TSTP Solution File: SWW469+5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n023.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  : 600s
% DateTime : Thu Jul 21 00:50:18 EDT 2022

% Result   : Theorem 2.31s 2.54s
% Output   : CNFRefutation 2.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :  100
% Syntax   : Number of formulae    :  637 ( 410 unt;  37 typ;   0 def)
%            Number of atoms       : 3127 (1363 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives : 34825 ( 899   ~; 869   |;  34   &;32931   @)
%                                         (  20 <=>;  72  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   67 (  67   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   40 (  37 usr;  11 con; 0-7 aty)
%            Number of variables   : 2168 (   0   ^2164   !;   4   ?;2168   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_bool,type,
    bool: $i ).

thf(tp_cl_HOL_Oequal,type,
    cl_HOL_Oequal: $i > $o ).

thf(tp_collect,type,
    collect: $i > $i ).

thf(tp_com,type,
    com: $i ).

thf(tp_enum,type,
    enum: $i > $o ).

thf(tp_equal_equal,type,
    equal_equal: $i > $i ).

thf(tp_fequal,type,
    fequal: $i > $i ).

thf(tp_fun,type,
    fun: $i > $i > $i ).

thf(tp_hAPP,type,
    hAPP: $i > $i > $i > $i > $i ).

thf(tp_hBOOL,type,
    hBOOL: $i > $o ).

thf(tp_hoare_1580379338ep_set,type,
    hoare_1580379338ep_set: $i > $i ).

thf(tp_hoare_1883395792gleton,type,
    hoare_1883395792gleton: $i ).

thf(tp_hoare_2037801986triple,type,
    hoare_2037801986triple: $i > $i ).

thf(tp_hoare_244953527triple,type,
    hoare_244953527triple: $i > $i ).

thf(tp_hoare_509422987triple,type,
    hoare_509422987triple: $i > $i ).

thf(tp_induct_equal,type,
    induct_equal: $i > $i ).

thf(tp_induct_false,type,
    induct_false: $i ).

thf(tp_induct_true,type,
    induct_true: $i ).

thf(tp_member,type,
    member: $i > $i ).

thf(tp_node,type,
    node: $i > $i > $i ).

thf(tp_sK10_X_2,type,
    sK10_X_2: $i > $i > $i > $i ).

thf(tp_sK11_S,type,
    sK11_S: $i ).

thf(tp_sK12_SY158,type,
    sK12_SY158: $i ).

thf(tp_sK1_T,type,
    sK1_T: $i ).

thf(tp_sK2_X_2,type,
    sK2_X_2: $i > $i > $i > $i > $i ).

thf(tp_sK3_X_2,type,
    sK3_X_2: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK4_Y_2,type,
    sK4_Y_2: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK5_Y_2,type,
    sK5_Y_2: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK6_X_2,type,
    sK6_X_2: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_sK7_Y_2,type,
    sK7_Y_2: $i > $i > $i ).

thf(tp_sK8_Y_2,type,
    sK8_Y_2: $i > $i > $i > $i ).

thf(tp_sK9_X_2,type,
    sK9_X_2: $i > $i > $i ).

thf(tp_state,type,
    state: $i ).

thf(tp_sum_sum,type,
    sum_sum: $i > $i > $i ).

thf(tp_ti,type,
    ti: $i > $i > $i ).

thf(tp_type_definition,type,
    type_definition: $i > $i > $i ).

thf(tp_undefined,type,
    undefined: $i > $i ).

thf(1,axiom,
    ! [X_a: $i,X: $i,Y: $i] :
      ( ( ( ti @ X_a @ X )
       != ( ti @ X_a @ Y ) )
      | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

thf(2,axiom,
    ! [X_a: $i,X: $i,Y: $i] :
      ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
      | ( ( ti @ X_a @ X )
        = ( ti @ X_a @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

thf(3,axiom,
    ! [T_1: $i,A: $i] :
      ( ( ti @ T_1 @ ( ti @ T_1 @ A ) )
      = ( ti @ T_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).

thf(4,axiom,
    ! [T_1_1: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ T_1_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal) ).

thf(5,axiom,
    ! [T_2: $i,T_1_1: $i] : ( cl_HOL_Oequal @ ( sum_sum @ T_2 @ T_1_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).

thf(6,axiom,
    cl_HOL_Oequal @ state,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).

thf(7,axiom,
    cl_HOL_Oequal @ bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).

thf(8,axiom,
    cl_HOL_Oequal @ com,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).

thf(9,axiom,
    ! [T_2: $i,T_1_1: $i] :
      ( ( ( cl_HOL_Oequal @ T_1_1 )
        & ( enum @ T_2 ) )
     => ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).

thf(10,axiom,
    ! [T_2: $i,T_1_1: $i] :
      ( ( ( enum @ T_1_1 )
        & ( enum @ T_2 ) )
     => ( enum @ ( fun @ T_2 @ T_1_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).

thf(11,axiom,
    enum @ bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).

thf(12,axiom,
    ! [T_2: $i,T_1_1: $i] :
      ( ( ( enum @ T_1_1 )
        & ( enum @ T_2 ) )
     => ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).

