transformation,[],[f302]) ).

tff(f302,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
          & ( X0 != X3 ) )
        | ( ( X2 = X3 )
          & ( X0 = X3 ) )
        | ( X0 = X2 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
            | ( X0 = X3 ) )
          & ( ( X2 != X3 )
            | ( X0 != X3 ) )
          & ( X0 != X2 ) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0)) ) ),
    inference(flattening,[],[f301]) ).

tff(f301,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
          & ( X0 != X3 ) )
        | ( ( X2 = X3 )
          & ( X0 = X3 ) )
        | ( X0 = X2 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
            | ( X0 = X3 ) )
          & ( ( X2 != X3 )
            | ( X0 != X3 ) )
          & ( X0 != X2 ) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0)) ) ),
    inference(nnf_transformation,[],[f212]) ).

tff(f212,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
          | ( X0 = X3 ) )
        & ( ( X2 != X3 )
          | ( X0 != X3 ) )
        & ( X0 != X2 ) ) ),
    inference(ennf_transformation,[],[f135]) ).

tff(f135,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
    <=> ( ( ( X0 != X3 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1) )
        & ( ( X0 = X3 )
         => ( X2 != X3 ) )
        & ( X0 != X2 ) ) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X21: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X23: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X23),arrow_276188178_mkbot(X22,X21))
    <=> ( ( ( X7 != X21 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X23),X22) )
        & ( ( X7 = X21 )
         => ( X7 != X23 ) )
        & ( X21 != X23 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_11_in__mkbot) ).

tff(f1605,plain,
    ( spl83_8
    | spl83_18 ),
    inference(avatar_split_clause,[],[f632,f1603,f815]) ).

tff(f1603,plain,
    ( spl83_18
  <=> ! [X1: arrow_411405190le_alt] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_424895264_mktop(f(p),X1))
        | ( a = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_18])]) ).

tff(f632,plain,
    ! [X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_424895264_mktop(f(p),X1))
      | ( a = b )
      | ( a = X1 ) ),
    inference(resolution,[],[f351,f426]) ).

tff(f426,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
      | ( X2 = X3 )
      | ( X0 = X3 ) ),
    inference(cnf_transformation,[],[f300]) ).

tff(f300,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
          & ( X0 != X2 ) )
        | ( ( X2 = X3 )
          & ( X0 = X2 ) )
        | ( X0 = X3 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
            | ( X0 = X2 ) )
          & ( ( X2 != X3 )
            | ( X0 != X2 ) )
          & ( X0 != X3 ) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0)) ) ),
    inference(flattening,[],[f299]) ).

tff(f299,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
        | ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
          & ( X0 != X2 ) )
        | ( ( X2 = X3 )
          & ( X0 = X2 ) )
        | ( X0 = X3 ) )
      & ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
            | ( X0 = X2 ) )
          & ( ( X2 != X3 )
            | ( X0 != X2 ) )
          & ( X0 != X3 ) )
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0)) ) ),
    inference(nnf_transformation,[],[f211]) ).

tff(f211,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
    <=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
          | ( X0 = X2 ) )
        & ( ( X2 != X3 )
          | ( X0 != X2 ) )
        & ( X0 != X3 ) ) ),
    inference(ennf_transformation,[],[f134]) ).

tff(f134,plain,
    ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
    <=> ( ( ( X0 != X2 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1) )
        & ( ( X0 = X2 )
         => ( X2 != X3 ) )
        & ( X0 != X3 ) ) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X21: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X23: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X23),arrow_424895264_mktop(X22,X21))
    <=> ( ( ( X21 != X23 )
         => member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X23),X22) )
        & ( ( X21 = X23 )
         => ( X7 != X23 ) )
        & ( X7 != X21 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_39_in__mktop) ).

tff(f1409,plain,
    ~ spl83_17,
    inference(avatar_contradiction_clause,[],[f1408]) ).

tff(f1408,plain,
    ( $false
    | ~ spl83_17 ),
    inference(subsumption_resolution,[],[f1407,f369]) ).

tff(f1407,plain,
    ( ~ member(arrow_411405190le_alt,b,top_top(fun(arrow_411405190le_alt,bool)))
    | ~ spl83_17 ),
    inference(subsumption_resolution,[],[f1400,f369]) ).

tff(f1400,plain,
    ( ~ member(arrow_411405190le_alt,a,top_top(fun(arrow_411405190le_alt,bool)))
    | ~ member(arrow_411405190le_alt,b,top_top(fun(arrow_411405190le_alt,bool)))
    | ~ spl83_17 ),
    inference(resolution,[],[f1398,f357]) ).

tff(f1398,plain,
    ( ! [X11: fun(arrow_411405190le_alt,bool)] :
        ( ~ total_on(arrow_411405190le_alt,X11,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
        | ~ member(arrow_411405190le_alt,a,X11)
        | ~ member(arrow_411405190le_alt,b,X11) )
    | ~ spl83_17 ),
    inference(avatar_component_clause,[],[f1397]) ).

tff(f1397,plain,
    ( spl83_17
  <=> ! [X11: fun(arrow_411405190le_alt,bool)] :
        ( ~ member(arrow_411405190le_alt,a,X11)
        | ~ total_on(arrow_411405190le_alt,X11,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
        | ~ member(arrow_411405190le_alt,b,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_17])]) ).

tff(f1399,plain,
    ( spl83_17
    | spl83_8
    | spl83_16 ),
    inference(avatar_split_clause,[],[f609,f1391,f815,f1397]) ).

tff(f609,plain,
    ! [X11: fun(arrow_411405190le_alt,bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
      | ( a = b )
      | ~ member(arrow_411405190le_alt,a,X11)
      | ~ member(arrow_411405190le_alt,b,X11)
      | ~ total_on(arrow_411405190le_alt,X11,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    inference(resolution,[],[f350,f391]) ).

tff(f391,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool),X6: X0,X5: X0] :
      ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
      | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
      | ( X5 = X6 )
      | ~ member(X0,X6,X2)
      | ~ member(X0,X5,X2)
      | ~ total_on(X0,X2,X1) ),
    inference(cnf_transformation,[],[f275]) ).

tff(f1394,plain,
    ( ~ spl83_15
    | spl83_8
    | spl83_16 ),
    inference(avatar_split_clause,[],[f598,f1391,f815,f1387]) ).

