TSTP Solution File: SWW568_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW568_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 11:41:23 EDT 2024

% Result   : Theorem 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  257
% Syntax   : Number of formulae    :  507 ( 146 unt; 125 typ;   0 def)
%            Number of atoms       :  823 ( 298 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  734 ( 293   ~; 233   |;  66   &)
%                                         (  90 <=>;  52  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    8 (   1 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  190 ( 101   >;  89   *;   0   +;   0  <<)
%            Number of predicates  :   83 (  81 usr;  71 prp; 0-6 aty)
%            Number of functors    :  109 ( 109 usr;  19 con; 0-7 aty)
%            Number of variables   : 1368 (1067   !;  55   ?;1368   :)
%                                         ( 246  !>;   0  ?*;   0  @-;   0  @+)

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

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

tff(type_def_7,type,
    list: $tType > $tType ).

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

tff(type_def_9,type,
    option: $tType > $tType ).

tff(type_def_10,type,
    char: $tType ).

tff(type_def_11,type,
    ty: $tType ).

tff(type_def_12,type,
    val: $tType ).

tff(type_def_13,type,
    fun: ( $tType * $tType ) > $tType ).

tff(type_def_14,type,
    product_prod: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    cast: 
      !>[X0: $tType] : ( ( list(char) * exp(X0) ) > exp(X0) ) ).

tff(func_def_1,type,
    cond: 
      !>[X0: $tType] : ( ( exp(X0) * exp(X0) * exp(X0) ) > exp(X0) ) ).

tff(func_def_2,type,
    fAcc: 
      !>[X0: $tType] : ( ( exp(X0) * list(char) * list(char) ) > exp(X0) ) ).

tff(func_def_3,type,
    while: 
      !>[X0: $tType] : ( ( exp(X0) * exp(X0) ) > exp(X0) ) ).

tff(func_def_4,type,
    throw: 
      !>[X0: $tType] : ( exp(X0) > exp(X0) ) ).

tff(func_def_5,type,
    wf_J_mdecl: fun(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(list(char),fun(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))),bool))) ).

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

tff(func_def_7,type,
    product_Pair: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).

tff(func_def_8,type,
    produc1605651328_split: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).

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

tff(func_def_10,type,
    red: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) > fun(product_prod(product_prod(exp(list(char)),product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val)))),product_prod(exp(list(char)),product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val))))),bool) ).

tff(func_def_11,type,
    hp: product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val))) > fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).

tff(func_def_12,type,
    transitive_rtrancl: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > fun(product_prod(X0,X0),bool) ) ).

tff(func_def_13,type,
    class: list(char) > ty ).

tff(func_def_14,type,
    nt: ty ).

tff(func_def_15,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_16,type,
    fFalse: bool ).

tff(func_def_17,type,
    fTrue: bool ).

tff(func_def_18,type,
    c: list(char) ).

tff(func_def_19,type,
    d: list(char) ).

tff(func_def_20,type,
    e: fun(list(char),option(ty)) ).

tff(func_def_21,type,
    f: list(char) ).

tff(func_def_22,type,
    p: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) ).

tff(func_def_23,type,
    t: ty ).

tff(func_def_24,type,
    u: ty ).

tff(func_def_25,type,
    e_a: exp(list(char)) ).

tff(func_def_26,type,
    ea: exp(list(char)) ).

tff(func_def_27,type,
    h_a: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).

tff(func_def_28,type,
    ha: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).

tff(func_def_29,type,
    l_a: fun(list(char),option(val)) ).

tff(func_def_30,type,
    la: fun(list(char),option(val)) ).

tff(func_def_31,type,
    sK0: ty ).

tff(func_def_32,type,
    sK1: ty > list(char) ).

tff(func_def_33,type,
    sK2: ty > list(char) ).

tff(func_def_34,type,
    sK3: ( ty * fun(list(char),option(ty)) ) > ty ).

tff(func_def_35,type,
    sK4: ( ty * fun(list(char),option(ty)) ) > ty ).

tff(func_def_36,type,
    sK5: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_37,type,
    sK6: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_38,type,
    sK7: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_39,type,
    sK8: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_40,type,
    sK9: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_41,type,
    sK10: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_42,type,
    sK11: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_43,type,
    sK12: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_44,type,
    sK13: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_45,type,
    sK14: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_46,type,
    sK15: ty > list(char) ).

tff(func_def_47,type,
    sK16: 
      !>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * X0 * X0 ) > X0 ) ).

tff(func_def_48,type,
    sK17: 
      !>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * X0 * X0 ) > X0 ) ).

tff(func_def_49,type,
    sK18: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X1 ) ).

tff(func_def_50,type,
    sK19: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X0 ) ).

tff(func_def_51,type,
    sK20: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

tff(func_def_52,type,
    sK21: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

tff(func_def_53,type,
    sK22: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

tff(func_def_54,type,
    sK23: ( exp(list(char)) * fun(list(char),option(ty)) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) ) > ty ).

tff(func_def_55,type,
    sK24: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).

tff(func_def_56,type,
    sK25: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).

tff(func_def_57,type,
    sK26: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).

tff(func_def_58,type,
    sK27: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).

tff(func_def_59,type,
    sK28: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).

tff(func_def_60,type,
    sK29: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).

tff(func_def_61,type,
    sK30: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).

tff(func_def_62,type,
    sK31: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

tff(func_def_63,type,
    sK32: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

tff(func_def_64,type,
    sK33: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

tff(func_def_65,type,
    sK34: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

tff(func_def_66,type,
    sK35: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).

tff(func_def_67,type,
    sK36: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).

tff(func_def_68,type,
    sK37: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).

tff(func_def_69,type,
    sK38: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).

tff(func_def_70,type,
    sK39: 
      !>[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_71,type,
    sK40: 
      !>[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_72,type,
    sK41: 
      !>[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_73,type,
    sK42: 
      !>[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_74,type,
    sK43: 
      !>[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_75,type,
    sK44: ( ty * list(char) * list(char) * exp(list(char)) * fun(list(char),option(ty)) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) ) > list(char) ).

tff(func_def_76,type,
    sK45: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(product_prod(X1,X0),product_prod(X1,X0)),bool) * X0 * X1 * X0 * X1 ) > X1 ) ).

tff(func_def_77,type,
    sK46: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(product_prod(X1,X0),product_prod(X1,X0)),bool) * X0 * X1 * X0 * X1 ) > X0 ) ).

tff(func_def_78,type,
    sK47: 
      !>[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_79,type,
    sK48: 
      !>[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_80,type,
    sK49: 
      !>[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_81,type,
    sK50: 
      !>[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_82,type,
    sK51: 
      !>[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_83,type,
    sK52: 
      !>[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_84,type,
    sK53: 
      !>[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_85,type,
    sK54: 
      !>[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_86,type,
    sK55: 
      !>[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_87,type,
    sK56: 
      !>[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_88,type,
    sK57: 
      !>[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_89,type,
    sK58: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).

tff(func_def_90,type,
    sK59: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).

tff(func_def_91,type,
    sK60: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).

tff(func_def_92,type,
    sK61: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).

tff(func_def_93,type,
    sK62: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).

tff(func_def_94,type,
    sK63: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).

tff(func_def_95,type,
    sK64: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).

tff(func_def_96,type,
    sK65: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).

tff(func_def_97,type,
    sK66: 
      !>[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_98,type,
    sK67: 
      !>[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_99,type,
    sK68: 
      !>[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_100,type,
    sK69: 
      !>[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_101,type,
    sK70: 
      !>[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_102,type,
    sK71: 
      !>[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_103,type,
    sK72: ty ).

tff(pred_def_1,type,
    hconf: 
      !>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > $o ) ).

tff(pred_def_2,type,
    lconf: 
      !>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(list(char),option(val)) * fun(list(char),option(ty)) ) > $o ) ).

tff(pred_def_3,type,
    hext: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > $o ).

tff(pred_def_4,type,
    has_field: 
      !>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * list(char) * list(char) * ty * list(char) ) > $o ) ).

tff(pred_def_5,type,
    widen: 
      !>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * ty * ty ) > $o ) ).

tff(pred_def_6,type,
    typeSa976492716_sconf: ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) * fun(list(char),option(ty)) * product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val))) ) > $o ).

tff(pred_def_7,type,
    is_refT: ty > $o ).

tff(pred_def_8,type,
    wf_prog: 
      !>[X0: $tType] : ( ( fun(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),fun(list(char),fun(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))),bool))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) ) > $o ) ).

tff(pred_def_9,type,
    wTrt: ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(list(char),option(ty)) * exp(list(char)) * ty ) > $o ).

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

tff(pred_def_11,type,
    pp: bool > $o ).

tff(f896,plain,
    $false,
    inference(avatar_sat_refutation,[],[f523,f528,f533,f537,f541,f545,f549,f553,f558,f562,f567,f572,f577,f581,f585,f589,f593,f599,f603,f607,f611,f615,f619,f623,f633,f637,f641,f645,f650,f655,f659,f663,f668,f674,f678,f691,f695,f699,f703,f707,f714,f720,f724,f728,f732,f736,f740,f744,f757,f761,f765,f769,f773,f777,f781,f785,f789,f809,f813,f817,f829,f833,f837,f841,f848,f866,f870,f885,f889,f893,f895]) ).

tff(f895,plain,
    ( ~ spl73_7
    | ~ spl73_65 ),
    inference(avatar_contradiction_clause,[],[f894]) ).

tff(f894,plain,
    ( $false
    | ~ spl73_7
    | ~ spl73_65 ),
    inference(resolution,[],[f847,f548]) ).

tff(f548,plain,
    ( ! [X0: $tType,X2: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X1: ty] : widen(X0,X2,X1,X1)
    | ~ spl73_7 ),
    inference(avatar_component_clause,[],[f547]) ).

tff(f547,plain,
    ( spl73_7
  <=> ! [X0: $tType,X2: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X1: ty] : widen(X0,X2,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_7])]) ).

tff(f847,plain,
    ( ! [X0: ty] : ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t)
    | ~ spl73_65 ),
    inference(avatar_component_clause,[],[f846]) ).

tff(f846,plain,
    ( spl73_65
  <=> ! [X0: ty] : ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_65])]) ).

tff(f893,plain,
    spl73_70,
    inference(avatar_split_clause,[],[f394,f891]) ).

tff(f891,plain,
    ( spl73_70
  <=> ! [X1: $tType,X0: $tType,X8: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
        ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK9(X0,X1,X2),sK10(X0,X1,X2))))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_70])]) ).

tff(f394,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X8: product_prod(X0,X1)] :
      ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK9(X0,X1,X2),sK10(X0,X1,X2))))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f296,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2)))
        | ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK9(X0,X1,X2),sK10(X0,X1,X2))))
        | ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f293,f295,f294]) ).