thf(13,axiom,
    ! [X_a: $i,P: $i] :
      ( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ P )
      = ( ti @ ( fun @ X_a @ bool ) @ P ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Collect__def) ).

thf(14,axiom,
    ! [X_a: $i,X_1: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
    <=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_mem__def) ).

thf(15,axiom,
    ! [X_a: $i,X_b: $i,F: $i,G: $i] :
      ( ! [X_2: $i] :
          ( ( hAPP @ X_a @ X_b @ F @ X_2 )
          = ( hAPP @ X_a @ X_b @ G @ X_2 ) )
     => ( ( ti @ ( fun @ X_a @ X_b ) @ F )
        = ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ext) ).

thf(16,axiom,
    ! [X_a: $i,X_1: $i,Y_1: $i] :
      ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
    <=> ( ( ti @ X_a @ X_1 )
        = ( ti @ X_a @ Y_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_induct__equal__def) ).

thf(17,axiom,
    hBOOL @ induct_true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_induct__true__def) ).

thf(18,axiom,
    hBOOL @ induct_true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_induct__trueI) ).

thf(19,axiom,
    ! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
       => ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) )
         => ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_type__definition_ORep__induct) ).

thf(20,axiom,
    ! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( ! [Y_2: $i] :
            ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) ) ) )
       => ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_type__definition_OAbs__induct) ).

thf(21,axiom,
    ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ~ ! [Y_2: $i] :
            ( ( ( ti @ X_a @ X_1 )
              = ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) )
           => ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_type__definition_OAbs__cases) ).

thf(22,axiom,
    ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
       => ~ ! [X_2: $i] :
              ( ( ti @ X_b @ Y_1 )
             != ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_type__definition_ORep__cases) ).

thf(23,axiom,
    ~ ( hBOOL @ induct_false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_induct__false__def) ).

thf(24,axiom,
    ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_type__definition_ORep) ).

thf(25,axiom,
    ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
        = ( ti @ X_a @ X_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_type__definition_ORep__inverse) ).

thf(26,axiom,
    ! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
          = ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
      <=> ( ( ti @ X_a @ X_1 )
          = ( ti @ X_a @ Y_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_type__definition_ORep__inject) ).

thf(27,axiom,
    ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
       => ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
          = ( ti @ X_b @ Y_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_type__definition_OAbs__inverse) ).

thf(28,axiom,
    ! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
       => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
         => ( ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
              = ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
          <=> ( ( ti @ X_b @ X_1 )
              = ( ti @ X_b @ Y_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_type__definition_OAbs__inject) ).

thf(29,axiom,
    ! [X_a: $i,X_1: $i] :
      ~ ! [Y_2: $i] :
          ( ( X_1
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) )
         => ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Abs__triple__cases) ).

thf(30,axiom,
    ! [X_a: $i,X_1: $i,P: $i] :
      ( ! [Y_2: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
         => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) ) ) )
     => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Abs__triple__induct) ).

thf(31,axiom,
    ! [X_a: $i,Y_1: $i,X_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
       => ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
        <=> ( X_1 = Y_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Abs__triple__inject) ).

thf(32,axiom,
    ! [X_a: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_type__definition__triple) ).

thf(33,axiom,
    ! [X_a: $i,Y_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
     => ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
        = Y_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Abs__triple__inverse) ).

thf(34,axiom,
    ! [X_a: $i,Y_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
     => ~ ! [X_2: $i] :
            ( Y_1
           != ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Rep__triple__cases) ).

thf(35,axiom,
    ! [X_a: $i,P: $i,Y_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
     => ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) )
       => ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Rep__triple__induct) ).

thf(36,axiom,
    ! [X_a: $i,X_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Rep__triple) ).

thf(37,axiom,
    ! [X_a: $i,X_1: $i] :
      ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) )
      = X_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Rep__triple__inverse) ).

thf(38,axiom,
    ! [X_a: $i] :
      ( ( cl_HOL_Oequal @ X_a )
     => ( ( fequal @ X_a )
        = ( equal_equal @ X_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_eq__equal) ).

thf(39,axiom,
    ! [X_a: $i] :
      ( ( cl_HOL_Oequal @ X_a )
     => ! [X_1: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
        <=> ( ( ti @ X_a @ X_1 )
            = ( ti @ X_a @ Y_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_equal__eq) ).

thf(40,axiom,
    ! [X_a: $i] :
      ( ( cl_HOL_Oequal @ X_a )
     => ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_equal__refl) ).

thf(41,axiom,
    ! [X_a: $i] :
      ( ( cl_HOL_Oequal @ X_a )
     => ( ( equal_equal @ X_a )
        = ( fequal @ X_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_equal) ).

thf(42,axiom,
    ! [X_a: $i,X_1: $i,Y_1: $i] :
      ( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
        = ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
    <=> ( X_1 = Y_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).

thf(43,axiom,
    ! [X_a: $i,X_1: $i,Y_1: $i] :
      ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
    <=> ( X_1 = Y_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).

