Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SCT223_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 12:37:48 PM UTC 2026

% Result   : Theorem 7.39s 1.69s
% Output   : Refutation 7.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   93 (   8 unt;   0 typ;   2 def)
%            Number of atoms       :  188 (   4 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  178 (  83   ~;  82   |;   5   &)
%                                         (   7 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :   14 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   36 (  34 usr;   3 prp; 0-6 aty)
%            Number of functors    :  118 ( 118 usr;  19 con; 0-7 aty)
%            Number of variables   :   76 (   0 sgn  74   !;   2   ?;  76   :)

% 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,
    list: $tType > $tType ).

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

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

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

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

tff(func_def_2,type,
    arrow_1158827142_above: ( fun(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_319942042_below: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))) ).

tff(func_def_4,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_5,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_6,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).

tff(func_def_7,type,
    combc: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).

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

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

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

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

tff(func_def_12,type,
    insert: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_13,type,
    lexord: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > fun(product_prod(list(X0),list(X0)),bool) ) ).

tff(func_def_14,type,
    cons: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_15,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_16,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_17,type,
    partition: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > product_prod(list(X0),list(X0)) ) ).

tff(func_def_18,type,
    splice: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

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

tff(func_def_20,type,
    product_curry: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(product_prod(X0,X1),X2) * X0 * X1 ) > X2 ) ).

tff(func_def_21,type,
    produc1605651328_split: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).

tff(func_def_22,type,
    product_prod_rec: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).

tff(func_def_23,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_24,type,
    fFalse: bool ).

tff(func_def_25,type,
    fNot: fun(bool,bool) ).

tff(func_def_26,type,
    fTrue: bool ).

tff(func_def_27,type,
    fdisj: fun(bool,fun(bool,bool)) ).

tff(func_def_28,type,
    fequal: 
      !>[X0: $tType] : ( X0 > fun(X0,bool) ) ).

tff(func_def_29,type,
    f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_30,type,
    p1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_31,type,
    p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_32,type,
    a: arrow_411405190le_alt ).

tff(func_def_33,type,
    b: arrow_411405190le_alt ).

tff(func_def_34,type,
    c: arrow_411405190le_alt ).

tff(func_def_35,type,
    sK24: arrow_411405190le_alt ).

tff(func_def_36,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_37,type,
    sK26: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_38,type,
    sK27: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_39,type,
    sK28: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_40,type,
    sK29: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_41,type,
    sK30: ( arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_411405190le_alt ).

tff(func_def_42,type,
    sK31: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_43,type,
    sK32: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_44,type,
    sK33: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_45,type,
    sK34: ( arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_46,type,
    sK35: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_47,type,
    sK36: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ) > arrow_159774573e_indi ).

tff(func_def_48,type,
    sK37: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > arrow_411405190le_alt ).

tff(func_def_49,type,
    sK38: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > arrow_411405190le_alt ).

tff(func_def_50,type,
    sK39: ( arrow_159774573e_indi * fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ) > fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_51,type,
    sK40: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_52,type,
    sK41: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_53,type,
    sK42: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * fun(X1,X0) * fun(X1,bool) ) > X1 ) ).

tff(func_def_54,type,
    sK43: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_55,type,
    sK44: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_56,type,
    sK45: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X0,X1) * fun(X0,bool) ) > X0 ) ).

tff(func_def_57,type,
    sK46: arrow_411405190le_alt ).

tff(func_def_58,type,
    sK47: arrow_411405190le_alt ).

tff(func_def_59,type,
    sK48: arrow_411405190le_alt ).

tff(func_def_60,type,
    sK49: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_61,type,
    sK50: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * fun(X1,bool) ) > X1 ) ).

tff(func_def_62,type,
    sK51: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * fun(X1,X0) * fun(X1,bool) ) > X1 ) ).

tff(func_def_63,type,
    sK52: 
      !>[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_64,type,
    sK53: 
      !>[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_65,type,
    sK54: 
      !>[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_66,type,
    sK55: 
      !>[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_67,type,
    sK56: 
      !>[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_68,type,
    sK57: 
      !>[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_69,type,
    sK58: 
      !>[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_70,type,
    sK59: 
      !>[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_71,type,
    sK60: 
      !>[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_72,type,
    sK61: 
      !>[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_73,type,
    sK62: 
      !>[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_74,type,
    sK63: 
      !>[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_75,type,
    sK64: 
      !>[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_76,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) > X3 ) ).