tff(f294,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
     => pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f295,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
     => pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK9(X0,X1,X2),sK10(X0,X1,X2)))) ),
    introduced(choice_axiom,[]) ).

tff(f293,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    inference(rectify,[],[f292]) ).

tff(f292,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5)))
        | ! [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
    inference(nnf_transformation,[],[f125]) ).

tff(f125,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
    <=> ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ),
    inference(rectify,[],[f38]) ).

tff(f38,axiom,
    ! [X1: $tType,X2: $tType,X20: fun(product_prod(X1,X2),bool)] :
      ( ? [X30: product_prod(X1,X2)] : pp(aa(product_prod(X1,X2),bool,X20,X30))
    <=> ? [X31: X1,X32: X2] : pp(aa(product_prod(X1,X2),bool,X20,product_Pair(X1,X2,X31,X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_split__paired__Ex) ).

tff(f889,plain,
    spl73_69,
    inference(avatar_split_clause,[],[f393,f887]) ).

tff(f887,plain,
    ( spl73_69
  <=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
        ( pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK5(X0,X1,X2),sK6(X0,X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_69])]) ).

tff(f393,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
      ( pp(aa(product_prod(X0,X1),bool,X2,X3))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK5(X0,X1,X2),sK6(X0,X1,X2)))) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f291,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK5(X0,X1,X2),sK6(X0,X1,X2)))) )
      & ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f288,f290,f289]) ).

tff(f289,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5)))
     => ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,sK5(X0,X1,X2),sK6(X0,X1,X2)))) ),
    introduced(choice_axiom,[]) ).

tff(f290,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8))
     => ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f288,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
    inference(rectify,[],[f287]) ).

tff(f287,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
        | ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) )
      & ( ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5)))
        | ? [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
    inference(nnf_transformation,[],[f124]) ).

tff(f124,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
      ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
    <=> ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X1: $tType,X2: $tType,X20: fun(product_prod(X1,X2),bool)] :
      ( ! [X30: product_prod(X1,X2)] : pp(aa(product_prod(X1,X2),bool,X20,X30))
    <=> ! [X31: X1,X32: X2] : pp(aa(product_prod(X1,X2),bool,X20,product_Pair(X1,X2,X31,X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_split__paired__All) ).

tff(f885,plain,
    spl73_68,
    inference(avatar_split_clause,[],[f363,f882]) ).

tff(f882,plain,
    ( spl73_68
  <=> typeSa976492716_sconf(p,e,product_Pair(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val)),ha,la)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_68])]) ).

tff(f363,plain,
    typeSa976492716_sconf(p,e,product_Pair(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val)),ha,la)),
    inference(cnf_transformation,[],[f15]) ).

tff(f15,axiom,
    typeSa976492716_sconf(p,e,product_Pair(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val)),ha,la)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_FAccRed_I3_J) ).

tff(f870,plain,
    spl73_67,
    inference(avatar_split_clause,[],[f395,f868]) ).

tff(f868,plain,
    ( spl73_67
  <=> ! [X1: $tType,X0: $tType,X4: X0,X5: X1,X2: fun(product_prod(X0,X1),bool)] :
        ( pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2)))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_67])]) ).

tff(f395,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
      ( pp(aa(product_prod(X0,X1),bool,X2,sK8(X0,X1,X2)))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X4,X5))) ),
    inference(cnf_transformation,[],[f296]) ).

tff(f866,plain,
    spl73_66,
    inference(avatar_split_clause,[],[f392,f864]) ).

tff(f864,plain,
    ( spl73_66
  <=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
        ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
        | ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_66])]) ).

tff(f392,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
      ( pp(aa(product_prod(X0,X1),bool,X2,product_Pair(X0,X1,X6,X7)))
      | ~ pp(aa(product_prod(X0,X1),bool,X2,sK7(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f848,plain,
    ( spl73_65
    | ~ spl73_12
    | ~ spl73_8
    | ~ spl73_60 ),
    inference(avatar_split_clause,[],[f823,f815,f551,f569,f846]) ).

tff(f569,plain,
    ( spl73_12
  <=> wTrt(p,h_a,e,e_a,nt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_12])]) ).

tff(f551,plain,
    ( spl73_8
  <=> ! [X0: ty] :
        ( ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t)
        | ~ wTrt(p,h_a,e,fAcc(list(char),e_a,f,d),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_8])]) ).

tff(f815,plain,
    ( spl73_60
  <=> ! [X5: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X6: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),X4: fun(list(char),option(ty)),X0: ty,X3: exp(list(char)),X2: list(char),X1: list(char)] :
        ( wTrt(X6,X5,X4,fAcc(list(char),X3,X2,X1),X0)
        | ~ wTrt(X6,X5,X4,X3,nt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_60])]) ).

tff(f823,plain,
    ( ! [X0: ty] :
        ( ~ wTrt(p,h_a,e,e_a,nt)
        | ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t) )
    | ~ spl73_8
    | ~ spl73_60 ),
    inference(resolution,[],[f816,f552]) ).

tff(f552,plain,
    ( ! [X0: ty] :
        ( ~ wTrt(p,h_a,e,fAcc(list(char),e_a,f,d),X0)
        | ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t) )
    | ~ spl73_8 ),
    inference(avatar_component_clause,[],[f551]) ).

tff(f816,plain,
    ( ! [X2: list(char),X3: exp(list(char)),X0: ty,X1: list(char),X6: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),X4: fun(list(char),option(ty)),X5: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
        ( wTrt(X6,X5,X4,fAcc(list(char),X3,X2,X1),X0)
        | ~ wTrt(X6,X5,X4,X3,nt) )
    | ~ spl73_60 ),
    inference(avatar_component_clause,[],[f815]) ).

tff(f841,plain,
    spl73_64,
    inference(avatar_split_clause,[],[f449,f839]) ).

tff(f839,plain,
    ( spl73_64
  <=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X0,fun(X2,X1)),X4: X0,X3: X2] : ( aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) = produc1605651328_split(X0,X2,X1,X5,product_Pair(X0,X2,X4,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_64])]) ).

tff(f449,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) = produc1605651328_split(X0,X2,X1,X5,product_Pair(X0,X2,X4,X3)) ),
    inference(cnf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) = produc1605651328_split(X0,X2,X1,X5,product_Pair(X0,X2,X4,X3)) ),
    inference(rectify,[],[f72]) ).

tff(f72,axiom,
    ! [X2: $tType,X1: $tType,X3: $tType,X35: X3,X36: X2,X75: fun(X2,fun(X3,X1))] : ( produc1605651328_split(X2,X3,X1,X75,product_Pair(X2,X3,X36,X35)) = aa(X3,X1,aa(X2,fun(X3,X1),X75,X36),X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_internal__split__conv) ).

tff(f837,plain,
    spl73_63,
    inference(avatar_split_clause,[],[f448,f835]) ).

tff(f835,plain,
    ( spl73_63
  <=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( product_prod_rec(X0,X2,X1,X5,product_Pair(X0,X2,X4,X3)) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_63])]) ).

tff(f448,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( product_prod_rec(X0,X2,X1,X5,product_Pair(X0,X2,X4,X3)) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( product_prod_rec(X0,X2,X1,X5,product_Pair(X0,X2,X4,X3)) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) ),
    inference(rectify,[],[f44]) ).

tff(f44,axiom,
    ! [X2: $tType,X1: $tType,X3: $tType,X35: X3,X36: X2,X63: fun(X2,fun(X3,X1))] : ( product_prod_rec(X2,X3,X1,X63,product_Pair(X2,X3,X36,X35)) = aa(X3,X1,aa(X2,fun(X3,X1),X63,X36),X35) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod_Orecs) ).

tff(f833,plain,
    spl73_62,
    inference(avatar_split_clause,[],[f418,f831]) ).

tff(f831,plain,
    ( spl73_62
  <=> ! [X1: $tType,X0: $tType,X4: fun(X1,option(X0)),X3: fun(X1,option(X0)),X2: fun(X1,option(X0))] : ( map_add(X1,X0,X4,map_add(X1,X0,X3,X2)) = map_add(X1,X0,map_add(X1,X0,X4,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_62])]) ).

tff(f418,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,option(X0)),X3: fun(X1,option(X0)),X4: fun(X1,option(X0))] : ( map_add(X1,X0,X4,map_add(X1,X0,X3,X2)) = map_add(X1,X0,map_add(X1,X0,X4,X3),X2) ),
    inference(cnf_transformation,[],[f143]) ).

tff(f143,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,option(X0)),X3: fun(X1,option(X0)),X4: fun(X1,option(X0))] : ( map_add(X1,X0,X4,map_add(X1,X0,X3,X2)) = map_add(X1,X0,map_add(X1,X0,X4,X3),X2) ),
    inference(rectify,[],[f53]) ).

tff(f53,axiom,
    ! [X2: $tType,X1: $tType,X67: fun(X1,option(X2)),X68: fun(X1,option(X2)),X69: fun(X1,option(X2))] : ( map_add(X1,X2,X69,map_add(X1,X2,X68,X67)) = map_add(X1,X2,map_add(X1,X2,X69,X68),X67) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_map__add__assoc) ).

tff(f829,plain,
    spl73_61,
    inference(avatar_split_clause,[],[f421,f827]) ).

tff(f827,plain,
    ( spl73_61
  <=> ! [X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),X0: ty,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(list(char),option(ty)),X1: exp(list(char))] :
        ( wTrt(X4,X3,X2,X1,sK23(X1,X2,X3,X4))
        | ~ wTrt(X4,X3,X2,throw(list(char),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_61])]) ).

tff(f421,plain,
    ! [X2: fun(list(char),option(ty)),X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X0: ty,X1: exp(list(char)),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X4,X3,X2,X1,sK23(X1,X2,X3,X4))
      | ~ wTrt(X4,X3,X2,throw(list(char),X1),X0) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f314,plain,
    ! [X0: ty,X1: exp(list(char)),X2: fun(list(char),option(ty)),X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( ( is_refT(sK23(X1,X2,X3,X4))
        & wTrt(X4,X3,X2,X1,sK23(X1,X2,X3,X4)) )
      | ~ wTrt(X4,X3,X2,throw(list(char),X1),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f217,f313]) ).

tff(f313,plain,
    ! [X1: exp(list(char)),X2: fun(list(char),option(ty)),X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( ? [X5: ty] :
          ( is_refT(X5)
          & wTrt(X4,X3,X2,X1,X5) )
     => ( is_refT(sK23(X1,X2,X3,X4))
        & wTrt(X4,X3,X2,X1,sK23(X1,X2,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f217,plain,
    ! [X0: ty,X1: exp(list(char)),X2: fun(list(char),option(ty)),X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( ? [X5: ty] :
          ( is_refT(X5)
          & wTrt(X4,X3,X2,X1,X5) )
      | ~ wTrt(X4,X3,X2,throw(list(char),X1),X0) ),
    inference(ennf_transformation,[],[f146]) ).