thf(44,axiom,
    ( ( hBOOL @ hoare_1883395792gleton )
  <=> ? [S: $i,T: $i] :
        ( ( ti @ state @ S )
       != ( ti @ state @ T ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).

thf(45,axiom,
    ! [X_b: $i] :
      ( ( ti @ ( fun @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( member @ X_b ) )
      = ( member @ X_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).

thf(46,axiom,
    ! [X_a: $i,X_b: $i,B_1: $i,B_2: $i] :
      ( ( ti @ X_a @ ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) )
      = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).

thf(47,axiom,
    ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
      ( ( hAPP @ X_b @ X_a @ B_1 @ ( ti @ X_b @ B_2 ) )
      = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).

thf(48,axiom,
    ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
      ( ( hAPP @ X_b @ X_a @ ( ti @ ( fun @ X_b @ X_a ) @ B_1 ) @ B_2 )
      = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).

thf(49,axiom,
    ! [X_a: $i] :
      ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
      = ( fequal @ X_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).

thf(50,axiom,
    ! [X_a: $i,X_b: $i] :
      ( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) ) @ ( type_definition @ X_a @ X_b ) )
      = ( type_definition @ X_a @ X_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Typedef_Otype__definition_res) ).

thf(51,axiom,
    ! [X_a: $i] :
      ( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
      = ( collect @ X_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).

thf(52,axiom,
    ! [X_a: $i] :
      ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ X_a ) )
      = ( hoare_1580379338ep_set @ X_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res) ).

thf(53,axiom,
    ! [X_a: $i] :
      ( ( ti @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) )
      = ( hoare_2037801986triple @ X_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res) ).

thf(54,axiom,
    ! [X_a: $i] :
      ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) )
      = ( hoare_244953527triple @ X_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res) ).

thf(55,axiom,
    ! [X_a: $i] :
      ( ( ti @ X_a @ ( undefined @ X_a ) )
      = ( undefined @ X_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).

thf(56,axiom,
    ( ( ti @ bool @ induct_true )
    = induct_true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__true_res) ).

thf(57,axiom,
    ( ( ti @ bool @ induct_false )
    = induct_false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__false_res) ).

thf(58,axiom,
    ! [X_a: $i] :
      ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( induct_equal @ X_a ) )
      = ( induct_equal @ X_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__equal_res) ).

thf(59,axiom,
    ! [X_a: $i] :
      ( ( cl_HOL_Oequal @ X_a )
     => ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
        = ( equal_equal @ X_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oequal__class_Oequal_res) ).

thf(60,axiom,
    hBOOL @ hoare_1883395792gleton,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(61,axiom,
    ! [B_1: $i] :
      ( ( hBOOL @ ( ti @ bool @ B_1 ) )
    <=> ( hBOOL @ B_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).

thf(62,axiom,
    ( ( ti @ bool @ hoare_1883395792gleton )
    = hoare_1883395792gleton ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res) ).

thf(63,conjecture,
    ! [T: $i] :
      ~ ! [S: $i] :
          ( ( ti @ state @ S )
          = ( ti @ state @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(64,negated_conjecture,
    ( ( ! [T: $i] :
          ~ ! [S: $i] :
              ( ( ti @ state @ S )
              = ( ti @ state @ T ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[63]) ).

thf(65,plain,
    ( ( ! [T: $i] :
          ~ ! [S: $i] :
              ( ( ti @ state @ S )
              = ( ti @ state @ T ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[64]) ).