tff(f1387,plain,
    ( spl83_15
  <=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),arrow_1985332922le_Lin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_15])]) ).

tff(f598,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
    | ( a = b )
    | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),arrow_1985332922le_Lin) ),
    inference(resolution,[],[f350,f388]) ).

tff(f388,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f270,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2) ) )
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(nnf_transformation,[],[f198]) ).

tff(f198,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) )
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(flattening,[],[f197]) ).

tff(f197,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) )
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f116]) ).

tff(f116,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
     => ( ( X0 != X1 )
       => ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
        <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) ) ) ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X23: arrow_411405190le_alt,X7: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X22,arrow_1985332922le_Lin)
     => ( ( X7 != X23 )
       => ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X23),X22)
        <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X23),X7),X22) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_23_notin__Lin__iff) ).

tff(f1345,plain,
    ( ~ spl83_5
    | spl83_14
    | ~ spl83_4 ),
    inference(avatar_split_clause,[],[f708,f694,f1343,f711]) ).

tff(f1343,plain,
    ( spl83_14
  <=> ! [X9: fun(arrow_411405190le_alt,bool)] :
        ( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X9),f(p)))
        | ~ total_on(arrow_411405190le_alt,X9,f(p)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_14])]) ).

tff(f708,plain,
    ( ! [X9: fun(arrow_411405190le_alt,bool)] :
        ( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X9),f(p)))
        | ~ total_on(arrow_411405190le_alt,X9,f(p))
        | ~ irrefl(arrow_411405190le_alt,f(p)) )
    | ~ spl83_4 ),
    inference(resolution,[],[f696,f402]) ).

tff(f402,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
      ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
      | ~ total_on(X0,X2,X1)
      | ~ irrefl(X0,X1)
      | ~ trans(X0,X1) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f278,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
        | ~ total_on(X0,X2,X1)
        | ~ irrefl(X0,X1)
        | ~ trans(X0,X1) )
      & ( ( total_on(X0,X2,X1)
          & irrefl(X0,X1)
          & trans(X0,X1) )
        | ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
    inference(flattening,[],[f277]) ).

tff(f277,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
        | ~ total_on(X0,X2,X1)
        | ~ irrefl(X0,X1)
        | ~ trans(X0,X1) )
      & ( ( total_on(X0,X2,X1)
          & irrefl(X0,X1)
          & trans(X0,X1) )
        | ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
    inference(nnf_transformation,[],[f120]) ).

tff(f120,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
      ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
    <=> ( total_on(X0,X2,X1)
        & irrefl(X0,X1)
        & trans(X0,X1) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X0: $tType,X5: fun(product_prod(X0,X0),bool),X16: fun(X0,bool)] :
      ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X16),X5))
    <=> ( total_on(X0,X16,X5)
        & irrefl(X0,X5)
        & trans(X0,X5) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_9_strict__linear__order__on__def) ).

tff(f1192,plain,
    ( spl83_8
    | spl83_13 ),
    inference(avatar_split_clause,[],[f643,f1190,f815]) ).

tff(f1190,plain,
    ( spl83_13
  <=> ! [X20: arrow_411405190le_alt,X21: arrow_411405190le_alt] :
        ( sP2(f(p),b,a,X20,X21)
        | ( a = X20 )
        | ( b = X20 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_13])]) ).

tff(f643,plain,
    ! [X21: arrow_411405190le_alt,X20: arrow_411405190le_alt] :
      ( sP2(f(p),b,a,X20,X21)
      | ( b = X20 )
      | ( a = X20 )
      | ( a = b ) ),
    inference(resolution,[],[f351,f471]) ).

tff(f471,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X1 = X3 )
      | ( X2 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f1182,plain,
    ( spl83_8
    | spl83_12 ),
    inference(avatar_split_clause,[],[f635,f1180,f815]) ).

tff(f1180,plain,
    ( spl83_12
  <=> ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
        ( sP0(f(p),b,a,X4,X5)
        | ( b = X4 )
        | ( a = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_12])]) ).

tff(f635,plain,
    ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( sP0(f(p),b,a,X4,X5)
      | ( a = X4 )
      | ( b = X4 )
      | ( a = b ) ),
    inference(resolution,[],[f351,f450]) ).

tff(f450,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X2 = X3 )
      | ( X1 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f1118,plain,
    ( spl83_11
    | spl83_8 ),
    inference(avatar_split_clause,[],[f903,f815,f1116]) ).

tff(f1116,plain,
    ( spl83_11
  <=> ! [X40: arrow_411405190le_alt] : sP2(f(p),b,a,X40,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_11])]) ).

tff(f903,plain,
    ! [X40: arrow_411405190le_alt] :
      ( ( a = b )
      | sP2(f(p),b,a,X40,a) ),
    inference(global_subsumption,[],[f354,f353,f352,f357,f356,f355,f358,f589,f590,f591,f592,f595,f597,f604,f624,f626,f622,f627,f641,f642,f649,f650,f652,f657,f661,f663,f667,f668,f736,f737,f732,f738,f734,f794,f773,f755,f743,f678,f676,f675,f665,f664,f662,f660,f655,f647,f645,f639,f637,f633,f631,f629,f619,f618,f616,f614,f607,f605,f603,f602,f601,f600,f351,f350,f598,f606,f609,f612,f632,f634,f635,f636,f638,f640,f643,f644,f646,f648,f651,f902,f656]) ).

tff(f656,plain,
    ! [X40: arrow_411405190le_alt] :
      ( sP2(f(p),b,a,X40,a)
      | ( a = X40 )
      | ( a = b ) ),
    inference(resolution,[],[f351,f557]) ).

tff(f557,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X4,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X3 = X4 )
      | ( X1 = X4 ) ),
    inference(equality_resolution,[],[f473]) ).

tff(f473,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X2 != X4 )
      | ( X2 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f902,plain,
    ! [X36: arrow_411405190le_alt] :
      ( sP0(f(p),b,a,X36,b)
      | ( a = b ) ),
    inference(global_subsumption,[],[f354,f353,f352,f357,f356,f355,f358,f589,f590,f591,f592,f595,f597,f604,f624,f626,f622,f627,f641,f642,f649,f650,f652,f656,f657,f661,f663,f667,f668,f736,f737,f732,f738,f734,f794,f773,f755,f743,f678,f676,f675,f665,f664,f662,f660,f655,f647,f645,f639,f637,f633,f631,f629,f619,f618,f616,f614,f607,f605,f603,f602,f601,f600,f351,f350,f598,f606,f609,f612,f632,f634,f635,f636,f638,f640,f643,f644,f646,f648,f651]) ).