tff(func_def_77,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) > X2 ) ).

tff(func_def_78,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) > X1 ) ).

tff(func_def_79,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) > X0 ) ).

tff(func_def_80,type,
    sK69: 
      !>[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_81,type,
    sK70: 
      !>[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_82,type,
    sK71: 
      !>[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_83,type,
    sK72: 
      !>[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_84,type,
    sK73: 
      !>[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_85,type,
    sK74: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

tff(func_def_86,type,
    sK75: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

tff(func_def_87,type,
    sK76: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

tff(func_def_88,type,
    sK77: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

tff(func_def_89,type,
    sK78: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_90,type,
    sK79: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).

tff(func_def_91,type,
    sK80: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).

tff(func_def_92,type,
    sK81: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).

tff(func_def_93,type,
    sK82: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).

tff(func_def_94,type,
    sK83: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).

tff(func_def_95,type,
    sK84: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).

tff(func_def_96,type,
    sK85: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).

tff(func_def_97,type,
    sK86: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

tff(func_def_98,type,
    sK87: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

tff(func_def_99,type,
    sK88: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

tff(func_def_100,type,
    sK89: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X1 ) ).

tff(func_def_101,type,
    sK90: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X0 ) ).

tff(func_def_102,type,
    sK91: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_103,type,
    sK92: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_104,type,
    sK93: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_105,type,
    sK94: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_106,type,
    sK95: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_107,type,
    sK96: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_108,type,
    sK97: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_109,type,
    sK98: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_110,type,
    sK99: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_111,type,
    sK100: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_112,type,
    sK101: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_113,type,
    sK102: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_114,type,
    sK103: arrow_159774573e_indi ).

tff(pred_def_1,type,
    arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_2,type,
    arrow_987702531ctator: ( fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).

tff(pred_def_3,type,
    arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

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

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

tff(pred_def_6,type,
    list_ex1: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $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 ) > $o ).

tff(pred_def_10,type,
    sP1: ( 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 ) > $o ).

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

tff(pred_def_13,type,
    sP4: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_14,type,
    sP5: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_15,type,
    sP6: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_16,type,
    sP7: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_17,type,
    sP8: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_18,type,
    sP9: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_19,type,
    sP10: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_20,type,
    sP11: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_21,type,
    sP12: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_22,type,
    sP13: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_23,type,
    sP14: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_24,type,
    sP15: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ) > $o ).

tff(pred_def_25,type,
    sP16: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).

tff(pred_def_26,type,
    sP17: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * fun(X1,bool) ) > $o ) ).

tff(pred_def_27,type,
    sP18: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > $o ) ).

tff(pred_def_28,type,
    sP19: 
      !>[X0: $tType] : ( fun(list(X0),bool) > $o ) ).

tff(pred_def_29,type,
    sP20: 
      !>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > $o ) ).

tff(pred_def_30,type,
    sP21: 
      !>[X0: $tType] : ( ( list(X0) * X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_31,type,
    sP22: 
      !>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * X0 * X0 * list(X0) * list(X0) ) > $o ) ).

tff(pred_def_32,type,
    sP23: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).

tff(f5,axiom,
    ! [X0: arrow_159774573e_indi] :
      ( member(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,X0))
    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) ).

tff(f6,axiom,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b))
    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) ).

tff(f7,axiom,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a))
    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096) ).

tff(f105,axiom,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

tff(f106,axiom,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

tff(f115,conjecture,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c))
    <=> member(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,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f116,negated_conjecture,
    ~ ! [X0: arrow_159774573e_indi] :
        ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c))
      <=> member(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,X0)) ),
    inference(negated_conjecture,[status(cth)],[f115]) ).

tff(f183,plain,
    ? [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c))
    <~> member(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,X0)) ),
    inference(ennf_transformation,[],[f116]) ).

tff(f222,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( member(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,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) )
      & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b))
        | ~ member(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,X0)) ) ),
    inference(nnf_transformation,[],[f5]) ).

tff(f223,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) )
      & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ) ),
    inference(nnf_transformation,[],[f6]) ).

tff(f224,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) )
      & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ) ),
    inference(nnf_transformation,[],[f7]) ).