thf(66,plain,
    ( ( ! [X_a: $i,X: $i,Y: $i] :
          ( ( ( ti @ X_a @ X )
           != ( ti @ X_a @ Y ) )
          | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(67,plain,
    ( ( ! [X_a: $i,X: $i,Y: $i] :
          ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
          | ( ( ti @ X_a @ X )
            = ( ti @ X_a @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(68,plain,
    ( ( ! [T_1: $i,A: $i] :
          ( ( ti @ T_1 @ ( ti @ T_1 @ A ) )
          = ( ti @ T_1 @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(69,plain,
    ( ( ! [T_1_1: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ T_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(70,plain,
    ( ( ! [T_2: $i,T_1_1: $i] : ( cl_HOL_Oequal @ ( sum_sum @ T_2 @ T_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(71,plain,
    ( ( cl_HOL_Oequal @ state )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(72,plain,
    ( ( cl_HOL_Oequal @ bool )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(73,plain,
    ( ( cl_HOL_Oequal @ com )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(74,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ( ( cl_HOL_Oequal @ T_1_1 )
            & ( enum @ T_2 ) )
         => ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(75,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ( ( enum @ T_1_1 )
            & ( enum @ T_2 ) )
         => ( enum @ ( fun @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(76,plain,
    ( ( enum @ bool )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(77,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ( ( enum @ T_1_1 )
            & ( enum @ T_2 ) )
         => ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(78,plain,
    ( ( ! [X_a: $i,P: $i] :
          ( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ P )
          = ( ti @ ( fun @ X_a @ bool ) @ P ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(79,plain,
    ( ( ! [X_a: $i,X_1: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
        <=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(80,plain,
    ( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
          ( ! [X_2: $i] :
              ( ( hAPP @ X_a @ X_b @ F @ X_2 )
              = ( hAPP @ X_a @ X_b @ G @ X_2 ) )
         => ( ( ti @ ( fun @ X_a @ X_b ) @ F )
            = ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(81,plain,
    ( ( ! [X_a: $i,X_1: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
        <=> ( ( ti @ X_a @ X_1 )
            = ( ti @ X_a @ Y_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(82,plain,
    ( ( hBOOL @ induct_true )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(83,plain,
    ( ( hBOOL @ induct_true )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(84,plain,
    ( ( ! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
           => ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) )
             => ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(85,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( ! [Y_2: $i] :
                ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) )
               => ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) ) ) )
           => ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(86,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ~ ! [Y_2: $i] :
                ( ( ( ti @ X_a @ X_1 )
                  = ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) )
               => ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(87,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
           => ~ ! [X_2: $i] :
                  ( ( ti @ X_b @ Y_1 )
                 != ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(88,plain,
    ( ( ~ ( hBOOL @ induct_false ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(89,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(90,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
            = ( ti @ X_a @ X_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(91,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
              = ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
          <=> ( ( ti @ X_a @ X_1 )
              = ( ti @ X_a @ Y_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(92,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
           => ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
              = ( ti @ X_b @ Y_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(93,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
           => ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
             => ( ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
                  = ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
              <=> ( ( ti @ X_b @ X_1 )
                  = ( ti @ X_b @ Y_1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(94,plain,
    ( ( ! [X_a: $i,X_1: $i] :
          ~ ! [Y_2: $i] :
              ( ( X_1
                = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) )
             => ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(95,plain,
    ( ( ! [X_a: $i,X_1: $i,P: $i] :
          ( ! [Y_2: $i] :
              ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
             => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) ) ) )
         => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(96,plain,
    ( ( ! [X_a: $i,Y_1: $i,X_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
         => ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
           => ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
                = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
            <=> ( X_1 = Y_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(97,plain,
    ( ( ! [X_a: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(98,plain,
    ( ( ! [X_a: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
         => ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
            = Y_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(99,plain,
    ( ( ! [X_a: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
         => ~ ! [X_2: $i] :
                ( Y_1
               != ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(100,plain,
    ( ( ! [X_a: $i,P: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
         => ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) )
           => ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(101,plain,
    ( ( ! [X_a: $i,X_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(102,plain,
    ( ( ! [X_a: $i,X_1: $i] :
          ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) )
          = X_1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(103,plain,
    ( ( ! [X_a: $i] :
          ( ( cl_HOL_Oequal @ X_a )
         => ( ( fequal @ X_a )
            = ( equal_equal @ X_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(104,plain,
    ( ( ! [X_a: $i] :
          ( ( cl_HOL_Oequal @ X_a )
         => ! [X_1: $i,Y_1: $i] :
              ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
            <=> ( ( ti @ X_a @ X_1 )
                = ( ti @ X_a @ Y_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(105,plain,
    ( ( ! [X_a: $i] :
          ( ( cl_HOL_Oequal @ X_a )
         => ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(106,plain,
    ( ( ! [X_a: $i] :
          ( ( cl_HOL_Oequal @ X_a )
         => ( ( equal_equal @ X_a )
            = ( fequal @ X_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(107,plain,
    ( ( ! [X_a: $i,X_1: $i,Y_1: $i] :
          ( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
            = ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
        <=> ( X_1 = Y_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(108,plain,
    ( ( ! [X_a: $i,X_1: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
        <=> ( X_1 = Y_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[43]) ).

thf(109,plain,
    ( ( ( hBOOL @ hoare_1883395792gleton )
    <=> ? [S: $i,T: $i] :
          ( ( ti @ state @ S )
         != ( ti @ state @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[44]) ).

thf(110,plain,
    ( ( ! [X_b: $i] :
          ( ( ti @ ( fun @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( member @ X_b ) )
          = ( member @ X_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[45]) ).

thf(111,plain,
    ( ( ! [X_a: $i,X_b: $i,B_1: $i,B_2: $i] :
          ( ( ti @ X_a @ ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) )
          = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[46]) ).

thf(112,plain,
    ( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
          ( ( hAPP @ X_b @ X_a @ B_1 @ ( ti @ X_b @ B_2 ) )
          = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[47]) ).

thf(113,plain,
    ( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
          ( ( hAPP @ X_b @ X_a @ ( ti @ ( fun @ X_b @ X_a ) @ B_1 ) @ B_2 )
          = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[48]) ).

thf(114,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
          = ( fequal @ X_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[49]) ).

thf(115,plain,
    ( ( ! [X_a: $i,X_b: $i] :
          ( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) ) @ ( type_definition @ X_a @ X_b ) )
          = ( type_definition @ X_a @ X_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[50]) ).

thf(116,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
          = ( collect @ X_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[51]) ).

thf(117,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ X_a ) )
          = ( hoare_1580379338ep_set @ X_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[52]) ).

thf(118,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) )
          = ( hoare_2037801986triple @ X_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[53]) ).

thf(119,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) )
          = ( hoare_244953527triple @ X_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[54]) ).