tff(f651,plain,
    ! [X36: arrow_411405190le_alt] :
      ( sP0(f(p),b,a,X36,b)
      | ( b = X36 )
      | ( a = b ) ),
    inference(resolution,[],[f351,f542]) ).

tff(f542,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP0(X0,X4,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X3 = X4 )
      | ( X2 = X4 ) ),
    inference(equality_resolution,[],[f452]) ).

tff(f452,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X1 != X4 )
      | ( X1 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f606,plain,
    ! [X8: arrow_411405190le_alt] :
      ( ( a = b )
      | ( a = X8 )
      | ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X8,a,X8,b) ),
    inference(resolution,[],[f350,f568]) ).

tff(f568,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X4 )
      | ( X2 = X3 )
      | ~ sP2(X0,X3,X2,X3,X4) ),
    inference(equality_resolution,[],[f461]) ).

tff(f461,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X4 )
      | ( X1 != X3 )
      | ( X2 = X3 )
      | ~ sP2(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f600,plain,
    ! [X0: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_424895264_mktop(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X0))
      | ( b = X0 ) ),
    inference(resolution,[],[f350,f422]) ).

tff(f422,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
      | ( X0 = X2 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0)) ),
    inference(cnf_transformation,[],[f300]) ).

tff(f601,plain,
    ! [X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_276188178_mkbot(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X1))
      | ( a = X1 ) ),
    inference(resolution,[],[f350,f429]) ).

tff(f429,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
      | ( X0 = X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0)) ),
    inference(cnf_transformation,[],[f302]) ).

tff(f602,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,a,X2,X3)
      | ( b = X2 )
      | ( a = X2 ) ),
    inference(resolution,[],[f350,f441]) ).

tff(f441,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X2 = X3 )
      | ( X1 = X3 )
      | ~ sP0(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f603,plain,
    ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
      ( ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,a,X4,X5)
      | ( a = X4 )
      | ( b = X4 ) ),
    inference(resolution,[],[f350,f462]) ).

tff(f462,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X1 = X3 )
      | ( X2 = X3 )
      | ~ sP2(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f605,plain,
    ! [X7: arrow_411405190le_alt] : ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X7,a,X7,b),
    inference(resolution,[],[f350,f554]) ).

tff(f554,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ~ sP0(X0,X3,X2,X3,X4) ),
    inference(equality_resolution,[],[f439]) ).

tff(f439,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X1 != X3 )
      | ~ sP0(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f607,plain,
    ! [X9: arrow_411405190le_alt] : ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,X9,X9,a),
    inference(resolution,[],[f350,f569]) ).

tff(f569,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ~ sP2(X0,X1,X3,X3,X4) ),
    inference(equality_resolution,[],[f460]) ).

tff(f460,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X2 != X3 )
      | ~ sP2(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f614,plain,
    ! [X22: $tType,X24: X22,X25: fun(product_prod(X22,X22),bool),X23: X22] :
      ( member(product_prod(X22,X22),aa(X22,product_prod(X22,X22),aa(X22,fun(X22,product_prod(X22,X22)),product_Pair(X22,X22),X23),X24),X25)
      | ~ member(product_prod(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22)),aa(product_prod(arrow_411405190le_alt,X22),product_prod(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22)),aa(product_prod(arrow_411405190le_alt,X22),fun(product_prod(arrow_411405190le_alt,X22),product_prod(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22))),product_Pair(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22)),aa(X22,product_prod(arrow_411405190le_alt,X22),aa(arrow_411405190le_alt,fun(X22,product_prod(arrow_411405190le_alt,X22)),product_Pair(arrow_411405190le_alt,X22),a),X23)),aa(X22,product_prod(arrow_411405190le_alt,X22),aa(arrow_411405190le_alt,fun(X22,product_prod(arrow_411405190le_alt,X22)),product_Pair(arrow_411405190le_alt,X22),b),X24)),lex_prod(arrow_411405190le_alt,X22,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X25)) ),
    inference(resolution,[],[f350,f527]) ).

tff(f527,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
      ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
      | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
      | ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f616,plain,
    ! [X10: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X10),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X10),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    inference(subsumption_resolution,[],[f608,f355]) ).

tff(f608,plain,
    ! [X10: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X10),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X10),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    inference(resolution,[],[f350,f381]) ).

tff(f381,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X6: X0,X7: X0,X5: X0] :
      ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
      | ~ trans(X0,X1) ),
    inference(cnf_transformation,[],[f269]) ).

tff(f618,plain,
    ! [X18: $tType,X21: fun(product_prod(X18,X18),bool),X19: X18,X20: X18] :
      ( ~ member(product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X20),product_apfst(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt,aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X19),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b))),lex_prod(X18,arrow_411405190le_alt,X21,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)))
      | member(product_prod(X18,X18),aa(X18,product_prod(X18,X18),aa(X18,fun(X18,product_prod(X18,X18)),product_Pair(X18,X18),X19),X20),X21) ),
    inference(forward_demodulation,[],[f617,f490]) ).

tff(f490,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X5,X4)),X3) ),
    inference(cnf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X5,X4)),X3) ),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X2: $tType,X0: $tType,X1: $tType,X23: X1,X7: X2,X43: fun(X2,X0)] : ( product_apfst(X2,X0,X1,X43,aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X7),X23)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),aa(X2,X0,X43,X7)),X23) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_72_apfst__conv) ).

tff(f617,plain,
    ! [X18: $tType,X21: fun(product_prod(X18,X18),bool),X19: X18,X20: X18] :
      ( ~ member(product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X20),aa(arrow_411405190le_alt,product_prod(product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(X18,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X19),a)),b)),lex_prod(X18,arrow_411405190le_alt,X21,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)))
      | member(product_prod(X18,X18),aa(X18,product_prod(X18,X18),aa(X18,fun(X18,product_prod(X18,X18)),product_Pair(X18,X18),X19),X20),X21) ),
    inference(forward_demodulation,[],[f613,f489]) ).