tff(f354,plain,
    ? [X0: arrow_159774573e_indi] :
      ( ( ~ member(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,X0))
        | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) )
      & ( member(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,X0))
        | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) ) ),
    inference(nnf_transformation,[],[f183]) ).

tff(f355,plain,
    ( ( ~ member(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,sK103))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),a),c)) )
    & ( member(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,sK103))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),a),c)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(X0,sK103)],[f354]) ).

tff(f361,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b))
      | ~ member(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,X0)) ),
    inference(cnf_transformation,[],[f222]) ).

tff(f362,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(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,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ),
    inference(cnf_transformation,[],[f222]) ).

tff(f363,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ),
    inference(cnf_transformation,[],[f223]) ).

tff(f364,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(cnf_transformation,[],[f223]) ).

tff(f365,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(cnf_transformation,[],[f224]) ).

tff(f366,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) ),
    inference(cnf_transformation,[],[f224]) ).

tff(f579,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    inference(cnf_transformation,[],[f105]) ).

tff(f580,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(cnf_transformation,[],[f106]) ).

tff(f589,plain,
    ( member(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,sK103))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),a),c)) ),
    inference(cnf_transformation,[],[f355]) ).

tff(f590,plain,
    ( ~ member(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,sK103))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),a),c)) ),
    inference(cnf_transformation,[],[f355]) ).

tff(f626,definition,
    ( spl104_1
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),a),c)) ),
    introduced(definition,[new_symbols(definition,[spl104_1])],[avatar_definition]) ).

tff(f627,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),a),c))
    | spl104_1 ),
    inference(avatar_component_clause,[],[f626]) ).

tff(f628,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),a),c))
    | ~ spl104_1 ),
    inference(avatar_component_clause,[],[f626]) ).

tff(f630,definition,
    ( spl104_2
  <=> member(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,sK103)) ),
    introduced(definition,[new_symbols(definition,[spl104_2])],[avatar_definition]) ).

tff(f633,plain,
    ( spl104_1
    | spl104_2 ),
    inference(avatar_split_clause,[],[f589,f630,f626]) ).

tff(f634,plain,
    ( ~ spl104_1
    | ~ spl104_2 ),
    inference(avatar_split_clause,[],[f590,f630,f626]) ).

tff(f661,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),c),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f365,f580]) ).

tff(f662,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) ),
    inference(forward_demodulation,[],[f366,f580]) ).

tff(f663,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ),
    inference(forward_demodulation,[],[f363,f580]) ).

tff(f664,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),b),c))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f364,f580]) ).

tff(f665,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),b),c))
      | ~ member(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,X0)) ),
    inference(forward_demodulation,[],[f361,f580]) ).

tff(f666,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),b),c))
      | member(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,X0)) ),
    inference(forward_demodulation,[],[f362,f580]) ).

tff(f667,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b)),a),c),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f661,f579]) ).

tff(f668,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c)),b),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) ),
    inference(forward_demodulation,[],[f662,f579]) ).

tff(f669,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c)),b),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ),
    inference(forward_demodulation,[],[f663,f579]) ).

tff(f670,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f664,f579]) ).

tff(f671,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c))
      | ~ member(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,X0)) ),
    inference(forward_demodulation,[],[f665,f579]) ).

tff(f672,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c))
      | member(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,X0)) ),
    inference(forward_demodulation,[],[f666,f579]) ).

tff(f673,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b))),a),c),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f667,f580]) ).

tff(f674,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),b),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) ),
    inference(forward_demodulation,[],[f668,f580]) ).

tff(f675,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),b),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ),
    inference(forward_demodulation,[],[f669,f580]) ).

tff(f676,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),a),b))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c)) ),
    inference(forward_demodulation,[],[f670,f580]) ).

tff(f677,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c)),b)),a),c),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f673,f579]) ).

tff(f678,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),a),c)) ),
    inference(forward_demodulation,[],[f674,f579]) ).

tff(f679,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)) ),
    inference(forward_demodulation,[],[f675,f579]) ).

tff(f680,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c)),b),a),b))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c)) ),
    inference(forward_demodulation,[],[f676,f579]) ).

tff(f681,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),b)),a),c),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f677,f580]) ).

tff(f682,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)),c),a))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f678,f580]) ).

tff(f683,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),b),c))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f679,f580]) ).