tff(f146,plain,
    ! [X0: ty,X1: exp(list(char)),X2: fun(list(char),option(ty)),X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X4,X3,X2,throw(list(char),X1),X0)
     => ~ ! [X5: ty] :
            ( wTrt(X4,X3,X2,X1,X5)
           => ~ is_refT(X5) ) ),
    inference(rectify,[],[f83]) ).

tff(f83,axiom,
    ! [X14: ty,X17: exp(list(char)),X18: fun(list(char),option(ty)),X19: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X20: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X20,X19,X18,throw(list(char),X17),X14)
     => ~ ! [X94: ty] :
            ( wTrt(X20,X19,X18,X17,X94)
           => ~ is_refT(X94) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_WTrt__elim__cases_I4_J) ).

tff(f817,plain,
    spl73_60,
    inference(avatar_split_clause,[],[f462,f815]) ).

tff(f462,plain,
    ! [X2: list(char),X3: exp(list(char)),X0: ty,X1: list(char),X6: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),X4: fun(list(char),option(ty)),X5: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
      ( wTrt(X6,X5,X4,fAcc(list(char),X3,X2,X1),X0)
      | ~ wTrt(X6,X5,X4,X3,nt) ),
    inference(cnf_transformation,[],[f244]) ).

tff(f244,plain,
    ! [X0: ty,X1: list(char),X2: list(char),X3: exp(list(char)),X4: fun(list(char),option(ty)),X5: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X6: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X6,X5,X4,fAcc(list(char),X3,X2,X1),X0)
      | ~ wTrt(X6,X5,X4,X3,nt) ),
    inference(ennf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: ty,X1: list(char),X2: list(char),X3: exp(list(char)),X4: fun(list(char),option(ty)),X5: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X6: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X6,X5,X4,X3,nt)
     => wTrt(X6,X5,X4,fAcc(list(char),X3,X2,X1),X0) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X14: ty,X15: list(char),X16: list(char),X17: exp(list(char)),X18: fun(list(char),option(ty)),X19: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X20: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X20,X19,X18,X17,nt)
     => wTrt(X20,X19,X18,fAcc(list(char),X17,X16,X15),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_WTrtFAccNT) ).

tff(f813,plain,
    spl73_59,
    inference(avatar_split_clause,[],[f451,f811]) ).

tff(f811,plain,
    ( spl73_59
  <=> ! [X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X0: ty,X3: fun(list(char),option(ty)),X2: exp(list(char)),X1: ty] :
        ( wTrt(X5,X4,X3,throw(list(char),X2),X0)
        | ~ is_refT(X1)
        | ~ wTrt(X5,X4,X3,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_59])]) ).

tff(f451,plain,
    ! [X2: exp(list(char)),X3: fun(list(char),option(ty)),X0: ty,X1: ty,X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X4,X3,throw(list(char),X2),X0)
      | ~ is_refT(X1)
      | ~ wTrt(X5,X4,X3,X2,X1) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f236,plain,
    ! [X0: ty,X1: ty,X2: exp(list(char)),X3: fun(list(char),option(ty)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X4,X3,throw(list(char),X2),X0)
      | ~ is_refT(X1)
      | ~ wTrt(X5,X4,X3,X2,X1) ),
    inference(flattening,[],[f235]) ).

tff(f235,plain,
    ! [X0: ty,X1: ty,X2: exp(list(char)),X3: fun(list(char),option(ty)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X4,X3,throw(list(char),X2),X0)
      | ~ is_refT(X1)
      | ~ wTrt(X5,X4,X3,X2,X1) ),
    inference(ennf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: ty,X1: ty,X2: exp(list(char)),X3: fun(list(char),option(ty)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X4,X3,X2,X1)
     => ( is_refT(X1)
       => wTrt(X5,X4,X3,throw(list(char),X2),X0) ) ),
    inference(rectify,[],[f74]) ).

tff(f74,axiom,
    ! [X14: ty,X88: ty,X17: exp(list(char)),X18: fun(list(char),option(ty)),X19: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X20: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X20,X19,X18,X17,X88)
     => ( is_refT(X88)
       => wTrt(X20,X19,X18,throw(list(char),X17),X14) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_WTrtThrow) ).

tff(f809,plain,
    ( spl73_58
    | ~ spl73_11
    | ~ spl73_47 ),
    inference(avatar_split_clause,[],[f750,f738,f564,f807]) ).

tff(f807,plain,
    ( spl73_58
  <=> ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
        ( ~ hext(h_a,X0)
        | wTrt(p,X0,e,e_a,sK72) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_58])]) ).

tff(f564,plain,
    ( spl73_11
  <=> wTrt(p,h_a,e,e_a,sK72) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_11])]) ).

tff(f738,plain,
    ( spl73_47
  <=> ! [X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X3: fun(list(char),option(ty)),X2: exp(list(char)),X1: ty] :
        ( wTrt(X5,X0,X3,X2,X1)
        | ~ hext(X4,X0)
        | ~ wTrt(X5,X4,X3,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_47])]) ).

tff(f750,plain,
    ( ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
        ( ~ hext(h_a,X0)
        | wTrt(p,X0,e,e_a,sK72) )
    | ~ spl73_11
    | ~ spl73_47 ),
    inference(resolution,[],[f739,f566]) ).

tff(f566,plain,
    ( wTrt(p,h_a,e,e_a,sK72)
    | ~ spl73_11 ),
    inference(avatar_component_clause,[],[f564]) ).

tff(f739,plain,
    ( ! [X2: exp(list(char)),X3: fun(list(char),option(ty)),X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: ty,X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
        ( ~ wTrt(X5,X4,X3,X2,X1)
        | ~ hext(X4,X0)
        | wTrt(X5,X0,X3,X2,X1) )
    | ~ spl73_47 ),
    inference(avatar_component_clause,[],[f738]) ).

tff(f789,plain,
    spl73_57,
    inference(avatar_split_clause,[],[f480,f787]) ).

tff(f787,plain,
    ( spl73_57
  <=> ! [X0: $tType,X5: list(char),X3: exp(X0),X4: list(char),X2: list(char),X6: exp(X0),X1: list(char)] :
        ( ( X1 = X4 )
        | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_57])]) ).

tff(f480,plain,
    ! [X0: $tType,X2: list(char),X3: exp(X0),X1: list(char),X6: exp(X0),X4: list(char),X5: list(char)] :
      ( ( X1 = X4 )
      | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f342]) ).

tff(f342,plain,
    ! [X0: $tType,X1: list(char),X2: list(char),X3: exp(X0),X4: list(char),X5: list(char),X6: exp(X0)] :
      ( ( ( fAcc(X0,X3,X2,X1) = fAcc(X0,X6,X5,X4) )
        | ( X1 != X4 )
        | ( X2 != X5 )
        | ( X3 != X6 ) )
      & ( ( ( X1 = X4 )
          & ( X2 = X5 )
          & ( X3 = X6 ) )
        | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ) ),
    inference(flattening,[],[f341]) ).

tff(f341,plain,
    ! [X0: $tType,X1: list(char),X2: list(char),X3: exp(X0),X4: list(char),X5: list(char),X6: exp(X0)] :
      ( ( ( fAcc(X0,X3,X2,X1) = fAcc(X0,X6,X5,X4) )
        | ( X1 != X4 )
        | ( X2 != X5 )
        | ( X3 != X6 ) )
      & ( ( ( X1 = X4 )
          & ( X2 = X5 )
          & ( X3 = X6 ) )
        | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ) ),
    inference(nnf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: $tType,X1: list(char),X2: list(char),X3: exp(X0),X4: list(char),X5: list(char),X6: exp(X0)] :
      ( ( fAcc(X0,X3,X2,X1) = fAcc(X0,X6,X5,X4) )
    <=> ( ( X1 = X4 )
        & ( X2 = X5 )
        & ( X3 = X6 ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X1: $tType,X5: list(char),X6: list(char),X7: exp(X1),X8: list(char),X9: list(char),X10: exp(X1)] :
      ( ( fAcc(X1,X10,X9,X8) = fAcc(X1,X7,X6,X5) )
    <=> ( ( X5 = X8 )
        & ( X6 = X9 )
        & ( X7 = X10 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_exp_Osimps_I7_J) ).

tff(f785,plain,
    spl73_56,
    inference(avatar_split_clause,[],[f479,f783]) ).

tff(f783,plain,
    ( spl73_56
  <=> ! [X0: $tType,X5: list(char),X3: exp(X0),X4: list(char),X6: exp(X0),X2: list(char),X1: list(char)] :
        ( ( X2 = X5 )
        | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_56])]) ).

tff(f479,plain,
    ! [X0: $tType,X2: list(char),X3: exp(X0),X1: list(char),X6: exp(X0),X4: list(char),X5: list(char)] :
      ( ( X2 = X5 )
      | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f342]) ).

tff(f781,plain,
    ( spl73_55
    | ~ spl73_9
    | ~ spl73_47 ),
    inference(avatar_split_clause,[],[f749,f738,f555,f779]) ).

tff(f779,plain,
    ( spl73_55
  <=> ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
        ( ~ hext(h_a,X0)
        | wTrt(p,X0,e,e_a,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_55])]) ).

tff(f555,plain,
    ( spl73_9
  <=> wTrt(p,h_a,e,e_a,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_9])]) ).

tff(f749,plain,
    ( ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
        ( ~ hext(h_a,X0)
        | wTrt(p,X0,e,e_a,sK0) )
    | ~ spl73_9
    | ~ spl73_47 ),
    inference(resolution,[],[f739,f557]) ).

tff(f557,plain,
    ( wTrt(p,h_a,e,e_a,sK0)
    | ~ spl73_9 ),
    inference(avatar_component_clause,[],[f555]) ).

tff(f777,plain,
    spl73_54,
    inference(avatar_split_clause,[],[f478,f775]) ).

tff(f775,plain,
    ( spl73_54
  <=> ! [X0: $tType,X5: list(char),X4: list(char),X2: list(char),X6: exp(X0),X3: exp(X0),X1: list(char)] :
        ( ( X3 = X6 )
        | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_54])]) ).

tff(f478,plain,
    ! [X0: $tType,X2: list(char),X3: exp(X0),X1: list(char),X6: exp(X0),X4: list(char),X5: list(char)] :
      ( ( X3 = X6 )
      | ( fAcc(X0,X3,X2,X1) != fAcc(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f342]) ).