tff(f489,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),aa(X2,X1,X5,X3)) ),
    inference(cnf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),aa(X2,X1,X5,X3)) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X0: $tType,X1: $tType,X2: $tType,X23: X2,X7: X0,X43: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X43,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X7),X23)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),aa(X2,X1,X43,X23)) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_51_apsnd__conv) ).

tff(f613,plain,
    ! [X18: $tType,X21: fun(product_prod(X18,X18),bool),X19: X18,X20: X18] :
      ( member(product_prod(X18,X18),aa(X18,product_prod(X18,X18),aa(X18,fun(X18,product_prod(X18,X18)),product_Pair(X18,X18),X19),X20),X21)
      | ~ member(product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),aa(product_prod(X18,arrow_411405190le_alt),product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),aa(product_prod(X18,arrow_411405190le_alt),fun(product_prod(X18,arrow_411405190le_alt),product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt))),product_Pair(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),aa(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X19),a)),aa(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X20),b)),lex_prod(X18,arrow_411405190le_alt,X21,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))) ),
    inference(resolution,[],[f350,f527]) ).

tff(f619,plain,
    ~ pp(aa(arrow_411405190le_alt,bool,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,bool),product_curry(arrow_411405190le_alt,arrow_411405190le_alt,bool,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),a),b)),
    inference(forward_demodulation,[],[f615,f488]) ).

tff(f488,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X1,X5: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) ),
    inference(cnf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X1,X5: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) ),
    inference(rectify,[],[f42]) ).

tff(f42,axiom,
    ! [X0: $tType,X1: $tType,X2: $tType,X14: X2,X15: X1,X43: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X43),X15),X14) = aa(product_prod(X1,X2),X0,X43,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X15),X14)) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_41_curry__conv) ).

tff(f615,plain,
    ~ pp(aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b))),
    inference(resolution,[],[f350,f398]) ).

tff(f398,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( member(X0,X2,X1)
      | ~ pp(aa(X0,bool,X1,X2)) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f276,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) )
      & ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f119]) ).

tff(f119,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( member(X0,X2,X1)
    <=> pp(aa(X0,bool,X1,X2)) ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X0: $tType,X16: fun(X0,bool),X7: X0] :
      ( member(X0,X7,X16)
    <=> pp(aa(X0,bool,X16,X7)) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_76_mem__def) ).

tff(f631,plain,
    ! [X0: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_424895264_mktop(f(p),X0))
      | ( b = X0 )
      | ( a = X0 ) ),
    inference(resolution,[],[f351,f425]) ).

tff(f425,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
      | ( X0 = X2 )
      | ( X0 = X3 ) ),
    inference(cnf_transformation,[],[f300]) ).

tff(f633,plain,
    ! [X2: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_276188178_mkbot(f(p),X2))
      | ( a = X2 )
      | ( b = X2 ) ),
    inference(resolution,[],[f351,f432]) ).

tff(f432,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
      | ( X0 = X3 )
      | ( X0 = X2 ) ),
    inference(cnf_transformation,[],[f302]) ).

tff(f637,plain,
    ! [X8: arrow_411405190le_alt,X9: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X8),f(p))
      | sP0(f(p),X8,a,X9,b)
      | ( a = X9 )
      | ( a = X8 ) ),
    inference(resolution,[],[f351,f451]) ).

tff(f639,plain,
    ! [X12: arrow_411405190le_alt,X13: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X12),b),f(p))
      | sP0(f(p),b,X12,X13,a)
      | ( b = X13 )
      | ( b = X12 ) ),
    inference(resolution,[],[f351,f454]) ).

tff(f645,plain,
    ! [X24: arrow_411405190le_alt,X25: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X24),b),f(p))
      | sP2(f(p),b,X24,X25,a)
      | ( b = X25 )
      | ( b = X24 ) ),
    inference(resolution,[],[f351,f472]) ).

tff(f647,plain,
    ! [X28: arrow_411405190le_alt,X29: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X28),f(p))
      | sP2(f(p),X28,a,X29,b)
      | ( a = X29 )
      | ( a = X28 ) ),
    inference(resolution,[],[f351,f475]) ).

tff(f655,plain,
    ! [X39: arrow_411405190le_alt] :
      ( sP0(f(p),X39,a,X39,b)
      | ( a = X39 ) ),
    inference(resolution,[],[f351,f551]) ).

tff(f551,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP0(X0,X3,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X3 ) ),
    inference(equality_resolution,[],[f443]) ).

tff(f443,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ( X1 != X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f660,plain,
    ! [X43: arrow_411405190le_alt] :
      ( sP2(f(p),b,X43,X43,a)
      | ( b = X43 ) ),
    inference(resolution,[],[f351,f566]) ).

tff(f566,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X3,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X3 ) ),
    inference(equality_resolution,[],[f464]) ).

tff(f464,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ( X2 != X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f662,plain,
    ! [X45: arrow_411405190le_alt] :
      ( sP0(f(p),b,X45,X45,a)
      | ( b = X45 ) ),
    inference(resolution,[],[f351,f582]) ).

tff(f582,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X3,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X3 ) ),
    inference(duplicate_literal_removal,[],[f544]) ).

tff(f544,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X3,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X3 )
      | ( X1 = X3 ) ),
    inference(equality_resolution,[],[f448]) ).

tff(f448,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ( X2 != X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f664,plain,
    ! [X47: arrow_411405190le_alt] :
      ( sP2(f(p),X47,a,X47,b)
      | ( a = X47 ) ),
    inference(resolution,[],[f351,f586]) ).

tff(f586,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP2(X0,X3,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X3 ) ),
    inference(duplicate_literal_removal,[],[f559]) ).

tff(f559,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP2(X0,X3,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X3 )
      | ( X2 = X3 ) ),
    inference(equality_resolution,[],[f469]) ).