tff(f684,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),b),a),b))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c)) ),
    inference(forward_demodulation,[],[f680,f580]) ).

tff(f685,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b)),a),c),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b),a)) ),
    inference(forward_demodulation,[],[f681,f579]) ).

tff(f686,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),b)),a),c),a))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f682,f579]) ).

tff(f687,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c)) ),
    inference(forward_demodulation,[],[f683,f579]) ).

tff(f688,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),X0),b),c)) ),
    inference(forward_demodulation,[],[f684,f579]) ).

tff(f689,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b)),a),b))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b)),a),c),a)) ),
    inference(forward_demodulation,[],[f685,f580]) ).

tff(f690,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c),b))),a),c),a))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f686,f580]) ).

tff(f691,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c)),b),a),b))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b)),a),c),a)) ),
    inference(forward_demodulation,[],[f689,f579]) ).

tff(f692,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),c)),b)),a),c),a))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f690,f579]) ).

tff(f693,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),b),a),b))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b)),a),c),a)) ),
    inference(forward_demodulation,[],[f691,f580]) ).

tff(f694,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),b)),a),c),a))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f692,f580]) ).

tff(f695,plain,
    ! [X0: arrow_159774573e_indi] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b)),a),c),a))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f693,f579]) ).

tff(f696,plain,
    ! [X0: arrow_159774573e_indi] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b)),a),c),a))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),X0)),b),a),b)) ),
    inference(forward_demodulation,[],[f694,f579]) ).

tff(f697,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),c),a))
    | spl104_1 ),
    inference(forward_demodulation,[],[f627,f580]) ).

tff(f698,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b)),a),c),a))
    | spl104_1 ),
    inference(forward_demodulation,[],[f697,f579]) ).

tff(f699,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b))),a),c),a))
    | spl104_1 ),
    inference(forward_demodulation,[],[f698,f580]) ).

tff(f700,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c)),b)),a),c),a))
    | spl104_1 ),
    inference(forward_demodulation,[],[f699,f579]) ).

tff(f701,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103))),b)),a),c),a))
    | spl104_1 ),
    inference(forward_demodulation,[],[f700,f580]) ).

tff(f702,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),sK103)),b)),a),c),a))
    | spl104_1 ),
    inference(forward_demodulation,[],[f701,f579]) ).

tff(f806,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),sK103)),b),a),b))
    | spl104_1 ),
    inference(resolution,[],[f695,f702]) ).

tff(f808,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),sK103),b),c))
    | spl104_1 ),
    inference(resolution,[],[f806,f687]) ).

tff(f809,plain,
    ( ~ member(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,sK103))
    | spl104_1 ),
    inference(resolution,[],[f808,f671]) ).

tff(f810,plain,
    ( ~ spl104_2
    | spl104_1 ),
    inference(avatar_split_clause,[],[f809,f626,f630]) ).

tff(f811,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b),a)),c),a))
    | ~ spl104_1 ),
    inference(forward_demodulation,[],[f628,f580]) ).

tff(f812,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b)),b)),a),c),a))
    | ~ spl104_1 ),
    inference(forward_demodulation,[],[f811,f579]) ).

tff(f813,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c),b))),a),c),a))
    | ~ spl104_1 ),
    inference(forward_demodulation,[],[f812,f580]) ).

tff(f814,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_319942042_below,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103)),c)),b)),a),c),a))
    | ~ spl104_1 ),
    inference(forward_demodulation,[],[f813,f579]) ).

tff(f815,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK103))),b)),a),c),a))
    | ~ spl104_1 ),
    inference(forward_demodulation,[],[f814,f580]) ).

tff(f816,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_411405190le_alt,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,b),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),sK103)),b)),a),c),a))
    | ~ spl104_1 ),
    inference(forward_demodulation,[],[f815,f579]) ).

tff(f817,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_411405190le_alt,arrow_319942042_below,aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_159774573e_indi,combc(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),arrow_319942042_below,c),p),sK103)),b),a),b))
    | ~ spl104_1 ),
    inference(resolution,[],[f816,f696]) ).

tff(f818,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,c),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combc(arrow_411405190le_alt,arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),combb(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_411405190le_alt,fun(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_159774573e_indi,arrow_319942042_below,p),sK103),b),c))
    | ~ spl104_1 ),
    inference(resolution,[],[f817,f688]) ).