tff(f773,plain,
    spl73_53,
    inference(avatar_split_clause,[],[f476,f771]) ).

tff(f771,plain,
    ( spl73_53
  <=> ! [X0: $tType,X2: exp(X0),X6: exp(X0),X4: exp(X0),X3: exp(X0),X5: exp(X0),X1: exp(X0)] :
        ( ( X1 = X4 )
        | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_53])]) ).

tff(f476,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X6: exp(X0),X4: exp(X0),X5: exp(X0)] :
      ( ( X1 = X4 )
      | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f340,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0),X5: exp(X0),X6: exp(X0)] :
      ( ( ( cond(X0,X3,X2,X1) = cond(X0,X6,X5,X4) )
        | ( X1 != X4 )
        | ( X2 != X5 )
        | ( X3 != X6 ) )
      & ( ( ( X1 = X4 )
          & ( X2 = X5 )
          & ( X3 = X6 ) )
        | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ) ),
    inference(flattening,[],[f339]) ).

tff(f339,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0),X5: exp(X0),X6: exp(X0)] :
      ( ( ( cond(X0,X3,X2,X1) = cond(X0,X6,X5,X4) )
        | ( X1 != X4 )
        | ( X2 != X5 )
        | ( X3 != X6 ) )
      & ( ( ( X1 = X4 )
          & ( X2 = X5 )
          & ( X3 = X6 ) )
        | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ) ),
    inference(nnf_transformation,[],[f183]) ).

tff(f183,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0),X5: exp(X0),X6: exp(X0)] :
      ( ( cond(X0,X3,X2,X1) = cond(X0,X6,X5,X4) )
    <=> ( ( X1 = X4 )
        & ( X2 = X5 )
        & ( X3 = X6 ) ) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X1: $tType,X105: exp(X1),X95: exp(X1),X96: exp(X1),X106: exp(X1),X97: exp(X1),X98: exp(X1)] :
      ( ( cond(X1,X98,X97,X106) = cond(X1,X96,X95,X105) )
    <=> ( ( X105 = X106 )
        & ( X95 = X97 )
        & ( X96 = X98 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_exp_Osimps_I12_J) ).

tff(f769,plain,
    spl73_52,
    inference(avatar_split_clause,[],[f475,f767]) ).

tff(f767,plain,
    ( spl73_52
  <=> ! [X0: $tType,X6: exp(X0),X4: exp(X0),X3: exp(X0),X5: exp(X0),X2: exp(X0),X1: exp(X0)] :
        ( ( X2 = X5 )
        | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_52])]) ).

tff(f475,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X6: exp(X0),X4: exp(X0),X5: exp(X0)] :
      ( ( X2 = X5 )
      | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f765,plain,
    spl73_51,
    inference(avatar_split_clause,[],[f474,f763]) ).

tff(f763,plain,
    ( spl73_51
  <=> ! [X0: $tType,X5: exp(X0),X4: exp(X0),X2: exp(X0),X6: exp(X0),X3: exp(X0),X1: exp(X0)] :
        ( ( X3 = X6 )
        | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_51])]) ).

tff(f474,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X6: exp(X0),X4: exp(X0),X5: exp(X0)] :
      ( ( X3 = X6 )
      | ( cond(X0,X3,X2,X1) != cond(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f761,plain,
    spl73_50,
    inference(avatar_split_clause,[],[f454,f759]) ).

tff(f759,plain,
    ( spl73_50
  <=> ! [X1: $tType,X0: $tType,X5: X0,X4: X1,X3: X0,X2: X1] :
        ( ( X2 = X4 )
        | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_50])]) ).

tff(f454,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( X2 = X4 )
      | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f239,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( ( X2 = X4 )
        & ( X3 = X5 ) )
      | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ),
    inference(ennf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( product_Pair(X0,X1,X5,X4) = product_Pair(X0,X1,X3,X2) )
     => ~ ( ( X3 = X5 )
         => ( X2 != X4 ) ) ),
    inference(rectify,[],[f30]) ).

tff(f30,axiom,
    ! [X1: $tType,X2: $tType,X42: X2,X43: X1,X44: X2,X45: X1] :
      ( ( product_Pair(X1,X2,X45,X44) = product_Pair(X1,X2,X43,X42) )
     => ~ ( ( X43 = X45 )
         => ( X42 != X44 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Pair__inject) ).

tff(f757,plain,
    spl73_49,
    inference(avatar_split_clause,[],[f453,f755]) ).

tff(f755,plain,
    ( spl73_49
  <=> ! [X1: $tType,X0: $tType,X3: X0,X4: X1,X5: X0,X2: X1] :
        ( ( X3 = X5 )
        | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_49])]) ).

tff(f453,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
      ( ( X3 = X5 )
      | ( product_Pair(X0,X1,X5,X4) != product_Pair(X0,X1,X3,X2) ) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f744,plain,
    ( spl73_48
    | ~ spl73_5
    | ~ spl73_19 ),
    inference(avatar_split_clause,[],[f627,f601,f539,f742]) ).

tff(f742,plain,
    ( spl73_48
  <=> ! [X0: list(char)] :
        ( ( nt = class(X0) )
        | ( class(X0) = class(sK2(class(X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_48])]) ).

tff(f539,plain,
    ( spl73_5
  <=> ! [X1: list(char)] : is_refT(class(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_5])]) ).

tff(f601,plain,
    ( spl73_19
  <=> ! [X0: ty] :
        ( ( class(sK2(X0)) = X0 )
        | ( nt = X0 )
        | ~ is_refT(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_19])]) ).

tff(f627,plain,
    ( ! [X0: list(char)] :
        ( ( nt = class(X0) )
        | ( class(X0) = class(sK2(class(X0))) ) )
    | ~ spl73_5
    | ~ spl73_19 ),
    inference(resolution,[],[f602,f540]) ).

tff(f540,plain,
    ( ! [X1: list(char)] : is_refT(class(X1))
    | ~ spl73_5 ),
    inference(avatar_component_clause,[],[f539]) ).

tff(f602,plain,
    ( ! [X0: ty] :
        ( ~ is_refT(X0)
        | ( nt = X0 )
        | ( class(sK2(X0)) = X0 ) )
    | ~ spl73_19 ),
    inference(avatar_component_clause,[],[f601]) ).

tff(f740,plain,
    spl73_47,
    inference(avatar_split_clause,[],[f452,f738]) ).

tff(f452,plain,
    ! [X2: exp(list(char)),X3: fun(list(char),option(ty)),X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: ty,X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X0,X3,X2,X1)
      | ~ hext(X4,X0)
      | ~ wTrt(X5,X4,X3,X2,X1) ),
    inference(cnf_transformation,[],[f238]) ).

tff(f238,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: ty,X2: exp(list(char)),X3: fun(list(char),option(ty)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X0,X3,X2,X1)
      | ~ hext(X4,X0)
      | ~ wTrt(X5,X4,X3,X2,X1) ),
    inference(flattening,[],[f237]) ).

tff(f237,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: ty,X2: exp(list(char)),X3: fun(list(char),option(ty)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X0,X3,X2,X1)
      | ~ hext(X4,X0)
      | ~ wTrt(X5,X4,X3,X2,X1) ),
    inference(ennf_transformation,[],[f166]) ).

tff(f166,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: ty,X2: exp(list(char)),X3: fun(list(char),option(ty)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X5,X4,X3,X2,X1)
     => ( hext(X4,X0)
       => wTrt(X5,X0,X3,X2,X1) ) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ! [X61: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X14: ty,X17: exp(list(char)),X18: fun(list(char),option(ty)),X19: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X20: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( wTrt(X20,X19,X18,X17,X14)
     => ( hext(X19,X61)
       => wTrt(X20,X61,X18,X17,X14) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_WTrt__hext__mono) ).

tff(f736,plain,
    spl73_46,
    inference(avatar_split_clause,[],[f450,f734]) ).

tff(f734,plain,
    ( spl73_46
  <=> ! [X0: $tType,X3: fun(list(char),option(val)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X2: fun(list(char),option(ty)),X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
        ( lconf(X0,X5,X1,X3,X2)
        | ~ hext(X4,X1)
        | ~ lconf(X0,X5,X4,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_46])]) ).

tff(f450,plain,
    ! [X0: $tType,X2: fun(list(char),option(ty)),X3: fun(list(char),option(val)),X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( lconf(X0,X5,X1,X3,X2)
      | ~ hext(X4,X1)
      | ~ lconf(X0,X5,X4,X3,X2) ),
    inference(cnf_transformation,[],[f234]) ).

tff(f234,plain,
    ! [X0: $tType,X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(list(char),option(ty)),X3: fun(list(char),option(val)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( lconf(X0,X5,X1,X3,X2)
      | ~ hext(X4,X1)
      | ~ lconf(X0,X5,X4,X3,X2) ),
    inference(flattening,[],[f233]) ).

tff(f233,plain,
    ! [X0: $tType,X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(list(char),option(ty)),X3: fun(list(char),option(val)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( lconf(X0,X5,X1,X3,X2)
      | ~ hext(X4,X1)
      | ~ lconf(X0,X5,X4,X3,X2) ),
    inference(ennf_transformation,[],[f164]) ).

tff(f164,plain,
    ! [X0: $tType,X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(list(char),option(ty)),X3: fun(list(char),option(val)),X4: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X5: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( lconf(X0,X5,X4,X3,X2)
     => ( hext(X4,X1)
       => lconf(X0,X5,X1,X3,X2) ) ),
    inference(rectify,[],[f50]) ).

tff(f50,axiom,
    ! [X1: $tType,X61: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X18: fun(list(char),option(ty)),X62: fun(list(char),option(val)),X19: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X20: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X1))))))))] :
      ( lconf(X1,X20,X19,X62,X18)
     => ( hext(X19,X61)
       => lconf(X1,X20,X61,X62,X18) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_lconf__hext) ).

tff(f732,plain,
    spl73_45,
    inference(avatar_split_clause,[],[f422,f730]) ).

tff(f730,plain,
    ( spl73_45
  <=> ! [X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),X0: ty,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(list(char),option(ty)),X1: exp(list(char))] :
        ( is_refT(sK23(X1,X2,X3,X4))
        | ~ wTrt(X4,X3,X2,throw(list(char),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_45])]) ).

tff(f422,plain,
    ! [X2: fun(list(char),option(ty)),X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X0: ty,X1: exp(list(char)),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))))))))] :
      ( is_refT(sK23(X1,X2,X3,X4))
      | ~ wTrt(X4,X3,X2,throw(list(char),X1),X0) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f728,plain,
    spl73_44,
    inference(avatar_split_clause,[],[f420,f726]) ).