tff(f469,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ( X1 != X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X3 )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f665,plain,
    ! [X48: $tType,X50: X48,X51: fun(product_prod(X48,X48),bool),X49: X48] : member(product_prod(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48)),aa(product_prod(arrow_411405190le_alt,X48),product_prod(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48)),aa(product_prod(arrow_411405190le_alt,X48),fun(product_prod(arrow_411405190le_alt,X48),product_prod(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48))),product_Pair(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48)),aa(X48,product_prod(arrow_411405190le_alt,X48),aa(arrow_411405190le_alt,fun(X48,product_prod(arrow_411405190le_alt,X48)),product_Pair(arrow_411405190le_alt,X48),a),X49)),aa(X48,product_prod(arrow_411405190le_alt,X48),aa(arrow_411405190le_alt,fun(X48,product_prod(arrow_411405190le_alt,X48)),product_Pair(arrow_411405190le_alt,X48),b),X50)),lex_prod(arrow_411405190le_alt,X48,f(p),X51)),
    inference(resolution,[],[f351,f528]) ).

tff(f528,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
      ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
      | ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f675,plain,
    ! [X52: $tType,X54: fun(product_prod(X52,X52),bool),X53: X52] : member(product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),product_apfst(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt,aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b))),lex_prod(X52,arrow_411405190le_alt,X54,f(p))),
    inference(forward_demodulation,[],[f674,f490]) ).

tff(f674,plain,
    ! [X52: $tType,X54: fun(product_prod(X52,X52),bool),X53: X52] : member(product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),aa(arrow_411405190le_alt,product_prod(product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(X52,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),a)),b)),lex_prod(X52,arrow_411405190le_alt,X54,f(p))),
    inference(forward_demodulation,[],[f666,f489]) ).

tff(f666,plain,
    ! [X52: $tType,X54: fun(product_prod(X52,X52),bool),X53: X52] : member(product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),aa(product_prod(X52,arrow_411405190le_alt),product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),aa(product_prod(X52,arrow_411405190le_alt),fun(product_prod(X52,arrow_411405190le_alt),product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt))),product_Pair(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),aa(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),a)),aa(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),b)),lex_prod(X52,arrow_411405190le_alt,X54,f(p))),
    inference(resolution,[],[f351,f578]) ).

tff(f578,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1] :
      ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X4)),lex_prod(X0,X1,X3,X2))
      | ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2) ),
    inference(equality_resolution,[],[f529]) ).

tff(f529,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
      ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
      | ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
      | ( X5 != X7 ) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f676,plain,
    pp(aa(arrow_411405190le_alt,bool,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,bool),product_curry(arrow_411405190le_alt,arrow_411405190le_alt,bool,f(p)),a),b)),
    inference(forward_demodulation,[],[f671,f488]) ).

tff(f671,plain,
    pp(aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool,f(p),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b))),
    inference(resolution,[],[f351,f397]) ).

tff(f397,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( pp(aa(X0,bool,X1,X2))
      | ~ member(X0,X2,X1) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f678,plain,
    ! [X59: product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X60: fun(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),bool)] :
      ( ~ total_on(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),f(p),X60)
      | member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),aa(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),X59),b)),X60)
      | ( aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b) = X59 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X59,f(p))
      | member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_apfst(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),b),X59)),X60) ),
    inference(forward_demodulation,[],[f677,f490]) ).

tff(f677,plain,
    ! [X59: product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X60: fun(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),bool)] :
      ( member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),aa(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),X59),b)),X60)
      | member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b)),X59),X60)
      | ( aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b) = X59 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X59,f(p))
      | ~ total_on(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),f(p),X60) ),
    inference(forward_demodulation,[],[f672,f489]) ).

tff(f672,plain,
    ! [X59: product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X60: fun(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),bool)] :
      ( member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),X59),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b)),X60)
      | member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b)),X59),X60)
      | ( aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b) = X59 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X59,f(p))
      | ~ total_on(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),f(p),X60) ),
    inference(resolution,[],[f351,f391]) ).

tff(f743,plain,
    ! [X4: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X4),arrow_319942042_below(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X4,b))
      | ~ sP1(b,X4,a,X4,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    inference(resolution,[],[f605,f436]) ).

tff(f436,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP0(X4,X3,X2,X1,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),arrow_319942042_below(X4,X1,X0))
      | ~ sP1(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f306]) ).

tff(f306,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),arrow_319942042_below(X4,X1,X0))
          | ~ sP0(X4,X3,X2,X1,X0) )
        & ( sP0(X4,X3,X2,X1,X0)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),arrow_319942042_below(X4,X1,X0)) ) )
      | ~ sP1(X0,X1,X2,X3,X4) ),
    inference(rectify,[],[f305]) ).

tff(f305,plain,
    ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_319942042_below(X2,X4,X3))
          | ~ sP0(X2,X0,X1,X4,X3) )
        & ( sP0(X2,X0,X1,X4,X3)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_319942042_below(X2,X4,X3)) ) )
      | ~ sP1(X3,X4,X1,X0,X2) ),
    inference(nnf_transformation,[],[f246]) ).

tff(f246,plain,
    ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_319942042_below(X2,X4,X3))
      <=> sP0(X2,X0,X1,X4,X3) )
      | ~ sP1(X3,X4,X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f755,plain,
    ! [X4: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),b),arrow_1158827142_above(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),a,X4))
      | ~ sP3(a,X4,X4,b,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    inference(resolution,[],[f607,f457]) ).

tff(f457,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( sP2(X4,X3,X2,X1,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),arrow_1158827142_above(X4,X0,X1))
      | ~ sP3(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f311]) ).

tff(f311,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),arrow_1158827142_above(X4,X0,X1))
          | ~ sP2(X4,X3,X2,X1,X0) )
        & ( sP2(X4,X3,X2,X1,X0)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),arrow_1158827142_above(X4,X0,X1)) ) )
      | ~ sP3(X0,X1,X2,X3,X4) ),
    inference(rectify,[],[f310]) ).

tff(f310,plain,
    ! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_1158827142_above(X2,X4,X3))
          | ~ sP2(X2,X0,X1,X3,X4) )
        & ( sP2(X2,X0,X1,X3,X4)
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_1158827142_above(X2,X4,X3)) ) )
      | ~ sP3(X4,X3,X1,X0,X2) ),
    inference(nnf_transformation,[],[f249]) ).

tff(f249,plain,
    ! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_1158827142_above(X2,X4,X3))
      <=> sP2(X2,X0,X1,X3,X4) )
      | ~ sP3(X4,X3,X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

tff(f773,plain,
    ! [X8: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
      ( ( b = X7 )
      | ( a = X7 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_319942042_below(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X7,X8))
      | ~ sP1(X8,X7,a,b,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    inference(resolution,[],[f602,f436]) ).