tff(f820,plain,
    ( member(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,sK103))
    | ~ spl104_1 ),
    inference(resolution,[],[f818,f672]) ).

tff(f821,plain,
    ( spl104_2
    | ~ spl104_1 ),
    inference(avatar_split_clause,[],[f820,f626,f630]) ).

cnf(s2,plain,
    ( spl104_1
    | spl104_2 ),
    inference(sat_conversion,[],[f633]) ).

cnf(s4,plain,
    ( ~ spl104_1
    | ~ spl104_2 ),
    inference(sat_conversion,[],[f634]) ).

cnf(s296,plain,
    ( spl104_1
    | ~ spl104_2 ),
    inference(sat_conversion,[],[f810]) ).

cnf(s302,plain,
    ( ~ spl104_1
    | spl104_2 ),
    inference(sat_conversion,[],[f821]) ).

cnf(s303,plain,
    spl104_1,
    inference(rat,[],[s2,s296]) ).

cnf(s304,plain,
    spl104_2,
    inference(rat,[],[s302,s303]) ).

cnf(s305,plain,
    $false,
    inference(rat,[],[s4,s304,s303]) ).

tff(f822,plain,
    $false,
    inference(avatar_sat_refutation,[],[s305]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT223_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38  % Computer : n009.cluster.edu
% 0.11/0.38  % Model    : x86_64 x86_64
% 0.11/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38  % Memory   : 8046.5625MB
% 0.11/0.38  % OS       : Linux 6.8.0-71-generic
% 0.11/0.38  % CPULimit : 300
% 0.11/0.38  % WCLimit  : 300
% 0.11/0.38  % DateTime : Mon Sep 28 00:00:58 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41  Running first-order model finding
% 0.11/0.41  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.39/1.61  % (2548346)Will run a generic schedule for satisfiability detection.
% 7.39/1.61  % (2548355)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2902403871:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.39/1.61  % (2548352)% WARNING: option uhcvi not known.
% 7.39/1.61  % (2548351)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=854682030_2999 on theBenchmark for (2999ds/0Mi)
% 7.39/1.61  % (2548352)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2258819827:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.39/1.61  % (2548353)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=201601806:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.39/1.61  % (2548354)dis+10_1_sil=32000:sp=arity:random_seed=83398748:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.39/1.61  % (2548356)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3381737025:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.39/1.61  % (2548357)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2616454205:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.39/1.61  % Exception at run slice level
% 7.39/1.61  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.61  % (2548365)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1509584808:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 7.39/1.61  % (2548355)Instruction limit reached! 
% 7.39/1.61  % (2548355)------------------------------
% 7.39/1.61  % (2548355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.61  % (2548355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.61  % (2548355)CaDiCaL version: 2.1.3
% 7.39/1.61  % (2548355)Termination reason: Instruction limit
% 7.39/1.61  % (2548355)Termination phase: Saturation
% 7.39/1.61  % (2548355)Time elapsed: 0.040 s
% 7.39/1.61  % (2548355)Peak memory usage: 13 MB
% 7.39/1.61  % (2548355)Instructions burned: 118 (million)
% 7.39/1.61  % Exception at run slice level
% 7.39/1.61  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.61  % (2548367)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3742381208:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 7.39/1.61  % (2548368)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2180147627:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 7.39/1.61  % (2548354)Instruction limit reached! 
% 7.39/1.61  % (2548354)------------------------------
% 7.39/1.61  % (2548354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.61  % (2548354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.61  % (2548354)CaDiCaL version: 2.1.3
% 7.39/1.61  % (2548354)Termination reason: Instruction limit
% 7.39/1.61  % (2548354)Termination phase: Saturation
% 7.39/1.61  % (2548354)Time elapsed: 0.063 s
% 7.39/1.61  % (2548354)Peak memory usage: 12 MB
% 7.39/1.61  % (2548354)Instructions burned: 104 (million)
% 7.39/1.61  % (2548356)Instruction limit reached! 
% 7.39/1.61  % (2548356)------------------------------
% 7.39/1.61  % (2548356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.61  % (2548356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.61  % (2548356)CaDiCaL version: 2.1.3
% 7.39/1.61  % (2548356)Termination reason: Instruction limit
% 7.39/1.61  % (2548356)Termination phase: Saturation
% 7.39/1.61  % (2548356)Time elapsed: 0.081 s
% 7.39/1.61  % (2548356)Peak memory usage: 13 MB
% 7.39/1.61  % (2548356)Instructions burned: 132 (million)