tff(f726,plain,
    ( spl73_44
  <=> ! [X0: $tType,X2: ty,X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X3: ty,X1: ty] :
        ( widen(X0,X4,X3,X1)
        | ~ widen(X0,X4,X2,X1)
        | ~ widen(X0,X4,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_44])]) ).

tff(f420,plain,
    ! [X0: $tType,X2: ty,X3: ty,X1: ty,X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( widen(X0,X4,X3,X1)
      | ~ widen(X0,X4,X2,X1)
      | ~ widen(X0,X4,X3,X2) ),
    inference(cnf_transformation,[],[f216]) ).

tff(f216,plain,
    ! [X0: $tType,X1: ty,X2: ty,X3: ty,X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( widen(X0,X4,X3,X1)
      | ~ widen(X0,X4,X2,X1)
      | ~ widen(X0,X4,X3,X2) ),
    inference(flattening,[],[f215]) ).

tff(f215,plain,
    ! [X0: $tType,X1: ty,X2: ty,X3: ty,X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( widen(X0,X4,X3,X1)
      | ~ widen(X0,X4,X2,X1)
      | ~ widen(X0,X4,X3,X2) ),
    inference(ennf_transformation,[],[f145]) ).

tff(f145,plain,
    ! [X0: $tType,X1: ty,X2: ty,X3: ty,X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( widen(X0,X4,X3,X2)
     => ( widen(X0,X4,X2,X1)
       => widen(X0,X4,X3,X1) ) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X1: $tType,X11: ty,X21: ty,X22: ty,X12: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X1))))))))] :
      ( widen(X1,X12,X22,X21)
     => ( widen(X1,X12,X21,X11)
       => widen(X1,X12,X22,X11) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_widen__trans) ).

tff(f724,plain,
    spl73_43,
    inference(avatar_split_clause,[],[f397,f722]) ).

tff(f722,plain,
    ( spl73_43
  <=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_43])]) ).

tff(f397,plain,
    ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X2 ),
    inference(cnf_transformation,[],[f300]) ).

tff(f300,plain,
    ! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f208,f299]) ).

tff(f299,plain,
    ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
      ( ? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 )
     => ( product_Pair(X0,X1,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X2 ) ),
    introduced(choice_axiom,[]) ).

tff(f208,plain,
    ! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
    ? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 ),
    inference(ennf_transformation,[],[f127]) ).

tff(f127,plain,
    ! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
      ~ ! [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) != X2 ),
    inference(rectify,[],[f56]) ).

tff(f56,axiom,
    ! [X1: $tType,X2: $tType,X70: product_prod(X1,X2)] :
      ~ ! [X71: X1,X72: X2] : ( product_Pair(X1,X2,X71,X72) != X70 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_PairE) ).

tff(f720,plain,
    spl73_42,
    inference(avatar_split_clause,[],[f396,f718]) ).

tff(f718,plain,
    ( spl73_42
  <=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK11(X0,X1,X2),sK12(X0,X1,X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_42])]) ).

tff(f396,plain,
    ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK11(X0,X1,X2),sK12(X0,X1,X2)) = X2 ),
    inference(cnf_transformation,[],[f298]) ).

tff(f298,plain,
    ! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK11(X0,X1,X2),sK12(X0,X1,X2)) = X2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f207,f297]) ).

tff(f297,plain,
    ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
      ( ? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 )
     => ( product_Pair(X0,X1,sK11(X0,X1,X2),sK12(X0,X1,X2)) = X2 ) ),
    introduced(choice_axiom,[]) ).

tff(f207,plain,
    ! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
    ? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 ),
    inference(ennf_transformation,[],[f126]) ).

tff(f126,plain,
    ! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
      ~ ! [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) != X2 ),
    inference(rectify,[],[f55]) ).

tff(f55,axiom,
    ! [X1: $tType,X2: $tType,X50: product_prod(X1,X2)] :
      ~ ! [X51: X1,X52: X2] : ( product_Pair(X1,X2,X51,X52) != X50 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_prod_Oexhaust) ).

tff(f714,plain,
    ( spl73_41
    | ~ spl73_5
    | ~ spl73_18 ),
    inference(avatar_split_clause,[],[f625,f597,f539,f712]) ).

tff(f712,plain,
    ( spl73_41
  <=> ! [X0: list(char)] :
        ( ( nt = class(X0) )
        | ( class(X0) = class(sK1(class(X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_41])]) ).

tff(f597,plain,
    ( spl73_18
  <=> ! [X0: ty] :
        ( ( class(sK1(X0)) = X0 )
        | ( nt = X0 )
        | ~ is_refT(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_18])]) ).

tff(f625,plain,
    ( ! [X0: list(char)] :
        ( ( nt = class(X0) )
        | ( class(X0) = class(sK1(class(X0))) ) )
    | ~ spl73_5
    | ~ spl73_18 ),
    inference(resolution,[],[f598,f540]) ).

tff(f598,plain,
    ( ! [X0: ty] :
        ( ~ is_refT(X0)
        | ( nt = X0 )
        | ( class(sK1(X0)) = X0 ) )
    | ~ spl73_18 ),
    inference(avatar_component_clause,[],[f597]) ).

tff(f707,plain,
    spl73_40,
    inference(avatar_split_clause,[],[f442,f705]) ).

tff(f705,plain,
    ( spl73_40
  <=> ! [X0: $tType,X2: exp(X0),X4: exp(X0),X3: exp(X0),X1: exp(X0)] :
        ( ( X1 = X3 )
        | ( while(X0,X2,X1) != while(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_40])]) ).

tff(f442,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X4: exp(X0)] :
      ( ( X1 = X3 )
      | ( while(X0,X2,X1) != while(X0,X4,X3) ) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f324,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0)] :
      ( ( ( while(X0,X2,X1) = while(X0,X4,X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( while(X0,X2,X1) != while(X0,X4,X3) ) ) ),
    inference(flattening,[],[f323]) ).

tff(f323,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0)] :
      ( ( ( while(X0,X2,X1) = while(X0,X4,X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( while(X0,X2,X1) != while(X0,X4,X3) ) ) ),
    inference(nnf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0)] :
      ( ( while(X0,X2,X1) = while(X0,X4,X3) )
    <=> ( ( X1 = X3 )
        & ( X2 = X4 ) ) ),
    inference(rectify,[],[f85]) ).

tff(f85,axiom,
    ! [X1: $tType,X95: exp(X1),X96: exp(X1),X97: exp(X1),X98: exp(X1)] :
      ( ( while(X1,X98,X97) = while(X1,X96,X95) )
    <=> ( ( X95 = X97 )
        & ( X96 = X98 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_exp_Osimps_I13_J) ).

tff(f703,plain,
    spl73_39,
    inference(avatar_split_clause,[],[f441,f701]) ).

tff(f701,plain,
    ( spl73_39
  <=> ! [X0: $tType,X4: exp(X0),X3: exp(X0),X2: exp(X0),X1: exp(X0)] :
        ( ( X2 = X4 )
        | ( while(X0,X2,X1) != while(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_39])]) ).

tff(f441,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X4: exp(X0)] :
      ( ( X2 = X4 )
      | ( while(X0,X2,X1) != while(X0,X4,X3) ) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f699,plain,
    spl73_38,
    inference(avatar_split_clause,[],[f439,f697]) ).

tff(f697,plain,
    ( spl73_38
  <=> ! [X0: $tType,X2: list(char),X4: list(char),X3: exp(X0),X1: exp(X0)] :
        ( ( X1 = X3 )
        | ( cast(X0,X2,X1) != cast(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_38])]) ).

tff(f439,plain,
    ! [X0: $tType,X2: list(char),X3: exp(X0),X1: exp(X0),X4: list(char)] :
      ( ( X1 = X3 )
      | ( cast(X0,X2,X1) != cast(X0,X4,X3) ) ),
    inference(cnf_transformation,[],[f322]) ).

tff(f322,plain,
    ! [X0: $tType,X1: exp(X0),X2: list(char),X3: exp(X0),X4: list(char)] :
      ( ( ( cast(X0,X2,X1) = cast(X0,X4,X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( cast(X0,X2,X1) != cast(X0,X4,X3) ) ) ),
    inference(flattening,[],[f321]) ).

tff(f321,plain,
    ! [X0: $tType,X1: exp(X0),X2: list(char),X3: exp(X0),X4: list(char)] :
      ( ( ( cast(X0,X2,X1) = cast(X0,X4,X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( cast(X0,X2,X1) != cast(X0,X4,X3) ) ) ),
    inference(nnf_transformation,[],[f156]) ).

tff(f156,plain,
    ! [X0: $tType,X1: exp(X0),X2: list(char),X3: exp(X0),X4: list(char)] :
      ( ( cast(X0,X2,X1) = cast(X0,X4,X3) )
    <=> ( ( X1 = X3 )
        & ( X2 = X4 ) ) ),
    inference(rectify,[],[f93]) ).

tff(f93,axiom,
    ! [X1: $tType,X7: exp(X1),X27: list(char),X10: exp(X1),X28: list(char)] :
      ( ( cast(X1,X28,X10) = cast(X1,X27,X7) )
    <=> ( ( X7 = X10 )
        & ( X27 = X28 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_exp_Osimps_I2_J) ).

tff(f695,plain,
    spl73_37,
    inference(avatar_split_clause,[],[f438,f693]) ).

tff(f693,plain,
    ( spl73_37
  <=> ! [X0: $tType,X4: list(char),X3: exp(X0),X2: list(char),X1: exp(X0)] :
        ( ( X2 = X4 )
        | ( cast(X0,X2,X1) != cast(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_37])]) ).

tff(f438,plain,
    ! [X0: $tType,X2: list(char),X3: exp(X0),X1: exp(X0),X4: list(char)] :
      ( ( X2 = X4 )
      | ( cast(X0,X2,X1) != cast(X0,X4,X3) ) ),
    inference(cnf_transformation,[],[f322]) ).

tff(f691,plain,
    spl73_36,
    inference(avatar_split_clause,[],[f387,f689]) ).

tff(f689,plain,
    ( spl73_36
  <=> ! [X0: $tType,X2: product_prod(X0,X0),X1: fun(product_prod(X0,X0),bool)] :
        ( member(product_prod(X0,X0),X2,transitive_rtrancl(X0,X1))
        | ~ member(product_prod(X0,X0),X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_36])]) ).

tff(f387,plain,
    ! [X0: $tType,X2: product_prod(X0,X0),X1: fun(product_prod(X0,X0),bool)] :
      ( member(product_prod(X0,X0),X2,transitive_rtrancl(X0,X1))
      | ~ member(product_prod(X0,X0),X2,X1) ),
    inference(cnf_transformation,[],[f206]) ).

tff(f206,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: product_prod(X0,X0)] :
      ( member(product_prod(X0,X0),X2,transitive_rtrancl(X0,X1))
      | ~ member(product_prod(X0,X0),X2,X1) ),
    inference(ennf_transformation,[],[f121]) ).