tff(f794,plain,
    ! [X8: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
      ( ( a = X7 )
      | ( b = X7 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),arrow_1158827142_above(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X8,X7))
      | ~ sP3(X8,X7,a,b,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
    inference(resolution,[],[f603,f457]) ).

tff(f738,plain,
    ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( ~ irrefl(arrow_411405190le_alt,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),X0)
      | ( X1 = X2 )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),X0)
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0)))
      | ~ trans(arrow_411405190le_alt,X0) ),
    inference(forward_demodulation,[],[f733,f409]) ).

tff(f409,plain,
    ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(cnf_transformation,[],[f125]) ).

tff(f125,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X1: $tType,X0: $tType,X55: X1,X56: X0] : ( aa(X1,X0,combk(X0,X1,X56),X55) = X56 ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',help_COMBK_1_1_U) ).

tff(f733,plain,
    ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
      ( ~ irrefl(arrow_411405190le_alt,X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0),i))
      | ( X1 = X2 )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),X0)
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0)))
      | ~ trans(arrow_411405190le_alt,X0) ),
    inference(superposition,[],[f358,f409]) ).

tff(f732,plain,
    ! [X8: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
      ( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))
      | ( X6 = X7 )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X7),f(X8))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X7),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,i))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK11(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))),sK11(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8))) ),
    inference(resolution,[],[f358,f380]) ).

tff(f380,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( irrefl(X0,X1)
      | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK11(X0,X1)),X1) ),
    inference(cnf_transformation,[],[f265]) ).

tff(f737,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: fun(arrow_411405190le_alt,bool)] :
      ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))
      | ( X2 = X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,i))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X4))
      | ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X5),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))) ),
    inference(subsumption_resolution,[],[f731,f399]) ).

tff(f399,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X1)
      | ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f731,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: fun(arrow_411405190le_alt,bool)] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,i))
      | ( X2 = X3 )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X4))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))
      | ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X5),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))) ),
    inference(resolution,[],[f358,f400]) ).

tff(f400,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
      ( irrefl(X0,X1)
      | ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f663,plain,
    ! [X46: arrow_411405190le_alt] :
      ( sP2(f(p),b,a,X46,a)
      | ( a = b ) ),
    inference(resolution,[],[f351,f585]) ).

tff(f585,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X4,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X4 ) ),
    inference(duplicate_literal_removal,[],[f556]) ).

tff(f556,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X4,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X4 ) ),
    inference(equality_resolution,[],[f474]) ).

tff(f474,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X2 != X4 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f661,plain,
    ! [X44: arrow_411405190le_alt] :
      ( sP0(f(p),b,a,X44,b)
      | ( a = b ) ),
    inference(resolution,[],[f351,f581]) ).

tff(f581,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP0(X0,X4,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X4 ) ),
    inference(duplicate_literal_removal,[],[f541]) ).

tff(f541,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP0(X0,X4,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X2 = X4 ) ),
    inference(equality_resolution,[],[f453]) ).

tff(f453,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
      | ( X1 != X4 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f657,plain,
    ! [X41: arrow_411405190le_alt] :
      ( sP2(f(p),X41,a,X41,b)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),X41),f(p))
      | ( a = X41 ) ),
    inference(resolution,[],[f351,f558]) ).

tff(f558,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
      ( sP2(X0,X3,X2,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),X0)
      | ( X2 = X3 ) ),
    inference(equality_resolution,[],[f470]) ).

tff(f470,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP2(X0,X1,X2,X3,X4)
      | ( X1 != X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f652,plain,
    ! [X37: arrow_411405190le_alt] :
      ( sP0(f(p),b,X37,X37,a)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X37),a),f(p))
      | ( b = X37 ) ),
    inference(resolution,[],[f351,f543]) ).

tff(f543,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X3,X3,X4)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X4),X0)
      | ( X1 = X3 ) ),
    inference(equality_resolution,[],[f449]) ).

tff(f449,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( sP0(X0,X1,X2,X3,X4)
      | ( X2 != X3 )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X4),X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f650,plain,
    ! [X34: arrow_411405190le_alt,X35: arrow_411405190le_alt] :
      ( sP2(f(p),X34,a,X35,b)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X34),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),X34),f(p))
      | ( a = X34 ) ),
    inference(resolution,[],[f351,f476]) ).

tff(f649,plain,
    ! [X32: arrow_411405190le_alt,X33: arrow_411405190le_alt] :
      ( sP2(f(p),b,X32,X33,a)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X32),b),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X32),a),f(p))
      | ( b = X32 ) ),
    inference(resolution,[],[f351,f476]) ).

tff(f642,plain,
    ! [X18: arrow_411405190le_alt,X19: arrow_411405190le_alt] :
      ( sP0(f(p),X18,a,X19,b)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X18),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),X18),f(p))
      | ( a = X18 ) ),
    inference(resolution,[],[f351,f455]) ).

tff(f641,plain,
    ! [X16: arrow_411405190le_alt,X17: arrow_411405190le_alt] :
      ( sP0(f(p),b,X16,X17,a)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X16),b),f(p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X16),a),f(p))
      | ( b = X16 ) ),
    inference(resolution,[],[f351,f455]) ).

tff(f627,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
    | ( a = b )
    | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f(p),arrow_1985332922le_Lin) ),
    inference(resolution,[],[f351,f389]) ).

tff(f389,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | ( X0 = X1 )
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f622,plain,
    ! [X0: fun(arrow_411405190le_alt,bool),X1: arrow_159774573e_indi] :
      ( ~ member(arrow_411405190le_alt,sK7(arrow_411405190le_alt,X0),X0)
      | total_on(arrow_411405190le_alt,X0,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X1)) ),
    inference(superposition,[],[f357,f375]) ).

tff(f375,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( top_top(fun(X0,bool)) = X1 )
      | ~ member(X0,sK7(X0,X1),X1) ),
    inference(cnf_transformation,[],[f259]) ).

tff(f259,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( top_top(fun(X0,bool)) = X1 )
      | ~ member(X0,sK7(X0,X1),X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f188,f258]) ).