% 7.39/1.61  % (2548371)ott-21_1_sil=16000:fs=off:random_seed=932695184:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 7.39/1.61  % (2548367)Instruction limit reached! 
% 7.39/1.61  % (2548367)------------------------------
% 7.39/1.61  % (2548367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.61  % (2548367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.61  % (2548367)CaDiCaL version: 2.1.3
% 7.39/1.61  % (2548367)Termination reason: Instruction limit
% 7.39/1.61  % (2548367)Termination phase: Saturation
% 7.39/1.61  % (2548367)Time elapsed: 0.043 s
% 7.39/1.61  % (2548367)Peak memory usage: 13 MB
% 7.39/1.61  % (2548367)Instructions burned: 133 (million)
% 7.39/1.61  % (2548357)Instruction limit reached! 
% 7.39/1.68  % (2548357)------------------------------
% 7.39/1.68  % (2548357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.68  % (2548357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.68  % (2548357)CaDiCaL version: 2.1.3
% 7.39/1.68  % (2548357)Termination reason: Instruction limit
% 7.39/1.68  % (2548357)Termination phase: Saturation
% 7.39/1.68  % (2548357)Time elapsed: 0.093 s
% 7.39/1.68  % (2548357)Peak memory usage: 13 MB
% 7.39/1.68  % (2548357)Instructions burned: 160 (million)
% 7.39/1.68  % (2548374)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3913689813:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 7.39/1.68  % (2548372)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=271864117:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 7.39/1.68  % Exception at run slice level
% 7.39/1.68  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.68  % (2548375)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1806161512:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 7.39/1.69  % (2548378)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1221584896:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 7.39/1.69  % Exception at run slice level
% 7.39/1.69  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.69  % (2548381)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2028757850:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 7.39/1.69  % (2548371)Instruction limit reached! 
% 7.39/1.69  % (2548371)------------------------------
% 7.39/1.69  % (2548371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548371)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548371)Termination reason: Instruction limit
% 7.39/1.69  % (2548371)Termination phase: Saturation
% 7.39/1.69  % (2548371)Time elapsed: 0.103 s
% 7.39/1.69  % (2548371)Peak memory usage: 13 MB
% 7.39/1.69  % (2548371)Instructions burned: 181 (million)
% 7.39/1.69  % (2548383)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2006179131:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 7.39/1.69  % (2548372)Instruction limit reached! 
% 7.39/1.69  % (2548372)------------------------------
% 7.39/1.69  % (2548372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548372)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548372)Termination reason: Instruction limit
% 7.39/1.69  % (2548372)Termination phase: Saturation
% 7.39/1.69  % (2548372)Time elapsed: 0.287 s
% 7.39/1.69  % (2548372)Peak memory usage: 14 MB
% 7.39/1.69  % (2548372)Instructions burned: 477 (million)
% 7.39/1.69  % (2548387)fmb+10_1_sil=64000:random_seed=2554191055:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 7.39/1.69  % (2548381)Instruction limit reached! 
% 7.39/1.69  % (2548381)------------------------------
% 7.39/1.69  % (2548381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548381)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548381)Termination reason: Instruction limit
% 7.39/1.69  % (2548381)Termination phase: Saturation
% 7.39/1.69  % (2548381)Time elapsed: 0.264 s
% 7.39/1.69  % (2548381)Peak memory usage: 16 MB
% 7.39/1.69  % (2548381)Instructions burned: 694 (million)
% 7.39/1.69  % (2548387)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.39/1.69  % Exception at run slice level
% 7.39/1.69  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.69  % (2548396)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2879411287:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 7.39/1.69  % (2548398)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1796639016:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 7.39/1.69  % Exception at run slice level
% 7.39/1.69  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.69  % Exception at run slice level
% 7.39/1.69  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.69  % (2548410)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3917650297:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 7.39/1.69  % (2548412)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1261605362:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 7.39/1.69  % (2548368)Instruction limit reached! 