tff(f121,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: product_prod(X0,X0)] :
      ( member(product_prod(X0,X0),X2,X1)
     => member(product_prod(X0,X0),X2,transitive_rtrancl(X0,X1)) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X1: $tType,X73: fun(product_prod(X1,X1),bool),X74: product_prod(X1,X1)] :
      ( member(product_prod(X1,X1),X74,X73)
     => member(product_prod(X1,X1),X74,transitive_rtrancl(X1,X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_r__into__rtrancl) ).

tff(f678,plain,
    spl73_35,
    inference(avatar_split_clause,[],[f375,f676]) ).

tff(f676,plain,
    ( spl73_35
  <=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( transitive_rtrancl(X0,X1) = transitive_rtrancl(X0,transitive_rtrancl(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_35])]) ).

tff(f375,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( transitive_rtrancl(X0,X1) = transitive_rtrancl(X0,transitive_rtrancl(X0,X1)) ),
    inference(cnf_transformation,[],[f112]) ).

tff(f112,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( transitive_rtrancl(X0,X1) = transitive_rtrancl(X0,transitive_rtrancl(X0,X1)) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X1: $tType,X73: fun(product_prod(X1,X1),bool)] : ( transitive_rtrancl(X1,X73) = transitive_rtrancl(X1,transitive_rtrancl(X1,X73)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rtrancl__idemp) ).

tff(f674,plain,
    spl73_34,
    inference(avatar_split_clause,[],[f362,f671]) ).

tff(f671,plain,
    ( spl73_34
  <=> has_field(product_prod(list(list(char)),exp(list(char))),p,c,f,t,d) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_34])]) ).

tff(f362,plain,
    has_field(product_prod(list(list(char)),exp(list(char))),p,c,f,t,d),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    has_field(product_prod(list(list(char)),exp(list(char))),p,c,f,t,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_has) ).

tff(f668,plain,
    spl73_33,
    inference(avatar_split_clause,[],[f498,f665]) ).

tff(f665,plain,
    ( spl73_33
  <=> widen(product_prod(list(list(char)),exp(list(char))),p,sK72,class(c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_33])]) ).

tff(f498,plain,
    widen(product_prod(list(list(char)),exp(list(char))),p,sK72,class(c)),
    inference(cnf_transformation,[],[f352]) ).

tff(f352,plain,
    ( widen(product_prod(list(list(char)),exp(list(char))),p,sK72,class(c))
    & wTrt(p,h_a,e,e_a,sK72) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f194,f351]) ).

tff(f351,plain,
    ( ? [X0: ty] :
        ( widen(product_prod(list(list(char)),exp(list(char))),p,X0,class(c))
        & wTrt(p,h_a,e,e_a,X0) )
   => ( widen(product_prod(list(list(char)),exp(list(char))),p,sK72,class(c))
      & wTrt(p,h_a,e,e_a,sK72) ) ),
    introduced(choice_axiom,[]) ).

tff(f194,plain,
    ? [X0: ty] :
      ( widen(product_prod(list(list(char)),exp(list(char))),p,X0,class(c))
      & wTrt(p,h_a,e,e_a,X0) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ? [X13: ty] :
      ( widen(product_prod(list(list(char)),exp(list(char))),p,X13,class(c))
      & wTrt(p,h_a,e,e_a,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096EX_AU_O_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_A_G_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_096) ).

tff(f663,plain,
    spl73_32,
    inference(avatar_split_clause,[],[f390,f661]) ).

tff(f661,plain,
    ( spl73_32
  <=> ! [X0: $tType,X2: exp(X0),X1: exp(X0)] :
        ( ( X1 = X2 )
        | ( throw(X0,X2) != throw(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_32])]) ).

tff(f390,plain,
    ! [X0: $tType,X2: exp(X0),X1: exp(X0)] :
      ( ( X1 = X2 )
      | ( throw(X0,X2) != throw(X0,X1) ) ),
    inference(cnf_transformation,[],[f286]) ).

tff(f286,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0)] :
      ( ( ( throw(X0,X2) = throw(X0,X1) )
        | ( X1 != X2 ) )
      & ( ( X1 = X2 )
        | ( throw(X0,X2) != throw(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f123]) ).

tff(f123,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0)] :
      ( ( throw(X0,X2) = throw(X0,X1) )
    <=> ( X1 = X2 ) ),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X1: $tType,X7: exp(X1),X10: exp(X1)] :
      ( ( throw(X1,X10) = throw(X1,X7) )
    <=> ( X7 = X10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_exp_Osimps_I14_J) ).

tff(f659,plain,
    spl73_31,
    inference(avatar_split_clause,[],[f384,f657]) ).

tff(f657,plain,
    ( spl73_31
  <=> ! [X0: $tType,X2: X0,X1: fun(product_prod(X0,X0),bool)] : member(product_prod(X0,X0),product_Pair(X0,X0,X2,X2),transitive_rtrancl(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_31])]) ).

tff(f384,plain,
    ! [X0: $tType,X2: X0,X1: fun(product_prod(X0,X0),bool)] : member(product_prod(X0,X0),product_Pair(X0,X0,X2,X2),transitive_rtrancl(X0,X1)),
    inference(cnf_transformation,[],[f118]) ).

tff(f118,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: X0] : member(product_prod(X0,X0),product_Pair(X0,X0,X2,X2),transitive_rtrancl(X0,X1)),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X1: $tType,X73: fun(product_prod(X1,X1),bool),X36: X1] : member(product_prod(X1,X1),product_Pair(X1,X1,X36,X36),transitive_rtrancl(X1,X73)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rtrancl_Ortrancl__refl) ).

tff(f655,plain,
    spl73_30,
    inference(avatar_split_clause,[],[f367,f652]) ).

tff(f652,plain,
    ( spl73_30
  <=> widen(product_prod(list(list(char)),exp(list(char))),p,sK0,class(c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_30])]) ).

tff(f367,plain,
    widen(product_prod(list(list(char)),exp(list(char))),p,sK0,class(c)),
    inference(cnf_transformation,[],[f272]) ).

tff(f272,plain,
    ( widen(product_prod(list(list(char)),exp(list(char))),p,sK0,class(c))
    & wTrt(p,h_a,e,e_a,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f197,f271]) ).

tff(f271,plain,
    ( ? [X0: ty] :
        ( widen(product_prod(list(list(char)),exp(list(char))),p,X0,class(c))
        & wTrt(p,h_a,e,e_a,X0) )
   => ( widen(product_prod(list(list(char)),exp(list(char))),p,sK0,class(c))
      & wTrt(p,h_a,e,e_a,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f197,plain,
    ? [X0: ty] :
      ( widen(product_prod(list(list(char)),exp(list(char))),p,X0,class(c))
      & wTrt(p,h_a,e,e_a,X0) ),
    inference(ennf_transformation,[],[f106]) ).

tff(f106,plain,
    ~ ! [X0: ty] :
        ( wTrt(p,h_a,e,e_a,X0)
       => ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,class(c)) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ~ ! [X13: ty] :
        ( wTrt(p,h_a,e,e_a,X13)
       => ~ widen(product_prod(list(list(char)),exp(list(char))),p,X13,class(c)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096_B_Bthesis_O_A_I_B_BU_O_A_091_124_AP_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_AU_059_AP_A_092_060turnstile_062_AU_A_092_060le_062_AClass_AC_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

tff(f650,plain,
    ( spl73_29
    | ~ spl73_7
    | ~ spl73_26 ),
    inference(avatar_split_clause,[],[f646,f635,f547,f648]) ).

tff(f648,plain,
    ( spl73_29
  <=> ! [X0: list(char)] : ( class(X0) = class(sK15(class(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_29])]) ).

tff(f635,plain,
    ( spl73_26
  <=> ! [X0: $tType,X2: list(char),X1: ty,X3: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
        ( ( class(sK15(X1)) = X1 )
        | ~ widen(X0,X3,class(X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_26])]) ).

tff(f646,plain,
    ( ! [X0: list(char)] : ( class(X0) = class(sK15(class(X0))) )
    | ~ spl73_7
    | ~ spl73_26 ),
    inference(resolution,[],[f636,f548]) ).

tff(f636,plain,
    ( ! [X0: $tType,X2: list(char),X3: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X1: ty] :
        ( ~ widen(X0,X3,class(X2),X1)
        | ( class(sK15(X1)) = X1 ) )
    | ~ spl73_26 ),
    inference(avatar_component_clause,[],[f635]) ).

tff(f645,plain,
    spl73_28,
    inference(avatar_split_clause,[],[f446,f643]) ).

tff(f643,plain,
    ( spl73_28
  <=> ! [X0: $tType,X2: list(char),X3: exp(X0),X4: exp(X0),X5: exp(X0),X1: list(char)] : ( fAcc(X0,X3,X2,X1) != while(X0,X5,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_28])]) ).

tff(f446,plain,
    ! [X0: $tType,X2: list(char),X3: exp(X0),X1: list(char),X4: exp(X0),X5: exp(X0)] : ( fAcc(X0,X3,X2,X1) != while(X0,X5,X4) ),
    inference(cnf_transformation,[],[f160]) ).

tff(f160,plain,
    ! [X0: $tType,X1: list(char),X2: list(char),X3: exp(X0),X4: exp(X0),X5: exp(X0)] : ( fAcc(X0,X3,X2,X1) != while(X0,X5,X4) ),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X1: $tType,X89: list(char),X90: list(char),X91: exp(X1),X101: exp(X1),X102: exp(X1)] : ( fAcc(X1,X91,X90,X89) != while(X1,X102,X101) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_exp_Osimps_I165_J) ).

tff(f641,plain,
    spl73_27,
    inference(avatar_split_clause,[],[f445,f639]) ).

tff(f639,plain,
    ( spl73_27
  <=> ! [X0: $tType,X2: exp(X0),X3: exp(X0),X4: exp(X0),X5: exp(X0),X1: exp(X0)] : ( cond(X0,X3,X2,X1) != while(X0,X5,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_27])]) ).

tff(f445,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X4: exp(X0),X5: exp(X0)] : ( cond(X0,X3,X2,X1) != while(X0,X5,X4) ),
    inference(cnf_transformation,[],[f159]) ).

tff(f159,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0),X5: exp(X0)] : ( cond(X0,X3,X2,X1) != while(X0,X5,X4) ),
    inference(rectify,[],[f100]) ).

tff(f100,axiom,
    ! [X1: $tType,X107: exp(X1),X99: exp(X1),X100: exp(X1),X101: exp(X1),X102: exp(X1)] : ( while(X1,X102,X101) != cond(X1,X100,X99,X107) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_exp_Osimps_I215_J) ).