tff(f258,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ? [X2: X0] : ~ member(X0,X2,X1)
     => ~ member(X0,sK7(X0,X1),X1) ),
    introduced(choice_axiom,[]) ).

tff(f188,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( top_top(fun(X0,bool)) = X1 )
      | ? [X2: X0] : ~ member(X0,X2,X1) ),
    inference(ennf_transformation,[],[f109]) ).

tff(f109,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ! [X2: X0] : member(X0,X2,X1)
     => ( top_top(fun(X0,bool)) = X1 ) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X0: $tType,X16: fun(X0,bool)] :
      ( ! [X28: X0] : member(X0,X28,X16)
     => ( top_top(fun(X0,bool)) = X16 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_18_UNIV__eq__I) ).

tff(f626,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi,X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
      | ( X1 = X2 ) ),
    inference(subsumption_resolution,[],[f625,f369]) ).

tff(f625,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi,X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
      | ( X1 = X2 )
      | ~ member(arrow_411405190le_alt,X2,top_top(fun(arrow_411405190le_alt,bool))) ),
    inference(subsumption_resolution,[],[f621,f369]) ).

tff(f621,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi,X1: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
      | ( X1 = X2 )
      | ~ member(arrow_411405190le_alt,X1,top_top(fun(arrow_411405190le_alt,bool)))
      | ~ member(arrow_411405190le_alt,X2,top_top(fun(arrow_411405190le_alt,bool))) ),
    inference(resolution,[],[f357,f391]) ).

tff(f624,plain,
    ! [X0: arrow_159774573e_indi] : pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),
    inference(subsumption_resolution,[],[f623,f355]) ).

tff(f623,plain,
    ! [X0: arrow_159774573e_indi] :
      ( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
    inference(subsumption_resolution,[],[f620,f356]) ).

tff(f620,plain,
    ! [X0: arrow_159774573e_indi] :
      ( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)))
      | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
    inference(resolution,[],[f357,f402]) ).

tff(f604,plain,
    ! [X6: arrow_411405190le_alt] :
      ( ( a = b )
      | ( b = X6 )
      | ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,X6,X6,a) ),
    inference(resolution,[],[f350,f553]) ).

tff(f553,plain,
    ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X4 )
      | ( X1 = X3 )
      | ~ sP0(X0,X1,X3,X3,X4) ),
    inference(equality_resolution,[],[f440]) ).

tff(f440,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X1),X0)
      | ( X1 = X4 )
      | ( X2 != X3 )
      | ( X1 = X3 )
      | ~ sP0(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f597,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3)),
    inference(resolution,[],[f356,f379]) ).

tff(f595,plain,
    ! [X14: arrow_159774573e_indi,X13: fun(arrow_411405190le_alt,bool)] :
      ( ~ total_on(arrow_411405190le_alt,X13,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14))
      | pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X13),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14))) ),
    inference(subsumption_resolution,[],[f593,f356]) ).

tff(f593,plain,
    ! [X14: arrow_159774573e_indi,X13: fun(arrow_411405190le_alt,bool)] :
      ( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X13),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14)))
      | ~ total_on(arrow_411405190le_alt,X13,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14))
      | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14)) ),
    inference(resolution,[],[f355,f402]) ).

tff(f592,plain,
    ! [X10: $tType,X11: arrow_159774573e_indi,X12: fun(X10,arrow_411405190le_alt)] : trans(X10,inv_image(arrow_411405190le_alt,X10,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X11),X12)),
    inference(resolution,[],[f355,f413]) ).

tff(f413,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
      ( trans(X1,inv_image(X0,X1,X3,X2))
      | ~ trans(X0,X3) ),
    inference(cnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
      ( trans(X1,inv_image(X0,X1,X3,X2))
      | ~ trans(X0,X3) ),
    inference(ennf_transformation,[],[f129]) ).

tff(f129,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X3)
     => trans(X1,inv_image(X0,X1,X3,X2)) ),
    inference(rectify,[],[f48]) ).

tff(f48,axiom,
    ! [X0: $tType,X1: $tType,X43: fun(X1,X0),X5: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X5)
     => trans(X1,inv_image(X0,X1,X5,X43)) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_47_trans__inv__image) ).

tff(f591,plain,
    ! [X7: $tType,X8: fun(product_prod(X7,X7),bool),X9: arrow_159774573e_indi] :
      ( ~ trans(X7,X8)
      | trans(product_prod(X7,arrow_411405190le_alt),lex_prod(X7,arrow_411405190le_alt,X8,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X9))) ),
    inference(resolution,[],[f355,f414]) ).

tff(f414,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
      ( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
      | ~ trans(X1,X2)
      | ~ trans(X0,X3) ),
    inference(cnf_transformation,[],[f207]) ).

tff(f207,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
      ( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
      | ~ trans(X1,X2)
      | ~ trans(X0,X3) ),
    inference(flattening,[],[f206]) ).

tff(f206,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
      ( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
      | ~ trans(X1,X2)
      | ~ trans(X0,X3) ),
    inference(ennf_transformation,[],[f130]) ).

tff(f130,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X3)
     => ( trans(X1,X2)
       => trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2)) ) ),
    inference(rectify,[],[f50]) ).

tff(f50,axiom,
    ! [X0: $tType,X1: $tType,X44: fun(product_prod(X1,X1),bool),X45: fun(product_prod(X0,X0),bool)] :
      ( trans(X0,X45)
     => ( trans(X1,X44)
       => trans(product_prod(X0,X1),lex_prod(X0,X1,X45,X44)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_49_trans__lex__prod) ).

tff(f590,plain,
    ! [X4: $tType,X6: fun(product_prod(X4,X4),bool),X5: arrow_159774573e_indi] :
      ( ~ trans(X4,X6)
      | trans(product_prod(arrow_411405190le_alt,X4),lex_prod(arrow_411405190le_alt,X4,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X5),X6)) ),
    inference(resolution,[],[f355,f414]) ).

tff(f589,plain,
    ! [X2: arrow_159774573e_indi,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X2))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X2))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X2)) ),
    inference(resolution,[],[f355,f478]) ).

tff(f352,plain,
    ( trans(arrow_411405190le_alt,f(p))
    | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f252,plain,
    ( ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
      & irrefl(arrow_411405190le_alt,f(p))
      & trans(arrow_411405190le_alt,f(p)) )
    | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f181,f251]) ).