% 7.39/1.69  % (2548368)------------------------------
% 7.39/1.69  % (2548368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548368)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548368)Termination reason: Instruction limit
% 7.39/1.69  % (2548368)Termination phase: Saturation
% 7.39/1.69  % (2548368)Time elapsed: 0.408 s
% 7.39/1.69  % (2548368)Peak memory usage: 18 MB
% 7.39/1.69  % (2548368)Instructions burned: 684 (million)
% 7.39/1.69  % (2548412)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 7.39/1.69  % (2548425)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=324235893:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 7.39/1.69  % Exception at run slice level
% 7.39/1.69  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.69  % (2548441)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2242157438:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 7.39/1.69  % Exception at run slice level
% 7.39/1.69  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.69  % (2548450)ott-2_1_sil=16000:newcnf=on:random_seed=825071586:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 7.39/1.69  % (2548383)Instruction limit reached! 
% 7.39/1.69  % (2548383)------------------------------
% 7.39/1.69  % (2548383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548383)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548383)Termination reason: Instruction limit
% 7.39/1.69  % (2548383)Termination phase: Saturation
% 7.39/1.69  % (2548383)Time elapsed: 0.494 s
% 7.39/1.69  % (2548383)Peak memory usage: 19 MB
% 7.39/1.69  % (2548383)Instructions burned: 880 (million)
% 7.39/1.69  % (2548527)ott+10_1_sil=32000:tgt=ground:random_seed=2683957988:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 7.39/1.69  % (2548375)Instruction limit reached! 
% 7.39/1.69  % (2548375)------------------------------
% 7.39/1.69  % (2548375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548375)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548375)Termination reason: Instruction limit
% 7.39/1.69  % (2548375)Termination phase: Saturation
% 7.39/1.69  % (2548375)Time elapsed: 0.671 s
% 7.39/1.69  % (2548375)Peak memory usage: 20 MB
% 7.39/1.69  % (2548375)Instructions burned: 1180 (million)
% 7.39/1.69  % (2548535)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2731938972:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 7.39/1.69  % Exception at run slice level
% 7.39/1.69  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.39/1.69  % (2548537)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=24776493:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 7.39/1.69  % (2548450)Instruction limit reached! 
% 7.39/1.69  % (2548450)------------------------------
% 7.39/1.69  % (2548450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548450)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548450)Termination reason: Instruction limit
% 7.39/1.69  % (2548450)Termination phase: Saturation
% 7.39/1.69  % (2548450)Time elapsed: 0.460 s
% 7.39/1.69  % (2548450)Peak memory usage: 19 MB
% 7.39/1.69  % (2548450)Instructions burned: 871 (million)
% 7.39/1.69  % (2548539)dis+21_1_sil=32000:sas=cadical:random_seed=1490051232:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 7.39/1.69  % (2548412)Instruction limit reached! 
% 7.39/1.69  % (2548412)------------------------------
% 7.39/1.69  % (2548412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548412)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548412)Termination reason: Instruction limit
% 7.39/1.69  % (2548412)Termination phase: Saturation
% 7.39/1.69  % (2548412)Time elapsed: 0.679 s
% 7.39/1.69  % (2548412)Peak memory usage: 22 MB
% 7.39/1.69  % (2548412)Instructions burned: 1473 (million)
% 7.39/1.69  % (2548553)ott+11_1_sil=16000:gs=on:random_seed=645895002:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 7.39/1.69  % (2548553) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2548346-2548553"...
% 7.39/1.69  % (2548553)...printing done.
% 7.39/1.69  % (2548553)Refutation found. Thanks to Tanya!
% 7.39/1.69  % SZS status Theorem for theBenchmark
% 7.39/1.69  % SZS output start Proof for theBenchmark
% See solution above
% 7.39/1.69  % (2548553)------------------------------
% 7.39/1.69  % (2548553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.69  % (2548553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.69  % (2548553)CaDiCaL version: 2.1.3
% 7.39/1.69  % (2548553)Termination reason: Refutation
% 7.39/1.69  % (2548553)Time elapsed: 0.044 s
% 7.39/1.69  % (2548553)Peak memory usage: 13 MB
% 7.39/1.69  % (2548553)Instructions burned: 73 (million)
% 7.39/1.69  % (2548346)Success in time 1.264 s
% 7.39/1.69  % Vampire exiting
%------------------------------------------------------------------------------