tff(f637,plain,
    spl73_26,
    inference(avatar_split_clause,[],[f402,f635]) ).

tff(f402,plain,
    ! [X0: $tType,X2: list(char),X3: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X1: ty] :
      ( ( class(sK15(X1)) = X1 )
      | ~ widen(X0,X3,class(X2),X1) ),
    inference(cnf_transformation,[],[f302]) ).

tff(f302,plain,
    ! [X0: $tType,X1: ty,X2: list(char),X3: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( ( class(sK15(X1)) = X1 )
      | ~ widen(X0,X3,class(X2),X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f209,f301]) ).

tff(f301,plain,
    ! [X1: ty] :
      ( ? [X4: list(char)] : ( class(X4) = X1 )
     => ( class(sK15(X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f209,plain,
    ! [X0: $tType,X1: ty,X2: list(char),X3: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( ? [X4: list(char)] : ( class(X4) = X1 )
      | ~ widen(X0,X3,class(X2),X1) ),
    inference(ennf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: $tType,X1: ty,X2: list(char),X3: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
      ( widen(X0,X3,class(X2),X1)
     => ? [X4: list(char)] : ( class(X4) = X1 ) ),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X1: $tType,X11: ty,X24: list(char),X12: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X1))))))))] :
      ( widen(X1,X12,class(X24),X11)
     => ? [X29: list(char)] : ( class(X29) = X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Class__widen) ).

tff(f633,plain,
    spl73_25,
    inference(avatar_split_clause,[],[f359,f630]) ).

tff(f630,plain,
    ( spl73_25
  <=> wTrt(p,ha,e,fAcc(list(char),ea,f,d),t) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_25])]) ).

tff(f359,plain,
    wTrt(p,ha,e,fAcc(list(char),ea,f,d),t),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    wTrt(p,ha,e,fAcc(list(char),ea,f,d),t),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_wt) ).

tff(f623,plain,
    spl73_24,
    inference(avatar_split_clause,[],[f416,f621]) ).

tff(f621,plain,
    ( spl73_24
  <=> ! [X0: $tType,X2: exp(X0),X4: list(char),X3: exp(X0),X1: exp(X0)] : ( while(X0,X2,X1) != cast(X0,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_24])]) ).

tff(f416,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X4: list(char)] : ( while(X0,X2,X1) != cast(X0,X4,X3) ),
    inference(cnf_transformation,[],[f141]) ).

tff(f141,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: list(char)] : ( while(X0,X2,X1) != cast(X0,X4,X3) ),
    inference(rectify,[],[f98]) ).

tff(f98,axiom,
    ! [X1: $tType,X101: exp(X1),X102: exp(X1),X91: exp(X1),X108: list(char)] : ( while(X1,X102,X101) != cast(X1,X108,X91) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_exp_Osimps_I64_J) ).

tff(f619,plain,
    spl73_23,
    inference(avatar_split_clause,[],[f414,f617]) ).

tff(f617,plain,
    ( spl73_23
  <=> ! [X0: $tType,X4: exp(X0),X3: list(char),X2: list(char),X1: exp(X0)] : ( throw(X0,X1) != fAcc(X0,X4,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_23])]) ).

tff(f414,plain,
    ! [X0: $tType,X2: list(char),X3: list(char),X1: exp(X0),X4: exp(X0)] : ( throw(X0,X1) != fAcc(X0,X4,X3,X2) ),
    inference(cnf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: $tType,X1: exp(X0),X2: list(char),X3: list(char),X4: exp(X0)] : ( throw(X0,X1) != fAcc(X0,X4,X3,X2) ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X1: $tType,X92: exp(X1),X89: list(char),X90: list(char),X91: exp(X1)] : ( throw(X1,X92) != fAcc(X1,X91,X90,X89) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_exp_Osimps_I166_J) ).

tff(f615,plain,
    spl73_22,
    inference(avatar_split_clause,[],[f412,f613]) ).

tff(f613,plain,
    ( spl73_22
  <=> ! [X0: $tType,X4: exp(X0),X3: exp(X0),X2: exp(X0),X1: exp(X0)] : ( throw(X0,X1) != cond(X0,X4,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_22])]) ).

tff(f412,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0),X4: exp(X0)] : ( throw(X0,X1) != cond(X0,X4,X3,X2) ),
    inference(cnf_transformation,[],[f137]) ).

tff(f137,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0),X4: exp(X0)] : ( throw(X0,X1) != cond(X0,X4,X3,X2) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X1: $tType,X92: exp(X1),X107: exp(X1),X99: exp(X1),X100: exp(X1)] : ( throw(X1,X92) != cond(X1,X100,X99,X107) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_exp_Osimps_I216_J) ).

tff(f611,plain,
    spl73_21,
    inference(avatar_split_clause,[],[f389,f609]) ).

tff(f609,plain,
    ( spl73_21
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_21])]) ).

tff(f389,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( member(X0,X2,X1)
      | ~ pp(aa(X0,bool,X1,X2)) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) )
      & ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f122]) ).

tff(f122,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( member(X0,X2,X1)
    <=> pp(aa(X0,bool,X1,X2)) ),
    inference(rectify,[],[f76]) ).

tff(f76,axiom,
    ! [X1: $tType,X93: fun(X1,bool),X55: X1] :
      ( member(X1,X55,X93)
    <=> pp(aa(X1,bool,X93,X55)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).

tff(f607,plain,
    spl73_20,
    inference(avatar_split_clause,[],[f388,f605]) ).

tff(f605,plain,
    ( spl73_20
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_20])]) ).

tff(f388,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( pp(aa(X0,bool,X1,X2))
      | ~ member(X0,X2,X1) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f603,plain,
    spl73_19,
    inference(avatar_split_clause,[],[f372,f601]) ).

tff(f372,plain,
    ! [X0: ty] :
      ( ( class(sK2(X0)) = X0 )
      | ( nt = X0 )
      | ~ is_refT(X0) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f279,plain,
    ! [X0: ty] :
      ( ( is_refT(X0)
        | ( ! [X1: list(char)] : ( class(X1) != X0 )
          & ( nt != X0 ) ) )
      & ( ( class(sK2(X0)) = X0 )
        | ( nt = X0 )
        | ~ is_refT(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f277,f278]) ).

tff(f278,plain,
    ! [X0: ty] :
      ( ? [X2: list(char)] : ( class(X2) = X0 )
     => ( class(sK2(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f277,plain,
    ! [X0: ty] :
      ( ( is_refT(X0)
        | ( ! [X1: list(char)] : ( class(X1) != X0 )
          & ( nt != X0 ) ) )
      & ( ? [X2: list(char)] : ( class(X2) = X0 )
        | ( nt = X0 )
        | ~ is_refT(X0) ) ),
    inference(rectify,[],[f276]) ).

tff(f276,plain,
    ! [X0: ty] :
      ( ( is_refT(X0)
        | ( ! [X1: list(char)] : ( class(X1) != X0 )
          & ( nt != X0 ) ) )
      & ( ? [X1: list(char)] : ( class(X1) = X0 )
        | ( nt = X0 )
        | ~ is_refT(X0) ) ),
    inference(flattening,[],[f275]) ).

tff(f275,plain,
    ! [X0: ty] :
      ( ( is_refT(X0)
        | ( ! [X1: list(char)] : ( class(X1) != X0 )
          & ( nt != X0 ) ) )
      & ( ? [X1: list(char)] : ( class(X1) = X0 )
        | ( nt = X0 )
        | ~ is_refT(X0) ) ),
    inference(nnf_transformation,[],[f111]) ).

tff(f111,plain,
    ! [X0: ty] :
      ( is_refT(X0)
    <=> ( ? [X1: list(char)] : ( class(X1) = X0 )
        | ( nt = X0 ) ) ),
    inference(rectify,[],[f46]) ).

tff(f46,axiom,
    ! [X14: ty] :
      ( is_refT(X14)
    <=> ( ? [X64: list(char)] : ( class(X64) = X14 )
        | ( nt = X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_is__refT__def) ).

tff(f599,plain,
    spl73_18,
    inference(avatar_split_clause,[],[f371,f597]) ).

tff(f371,plain,
    ! [X0: ty] :
      ( ( class(sK1(X0)) = X0 )
      | ( nt = X0 )
      | ~ is_refT(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f274,plain,
    ! [X0: ty] :
      ( ( class(sK1(X0)) = X0 )
      | ( nt = X0 )
      | ~ is_refT(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f199,f273]) ).

tff(f273,plain,
    ! [X0: ty] :
      ( ? [X1: list(char)] : ( class(X1) = X0 )
     => ( class(sK1(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f199,plain,
    ! [X0: ty] :
      ( ? [X1: list(char)] : ( class(X1) = X0 )
      | ( nt = X0 )
      | ~ is_refT(X0) ),
    inference(flattening,[],[f198]) ).

tff(f198,plain,
    ! [X0: ty] :
      ( ? [X1: list(char)] : ( class(X1) = X0 )
      | ( nt = X0 )
      | ~ is_refT(X0) ),
    inference(ennf_transformation,[],[f110]) ).

tff(f110,plain,
    ! [X0: ty] :
      ( is_refT(X0)
     => ( ( nt != X0 )
       => ~ ! [X1: list(char)] : ( class(X1) != X0 ) ) ),
    inference(rectify,[],[f48]) ).

tff(f48,axiom,
    ! [X11: ty] :
      ( is_refT(X11)
     => ( ( nt != X11 )
       => ~ ! [X26: list(char)] : ( class(X26) != X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_refTE) ).

tff(f593,plain,
    spl73_17,
    inference(avatar_split_clause,[],[f400,f591]) ).

tff(f591,plain,
    ( spl73_17
  <=> ! [X0: $tType,X3: exp(X0),X2: exp(X0),X1: exp(X0)] : ( throw(X0,X1) != while(X0,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_17])]) ).

tff(f400,plain,
    ! [X0: $tType,X2: exp(X0),X3: exp(X0),X1: exp(X0)] : ( throw(X0,X1) != while(X0,X3,X2) ),
    inference(cnf_transformation,[],[f130]) ).

tff(f130,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: exp(X0)] : ( throw(X0,X1) != while(X0,X3,X2) ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X1: $tType,X92: exp(X1),X99: exp(X1),X100: exp(X1)] : ( throw(X1,X92) != while(X1,X100,X99) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_exp_Osimps_I220_J) ).

tff(f589,plain,
    spl73_16,
    inference(avatar_split_clause,[],[f398,f587]) ).

tff(f587,plain,
    ( spl73_16
  <=> ! [X0: $tType,X3: list(char),X2: exp(X0),X1: exp(X0)] : ( throw(X0,X1) != cast(X0,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_16])]) ).