tff(f251,plain,
    ( ? [X0: arrow_159774573e_indi] :
        ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) )
   => ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
      | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f181,plain,
    ( ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
      & irrefl(arrow_411405190le_alt,f(p))
      & trans(arrow_411405190le_alt,f(p)) )
    | ? [X0: arrow_159774573e_indi] :
        ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ) ),
    inference(ennf_transformation,[],[f96]) ).

tff(f96,plain,
    ( ! [X0: arrow_159774573e_indi] :
        ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
        & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) )
   => ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
      & irrefl(arrow_411405190le_alt,f(p))
      & trans(arrow_411405190le_alt,f(p)) ) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ( ! [X28: arrow_159774573e_indi] :
        ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X28))
        & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X28))
        & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X28)) )
   => ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
      & irrefl(arrow_411405190le_alt,f(p))
      & trans(arrow_411405190le_alt,f(p)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_3) ).

tff(f353,plain,
    ( irrefl(arrow_411405190le_alt,f(p))
    | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f354,plain,
    ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
    | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f1110,plain,
    ( spl83_8
    | spl83_10 ),
    inference(avatar_split_clause,[],[f902,f1108,f815]) ).

tff(f1108,plain,
    ( spl83_10
  <=> ! [X36: arrow_411405190le_alt] : sP0(f(p),b,a,X36,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_10])]) ).

tff(f1063,plain,
    ( spl83_9
    | spl83_8 ),
    inference(avatar_split_clause,[],[f606,f815,f1061]) ).

tff(f1061,plain,
    ( spl83_9
  <=> ! [X8: arrow_411405190le_alt] :
        ( ( a = X8 )
        | ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X8,a,X8,b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_9])]) ).

tff(f865,plain,
    ( ~ spl83_5
    | ~ spl83_8 ),
    inference(avatar_contradiction_clause,[],[f864]) ).

tff(f864,plain,
    ( $false
    | ~ spl83_5
    | ~ spl83_8 ),
    inference(subsumption_resolution,[],[f820,f716]) ).

tff(f820,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),a),f(p))
    | ~ spl83_8 ),
    inference(backward_demodulation,[],[f351,f817]) ).

tff(f817,plain,
    ( ( a = b )
    | ~ spl83_8 ),
    inference(avatar_component_clause,[],[f815]) ).

tff(f818,plain,
    ( spl83_7
    | spl83_8 ),
    inference(avatar_split_clause,[],[f604,f815,f812]) ).

tff(f812,plain,
    ( spl83_7
  <=> ! [X6: arrow_411405190le_alt] :
        ( ( b = X6 )
        | ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,X6,X6,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_7])]) ).

tff(f722,plain,
    ( ~ spl83_1
    | ~ spl83_2
    | ~ spl83_3
    | spl83_6 ),
    inference(avatar_split_clause,[],[f354,f719,f690,f686,f682]) ).

tff(f682,plain,
    ( spl83_1
  <=> trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_1])]) ).

tff(f686,plain,
    ( spl83_2
  <=> irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_2])]) ).

tff(f690,plain,
    ( spl83_3
  <=> total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_3])]) ).

tff(f719,plain,
    ( spl83_6
  <=> total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl83_6])]) ).

tff(f714,plain,
    ( ~ spl83_1
    | ~ spl83_2
    | ~ spl83_3
    | spl83_5 ),
    inference(avatar_split_clause,[],[f353,f711,f690,f686,f682]) ).

tff(f703,plain,
    spl83_3,
    inference(avatar_contradiction_clause,[],[f702]) ).

tff(f702,plain,
    ( $false
    | spl83_3 ),
    inference(subsumption_resolution,[],[f692,f357]) ).

tff(f692,plain,
    ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | spl83_3 ),
    inference(avatar_component_clause,[],[f690]) ).

tff(f701,plain,
    spl83_2,
    inference(avatar_contradiction_clause,[],[f700]) ).

tff(f700,plain,
    ( $false
    | spl83_2 ),
    inference(subsumption_resolution,[],[f688,f356]) ).

tff(f688,plain,
    ( ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | spl83_2 ),
    inference(avatar_component_clause,[],[f686]) ).

tff(f699,plain,
    spl83_1,
    inference(avatar_contradiction_clause,[],[f698]) ).

tff(f698,plain,
    ( $false
    | spl83_1 ),
    inference(subsumption_resolution,[],[f684,f355]) ).

tff(f684,plain,
    ( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
    | spl83_1 ),
    inference(avatar_component_clause,[],[f682]) ).

tff(f697,plain,
    ( ~ spl83_1
    | ~ spl83_2
    | ~ spl83_3
    | spl83_4 ),
    inference(avatar_split_clause,[],[f352,f694,f690,f686,f682]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : SCT193_5 : TPTP v8.1.2. Released v6.0.0.
% 0.15/0.17  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.38  % Computer : n022.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit   : 300
% 0.17/0.38  % WCLimit    : 300
% 0.17/0.38  % DateTime   : Thu Aug 24 16:02:41 EDT 2023
% 0.17/0.38  % CPUTime    : 
% 0.17/0.38  This is a TF1_THM_EQU_NAR problem
% 0.17/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205
% 0.17/0.38  % (32318)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.43  % (32321)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.24/0.45  % (32322)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.24/0.45  % (32323)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.24/0.45  % (32320)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.24/0.45  % (32324)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.24/0.46  % (32322)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.24/0.46  % (32319)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.24/0.47  % (32325)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.24/0.47  % (32319)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.24/0.65  % (32321)First to succeed.
% 0.24/0.66  % (32321)Refutation found. Thanks to Tanya!
% 0.24/0.66  % SZS status Theorem for Vampire---4
% 0.24/0.66  % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.66  % (32321)------------------------------
% 0.24/0.66  % (32321)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.66  % (32321)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.66  % (32321)Termination reason: Refutation
% 0.24/0.66  
% 0.24/0.66  % (32321)Memory used [KB]: 15479
% 0.24/0.66  % (32321)Time elapsed: 0.230 s
% 0.24/0.66  % (32321)------------------------------
% 0.24/0.66  % (32321)------------------------------
% 0.24/0.66  % (32318)Success in time 0.279 s
% 0.24/0.66  % Vampire---4.8 exiting
%------------------------------------------------------------------------------