thf(120,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ X_a @ ( undefined @ X_a ) )
          = ( undefined @ X_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[55]) ).

thf(121,plain,
    ( ( ( ti @ bool @ induct_true )
      = induct_true )
    = $true ),
    inference(unfold_def,[status(thm)],[56]) ).

thf(122,plain,
    ( ( ( ti @ bool @ induct_false )
      = induct_false )
    = $true ),
    inference(unfold_def,[status(thm)],[57]) ).

thf(123,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( induct_equal @ X_a ) )
          = ( induct_equal @ X_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[58]) ).

thf(124,plain,
    ( ( ! [X_a: $i] :
          ( ( cl_HOL_Oequal @ X_a )
         => ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
            = ( equal_equal @ X_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[59]) ).

thf(125,plain,
    ( ( hBOOL @ hoare_1883395792gleton )
    = $true ),
    inference(unfold_def,[status(thm)],[60]) ).

thf(126,plain,
    ( ( ! [B_1: $i] :
          ( ( hBOOL @ ( ti @ bool @ B_1 ) )
        <=> ( hBOOL @ B_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[61]) ).

thf(127,plain,
    ( ( ( ti @ bool @ hoare_1883395792gleton )
      = hoare_1883395792gleton )
    = $true ),
    inference(unfold_def,[status(thm)],[62]) ).

thf(128,plain,
    ( ( ~ ! [SY157: $i] :
            ( ( ti @ state @ SY157 )
            = ( ti @ state @ sK1_T ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[65]) ).

thf(129,plain,
    ( ( ! [SY157: $i] :
          ( ( ti @ state @ SY157 )
          = ( ti @ state @ sK1_T ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[128]) ).

thf(130,plain,
    ( ( ! [X_a: $i,X: $i,Y: $i] :
          ( ( ( ti @ X_a @ X )
           != ( ti @ X_a @ Y ) )
          | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[66]) ).

thf(131,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ~ ( cl_HOL_Oequal @ T_1_1 )
          | ~ ( enum @ T_2 )
          | ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[74]) ).

thf(132,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ~ ( enum @ T_1_1 )
          | ~ ( enum @ T_2 )
          | ( enum @ ( fun @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[75]) ).

thf(133,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ~ ( enum @ T_1_1 )
          | ~ ( enum @ T_2 )
          | ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[77]) ).

thf(134,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
              | ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) )
          & ! [X_1: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) )
              | ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[79]) ).

thf(135,plain,
    ( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
          ( ( ( hAPP @ X_a @ X_b @ F @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) )
           != ( hAPP @ X_a @ X_b @ G @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) ) )
          | ( ( ti @ ( fun @ X_a @ X_b ) @ F )
            = ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[80]) ).

thf(136,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,Y_1: $i] :
              ( ( ( ti @ X_a @ X_1 )
               != ( ti @ X_a @ Y_1 ) )
              | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
          & ! [X_1: $i,Y_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
              | ( ( ti @ X_a @ X_1 )
                = ( ti @ X_a @ Y_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[81]) ).

thf(137,plain,
    ( ( ! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ ( sK3_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ P @ X_a @ X_b ) ) ) )
          | ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[84]) ).

thf(138,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) @ A_1 ) )
            & ~ ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) ) ) )
          | ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[85]) ).

thf(139,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( ( ( ti @ X_a @ X_1 )
              = ( hAPP @ X_b @ X_a @ Abs @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) )
            & ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) @ A_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[86]) ).

thf(140,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
          | ( ( ti @ X_b @ Y_1 )
            = ( hAPP @ X_a @ X_b @ Rep @ ( sK6_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ X_a @ X_b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[87]) ).

thf(141,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[89]) ).

thf(142,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i] :
          ( ! [A_1: $i] :
              ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
            = ( ti @ X_a @ X_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[90]) ).

thf(143,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i] :
          ( ( ! [Abs: $i,A_1: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
            | ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
             != ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
            | ( ( ti @ X_a @ X_1 )
              = ( ti @ X_a @ Y_1 ) ) )
          & ( ! [Abs: $i,A_1: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
            | ( ( ti @ X_a @ X_1 )
             != ( ti @ X_a @ Y_1 ) )
            | ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
              = ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[91]) ).

thf(144,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
          | ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
            = ( ti @ X_b @ Y_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[92]) ).

thf(145,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i] :
          ( ! [Abs: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
              | ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
               != ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
              | ( ( ti @ X_b @ X_1 )
                = ( ti @ X_b @ Y_1 ) ) )
          & ! [Abs: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
              | ( ( ti @ X_b @ X_1 )
               != ( ti @ X_b @ Y_1 ) )
              | ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
                = ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[93]) ).

thf(146,plain,
    ( ( ! [X_a: $i,X_1: $i] :
          ( ( X_1
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) )
          & ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[94]) ).

thf(147,plain,
    ( ( ! [X_a: $i,X_1: $i,P: $i] :
          ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
            & ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) ) ) )
          | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[95]) ).