tff(f398,plain,
    ! [X0: $tType,X2: exp(X0),X3: list(char),X1: exp(X0)] : ( throw(X0,X1) != cast(X0,X3,X2) ),
    inference(cnf_transformation,[],[f128]) ).

tff(f128,plain,
    ! [X0: $tType,X1: exp(X0),X2: exp(X0),X3: list(char)] : ( throw(X0,X1) != cast(X0,X3,X2) ),
    inference(rectify,[],[f95]) ).

tff(f95,axiom,
    ! [X1: $tType,X92: exp(X1),X91: exp(X1),X108: list(char)] : ( throw(X1,X92) != cast(X1,X108,X91) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_exp_Osimps_I66_J) ).

tff(f585,plain,
    spl73_15,
    inference(avatar_split_clause,[],[f386,f583]) ).

tff(f583,plain,
    ( spl73_15
  <=> ! [X2: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
        ( hext(X2,X0)
        | ~ hext(X1,X0)
        | ~ hext(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_15])]) ).

tff(f386,plain,
    ! [X2: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
      ( hext(X2,X0)
      | ~ hext(X1,X0)
      | ~ hext(X2,X1) ),
    inference(cnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
      ( hext(X2,X0)
      | ~ hext(X1,X0)
      | ~ hext(X2,X1) ),
    inference(flattening,[],[f204]) ).

tff(f204,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
      ( hext(X2,X0)
      | ~ hext(X1,X0)
      | ~ hext(X2,X1) ),
    inference(ennf_transformation,[],[f120]) ).

tff(f120,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X2: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
      ( hext(X2,X1)
     => ( hext(X1,X0)
       => hext(X2,X0) ) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X66: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X61: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X19: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] :
      ( hext(X19,X61)
     => ( hext(X61,X66)
       => hext(X19,X66) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_hext__trans) ).

tff(f581,plain,
    spl73_14,
    inference(avatar_split_clause,[],[f380,f579]) ).

tff(f579,plain,
    ( spl73_14
  <=> ! [X0: list(char),X1: list(char)] :
        ( ( X0 = X1 )
        | ( class(X0) != class(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_14])]) ).

tff(f380,plain,
    ! [X0: list(char),X1: list(char)] :
      ( ( X0 = X1 )
      | ( class(X0) != class(X1) ) ),
    inference(cnf_transformation,[],[f284]) ).

tff(f284,plain,
    ! [X0: list(char),X1: list(char)] :
      ( ( ( class(X0) = class(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( class(X0) != class(X1) ) ) ),
    inference(nnf_transformation,[],[f115]) ).

tff(f115,plain,
    ! [X0: list(char),X1: list(char)] :
      ( ( class(X0) = class(X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f22]) ).

tff(f22,axiom,
    ! [X27: list(char),X28: list(char)] :
      ( ( class(X28) = class(X27) )
    <=> ( X27 = X28 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Type_Oty_Oinject) ).

tff(f577,plain,
    spl73_13,
    inference(avatar_split_clause,[],[f358,f574]) ).

tff(f574,plain,
    ( spl73_13
  <=> wTrt(p,ha,e,ea,class(c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_13])]) ).

tff(f358,plain,
    wTrt(p,ha,e,ea,class(c)),
    inference(cnf_transformation,[],[f16]) ).

tff(f16,axiom,
    wTrt(p,ha,e,ea,class(c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_wte) ).

tff(f572,plain,
    spl73_12,
    inference(avatar_split_clause,[],[f499,f569]) ).

tff(f499,plain,
    wTrt(p,h_a,e,e_a,nt),
    inference(definition_unfolding,[],[f357,f356]) ).

tff(f356,plain,
    u = nt,
    inference(cnf_transformation,[],[f14]) ).

tff(f14,axiom,
    u = nt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096U_A_061_ANT_096) ).

tff(f357,plain,
    wTrt(p,h_a,e,e_a,u),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    wTrt(p,h_a,e,e_a,u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_wte_H) ).

tff(f567,plain,
    spl73_11,
    inference(avatar_split_clause,[],[f497,f564]) ).

tff(f497,plain,
    wTrt(p,h_a,e,e_a,sK72),
    inference(cnf_transformation,[],[f352]) ).

tff(f562,plain,
    spl73_10,
    inference(avatar_split_clause,[],[f383,f560]) ).

tff(f560,plain,
    ( spl73_10
  <=> ! [X0: $tType,X2: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X1: list(char)] : widen(X0,X2,nt,class(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_10])]) ).

tff(f383,plain,
    ! [X0: $tType,X2: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X1: list(char)] : widen(X0,X2,nt,class(X1)),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,plain,
    ! [X0: $tType,X1: list(char),X2: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] : widen(X0,X2,nt,class(X1)),
    inference(rectify,[],[f18]) ).

tff(f18,axiom,
    ! [X0: $tType,X24: list(char),X12: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] : widen(X0,X12,nt,class(X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_widen__null) ).

tff(f558,plain,
    spl73_9,
    inference(avatar_split_clause,[],[f366,f555]) ).

tff(f366,plain,
    wTrt(p,h_a,e,e_a,sK0),
    inference(cnf_transformation,[],[f272]) ).

tff(f553,plain,
    spl73_8,
    inference(avatar_split_clause,[],[f353,f551]) ).

tff(f353,plain,
    ! [X0: ty] :
      ( ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t)
      | ~ wTrt(p,h_a,e,fAcc(list(char),e_a,f,d),X0) ),
    inference(cnf_transformation,[],[f196]) ).

tff(f196,plain,
    ! [X0: ty] :
      ( ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t)
      | ~ wTrt(p,h_a,e,fAcc(list(char),e_a,f,d),X0) ),
    inference(ennf_transformation,[],[f105]) ).

tff(f105,plain,
    ~ ? [X0: ty] :
        ( widen(product_prod(list(list(char)),exp(list(char))),p,X0,t)
        & wTrt(p,h_a,e,fAcc(list(char),e_a,f,d),X0) ),
    inference(rectify,[],[f104]) ).

tff(f104,negated_conjecture,
    ~ ? [X109: ty] :
        ( widen(product_prod(list(list(char)),exp(list(char))),p,X109,t)
        & wTrt(p,h_a,e,fAcc(list(char),e_a,f,d),X109) ),
    inference(negated_conjecture,[],[f103]) ).

tff(f103,conjecture,
    ? [X109: ty] :
      ( widen(product_prod(list(list(char)),exp(list(char))),p,X109,t)
      & wTrt(p,h_a,e,fAcc(list(char),e_a,f,d),X109) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f549,plain,
    spl73_7,
    inference(avatar_split_clause,[],[f382,f547]) ).

tff(f382,plain,
    ! [X0: $tType,X2: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X1: ty] : widen(X0,X2,X1,X1),
    inference(cnf_transformation,[],[f116]) ).

tff(f116,plain,
    ! [X0: $tType,X1: ty,X2: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] : widen(X0,X2,X1,X1),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0: $tType,X11: ty,X12: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] : widen(X0,X12,X11,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_widen__refl) ).

tff(f545,plain,
    spl73_6,
    inference(avatar_split_clause,[],[f369,f543]) ).

tff(f543,plain,
    ( spl73_6
  <=> ! [X0: list(char)] : ( nt != class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_6])]) ).

tff(f369,plain,
    ! [X0: list(char)] : ( nt != class(X0) ),
    inference(cnf_transformation,[],[f108]) ).

tff(f108,plain,
    ! [X0: list(char)] : ( nt != class(X0) ),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X37: list(char)] : ( nt != class(X37) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Type_Oty_Osimps_I21_J) ).

tff(f541,plain,
    spl73_5,
    inference(avatar_split_clause,[],[f501,f539]) ).

tff(f501,plain,
    ! [X1: list(char)] : is_refT(class(X1)),
    inference(equality_resolution,[],[f374]) ).

tff(f374,plain,
    ! [X0: ty,X1: list(char)] :
      ( is_refT(X0)
      | ( class(X1) != X0 ) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f537,plain,
    spl73_4,
    inference(avatar_split_clause,[],[f368,f535]) ).

tff(f535,plain,
    ( spl73_4
  <=> ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] : hext(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_4])]) ).

tff(f368,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] : hext(X0,X0),
    inference(cnf_transformation,[],[f107]) ).

tff(f107,plain,
    ! [X0: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] : hext(X0,X0),
    inference(rectify,[],[f49]) ).

tff(f49,axiom,
    ! [X19: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val)))))] : hext(X19,X19),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_hext__refl) ).

tff(f533,plain,
    spl73_3,
    inference(avatar_split_clause,[],[f502,f530]) ).

tff(f530,plain,
    ( spl73_3
  <=> is_refT(nt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_3])]) ).

tff(f502,plain,
    is_refT(nt),
    inference(equality_resolution,[],[f373]) ).

tff(f373,plain,
    ! [X0: ty] :
      ( is_refT(X0)
      | ( nt != X0 ) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f528,plain,
    spl73_2,
    inference(avatar_split_clause,[],[f355,f525]) ).

tff(f525,plain,
    ( spl73_2
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_2])]) ).

tff(f355,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f523,plain,
    ~ spl73_1,
    inference(avatar_split_clause,[],[f354,f520]) ).

tff(f520,plain,
    ( spl73_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_1])]) ).

tff(f354,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWW568_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 19:30:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (27223)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39  % (27226)WARNING: value z3 for option sas not known
% 0.13/0.39  % (27225)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39  % (27227)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39  % (27226)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.39  % (27228)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.39  % (27224)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39  % (27229)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.39  % (27230)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.40  % (27230)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40  % Exception at run slice level
% 0.13/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.40  % Exception at run slice level
% 0.13/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.40  % Exception at run slice level
% 0.13/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.42  % (27228)First to succeed.
% 0.13/0.42  % (27231)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.42  % (27232)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.13/0.42  % (27233)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.13/0.42  % (27229)Also succeeded, but the first one will report.
% 0.21/0.42  % (27231)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42  % (27232)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42  % Exception at run slice level
% 0.21/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43  % (27228)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27223"
% 0.21/0.43  % (27228)Refutation found. Thanks to Tanya!
% 0.21/0.43  % SZS status Theorem for theBenchmark
% 0.21/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43  % (27228)------------------------------
% 0.21/0.43  % (27228)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.43  % (27228)Termination reason: Refutation
% 0.21/0.43  
% 0.21/0.43  % (27228)Memory used [KB]: 1383
% 0.21/0.43  % (27228)Time elapsed: 0.034 s
% 0.21/0.43  % (27228)Instructions burned: 59 (million)
% 0.21/0.43  % (27223)Success in time 0.072 s
%------------------------------------------------------------------------------