thf(148,plain,
    ( ( ! [X_a: $i] :
          ( ! [Y_1: $i,X_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
               != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
              | ( X_1 = Y_1 ) )
          & ! [Y_1: $i,X_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ( X_1 != Y_1 )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
                = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[96]) ).

thf(149,plain,
    ( ( ! [X_a: $i,Y_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
          | ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
            = Y_1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[98]) ).

thf(150,plain,
    ( ( ! [X_a: $i,Y_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
          | ( Y_1
            = ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK9_X_2 @ Y_1 @ X_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[99]) ).

thf(151,plain,
    ( ( ! [X_a: $i,P: $i,Y_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK10_X_2 @ Y_1 @ P @ X_a ) ) ) )
          | ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[100]) ).

thf(152,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ( fequal @ X_a )
            = ( equal_equal @ X_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[103]) ).

thf(153,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ! [X_1: $i,Y_1: $i] :
                ( ( ( ti @ X_a @ X_1 )
                 != ( ti @ X_a @ Y_1 ) )
                | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
            & ! [X_1: $i,Y_1: $i] :
                ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
                | ( ( ti @ X_a @ X_1 )
                  = ( ti @ X_a @ Y_1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[104]) ).

thf(154,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[105]) ).

thf(155,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ( equal_equal @ X_a )
            = ( fequal @ X_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[106]) ).

thf(156,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,Y_1: $i] :
              ( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
               != ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
              | ( X_1 = Y_1 ) )
          & ! [X_1: $i,Y_1: $i] :
              ( ( X_1 != Y_1 )
              | ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
                = ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[107]) ).

thf(157,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,Y_1: $i] :
              ( ( X_1 != Y_1 )
              | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) ) )
          & ! [X_1: $i,Y_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
              | ( X_1 = Y_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[108]) ).

thf(158,plain,
    ( ( ( ! [S: $i,T: $i] :
            ( ( ti @ state @ S )
            = ( ti @ state @ T ) )
        | ( hBOOL @ hoare_1883395792gleton ) )
      & ( ~ ( hBOOL @ hoare_1883395792gleton )
        | ( ( ti @ state @ sK11_S )
         != ( ti @ state @ sK12_SY158 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[109]) ).

thf(159,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
            = ( equal_equal @ X_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[124]) ).

thf(160,plain,
    ( ( ! [B_1: $i] :
          ( ~ ( hBOOL @ ( ti @ bool @ B_1 ) )
          | ( hBOOL @ B_1 ) )
      & ! [B_1: $i] :
          ( ~ ( hBOOL @ B_1 )
          | ( hBOOL @ ( ti @ bool @ B_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[126]) ).

thf(161,plain,
    ( ( ( ti @ bool @ hoare_1883395792gleton )
      = hoare_1883395792gleton )
    = $true ),
    inference(copy,[status(thm)],[127]) ).

thf(162,plain,
    ( ( ! [B_1: $i] :
          ( ~ ( hBOOL @ ( ti @ bool @ B_1 ) )
          | ( hBOOL @ B_1 ) )
      & ! [B_1: $i] :
          ( ~ ( hBOOL @ B_1 )
          | ( hBOOL @ ( ti @ bool @ B_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[160]) ).

thf(163,plain,
    ( ( hBOOL @ hoare_1883395792gleton )
    = $true ),
    inference(copy,[status(thm)],[125]) ).

thf(164,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
            = ( equal_equal @ X_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[159]) ).

thf(165,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( induct_equal @ X_a ) )
          = ( induct_equal @ X_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[123]) ).

thf(166,plain,
    ( ( ( ti @ bool @ induct_false )
      = induct_false )
    = $true ),
    inference(copy,[status(thm)],[122]) ).

thf(167,plain,
    ( ( ( ti @ bool @ induct_true )
      = induct_true )
    = $true ),
    inference(copy,[status(thm)],[121]) ).

thf(168,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ X_a @ ( undefined @ X_a ) )
          = ( undefined @ X_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[120]) ).

thf(169,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) )
          = ( hoare_244953527triple @ X_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[119]) ).

thf(170,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) )
          = ( hoare_2037801986triple @ X_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[118]) ).

thf(171,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ X_a ) )
          = ( hoare_1580379338ep_set @ X_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[117]) ).

thf(172,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
          = ( collect @ X_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[116]) ).

thf(173,plain,
    ( ( ! [X_a: $i,X_b: $i] :
          ( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) ) @ ( type_definition @ X_a @ X_b ) )
          = ( type_definition @ X_a @ X_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[115]) ).

thf(174,plain,
    ( ( ! [X_a: $i] :
          ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
          = ( fequal @ X_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[114]) ).

thf(175,plain,
    ( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
          ( ( hAPP @ X_b @ X_a @ ( ti @ ( fun @ X_b @ X_a ) @ B_1 ) @ B_2 )
          = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[113]) ).

thf(176,plain,
    ( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
          ( ( hAPP @ X_b @ X_a @ B_1 @ ( ti @ X_b @ B_2 ) )
          = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[112]) ).

thf(177,plain,
    ( ( ! [X_a: $i,X_b: $i,B_1: $i,B_2: $i] :
          ( ( ti @ X_a @ ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) )
          = ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(178,plain,
    ( ( ! [X_b: $i] :
          ( ( ti @ ( fun @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( member @ X_b ) )
          = ( member @ X_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(179,plain,
    ( ( ( ! [S: $i,T: $i] :
            ( ( ti @ state @ S )
            = ( ti @ state @ T ) )
        | ( hBOOL @ hoare_1883395792gleton ) )
      & ( ~ ( hBOOL @ hoare_1883395792gleton )
        | ( ( ti @ state @ sK11_S )
         != ( ti @ state @ sK12_SY158 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[158]) ).

thf(180,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,Y_1: $i] :
              ( ( X_1 != Y_1 )
              | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) ) )
          & ! [X_1: $i,Y_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
              | ( X_1 = Y_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[157]) ).

thf(181,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,Y_1: $i] :
              ( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
               != ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
              | ( X_1 = Y_1 ) )
          & ! [X_1: $i,Y_1: $i] :
              ( ( X_1 != Y_1 )
              | ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
                = ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[156]) ).

thf(182,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ( equal_equal @ X_a )
            = ( fequal @ X_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[155]) ).

thf(183,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[154]) ).

thf(184,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ! [X_1: $i,Y_1: $i] :
                ( ( ( ti @ X_a @ X_1 )
                 != ( ti @ X_a @ Y_1 ) )
                | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
            & ! [X_1: $i,Y_1: $i] :
                ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
                | ( ( ti @ X_a @ X_1 )
                  = ( ti @ X_a @ Y_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[153]) ).

thf(185,plain,
    ( ( ! [X_a: $i] :
          ( ~ ( cl_HOL_Oequal @ X_a )
          | ( ( fequal @ X_a )
            = ( equal_equal @ X_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[152]) ).

thf(186,plain,
    ( ( ! [X_a: $i,X_1: $i] :
          ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) )
          = X_1 ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(187,plain,
    ( ( ! [X_a: $i,X_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(188,plain,
    ( ( ! [X_a: $i,P: $i,Y_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK10_X_2 @ Y_1 @ P @ X_a ) ) ) )
          | ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[151]) ).

thf(189,plain,
    ( ( ! [X_a: $i,Y_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
          | ( Y_1
            = ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK9_X_2 @ Y_1 @ X_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[150]) ).

thf(190,plain,
    ( ( ! [X_a: $i,Y_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
          | ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
            = Y_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[149]) ).

thf(191,plain,
    ( ( ! [X_a: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(192,plain,
    ( ( ! [X_a: $i] :
          ( ! [Y_1: $i,X_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
               != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
              | ( X_1 = Y_1 ) )
          & ! [Y_1: $i,X_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
              | ( X_1 != Y_1 )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
                = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[148]) ).

thf(193,plain,
    ( ( ! [X_a: $i,X_1: $i,P: $i] :
          ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
            & ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) ) ) )
          | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[147]) ).

thf(194,plain,
    ( ( ! [X_a: $i,X_1: $i] :
          ( ( X_1
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) )
          & ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[146]) ).

thf(195,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i] :
          ( ! [Abs: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
              | ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
               != ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
              | ( ( ti @ X_b @ X_1 )
                = ( ti @ X_b @ Y_1 ) ) )
          & ! [Abs: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
              | ( ( ti @ X_b @ X_1 )
               != ( ti @ X_b @ Y_1 ) )
              | ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
                = ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[145]) ).

thf(196,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
          | ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
            = ( ti @ X_b @ Y_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[144]) ).

thf(197,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i] :
          ( ( ! [Abs: $i,A_1: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
            | ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
             != ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
            | ( ( ti @ X_a @ X_1 )
              = ( ti @ X_a @ Y_1 ) ) )
          & ( ! [Abs: $i,A_1: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
            | ( ( ti @ X_a @ X_1 )
             != ( ti @ X_a @ Y_1 ) )
            | ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
              = ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[143]) ).

thf(198,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i] :
          ( ! [A_1: $i] :
              ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
            = ( ti @ X_a @ X_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[142]) ).

thf(199,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[141]) ).

thf(200,plain,
    ( ( ~ ( hBOOL @ induct_false ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(201,plain,
    ( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
          | ( ( ti @ X_b @ Y_1 )
            = ( hAPP @ X_a @ X_b @ Rep @ ( sK6_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ X_a @ X_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[140]) ).

thf(202,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( ( ( ti @ X_a @ X_1 )
              = ( hAPP @ X_b @ X_a @ Abs @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) )
            & ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[139]) ).

thf(203,plain,
    ( ( ! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) @ A_1 ) )
            & ~ ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) ) ) )
          | ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[138]) ).

thf(204,plain,
    ( ( ! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
          | ~ ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ ( sK3_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ P @ X_a @ X_b ) ) ) )
          | ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[137]) ).

thf(205,plain,
    ( ( hBOOL @ induct_true )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(206,plain,
    ( ( hBOOL @ induct_true )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(207,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,Y_1: $i] :
              ( ( ( ti @ X_a @ X_1 )
               != ( ti @ X_a @ Y_1 ) )
              | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
          & ! [X_1: $i,Y_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
              | ( ( ti @ X_a @ X_1 )
                = ( ti @ X_a @ Y_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[136]) ).

thf(208,plain,
    ( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
          ( ( ( hAPP @ X_a @ X_b @ F @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) )
           != ( hAPP @ X_a @ X_b @ G @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) ) )
          | ( ( ti @ ( fun @ X_a @ X_b ) @ F )
            = ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[135]) ).

thf(209,plain,
    ( ( ! [X_a: $i] :
          ( ! [X_1: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
              | ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) )
          & ! [X_1: $i,A_1: $i] :
              ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) )
              | ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[134]) ).

thf(210,plain,
    ( ( ! [X_a: $i,P: $i] :
          ( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ P )
          = ( ti @ ( fun @ X_a @ bool ) @ P ) ) )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(211,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ~ ( enum @ T_1_1 )
          | ~ ( enum @ T_2 )
          | ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[133]) ).

thf(212,plain,
    ( ( enum @ bool )
    = $true ),
    inference(copy,[status(thm)],[76]) ).

thf(213,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ~ ( enum @ T_1_1 )
          | ~ ( enum @ T_2 )
          | ( enum @ ( fun @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[132]) ).

thf(214,plain,
    ( ( ! [T_2: $i,T_1_1: $i] :
          ( ~ ( cl_HOL_Oequal @ T_1_1 )
          | ~ ( enum @ T_2 )
          | ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[131]) ).

thf(215,plain,
    ( ( cl_HOL_Oequal @ com )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(216,plain,
    ( ( cl_HOL_Oequal @ bool )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(217,plain,
    ( ( cl_HOL_Oequal @ state )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(218,plain,
    ( ( ! [T_2: $i,T_1_1: $i] : ( cl_HOL_Oequal @ ( sum_sum @ T_2 @ T_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(219,plain,
    ( ( ! [T_1_1: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ T_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(220,plain,
    ( ( ! [T_1: $i,A: $i] :
          ( ( ti @ T_1 @ ( ti @ T_1 @ A ) )
          = ( ti @ T_1 @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(221,plain,
    ( ( ! [X_a: $i,X: $i,Y: $i] :
          ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
          | ( ( ti @ X_a @ X )
            = ( ti @ X_a @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(222,plain,
    ( ( ! [X_a: $i,X: $i,Y: $i] :
          ( ( ( ti @ X_a @ X )
           != ( ti @ X_a @ Y ) )
          | ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[130]) ).

thf(223,plain,
    ( ( ! [SY157: $i] :
          ( ( ti @ state @ SY157 )
          = ( ti @ state @ sK1_T ) ) )
    = $true ),
    inference(copy,[status(thm)],[129]) ).

thf(224,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( sK8_Y_2 @ SX2 @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
              | ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ SX2 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ ( sK8_Y_2 @ SX2 @ SX1 @ SX0 ) ) ) ) )
          | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[193]) ).

thf(225,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) @ SX5 ) )
          | ~ ( ( ( ti @ SX1 @ SX2 )
               != ( hAPP @ SX0 @ SX1 @ SX4 @ ( sK5_Y_2 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ ( sK5_Y_2 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[202]) ).

thf(226,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ( ! [SX5: $i,SX6: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
                | ( ( hAPP @ SX1 @ SX0 @ SX4 @ SX2 )
                 != ( hAPP @ SX1 @ SX0 @ SX4 @ SX3 ) )
                | ( ( ti @ SX1 @ SX2 )
                  = ( ti @ SX1 @ SX3 ) ) )
            | ~ ( ! [SX5: $i,SX6: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
                | ( ( ti @ SX1 @ SX2 )
                 != ( ti @ SX1 @ SX3 ) )
                | ( ( hAPP @ SX1 @ SX0 @ SX4 @ SX2 )
                  = ( hAPP @ SX1 @ SX0 @ SX4 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[197]) ).

thf(227,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
          ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
          | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ ( sK4_Y_2 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX6 ) )
              | ~ ~ ( hBOOL @ ( hAPP @ SX1 @ bool @ SX3 @ ( hAPP @ SX0 @ SX1 @ SX5 @ ( sK4_Y_2 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
          | ( hBOOL @ ( hAPP @ SX1 @ bool @ SX3 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[203]) ).

thf(228,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX1 ) @ SX2 ) )
                  | ( hBOOL @ ( hAPP @ SX0 @ bool @ SX2 @ SX1 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ SX2 @ SX1 ) )
                  | ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX1 ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[209]) ).

thf(229,plain,
    ( ( ~ ( ~ ( ! [SX0: $i,SX1: $i] :
                  ( ( ti @ state @ SX0 )
                  = ( ti @ state @ SX1 ) )
              | ( hBOOL @ hoare_1883395792gleton ) )
          | ~ ( ~ ( hBOOL @ hoare_1883395792gleton )
              | ( ( ti @ state @ sK11_S )
               != ( ti @ state @ sK12_SY158 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[179]) ).

thf(230,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ( ( ti @ SX0 @ SX1 )
                   != ( ti @ SX0 @ SX2 ) )
                  | ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( induct_equal @ SX0 ) @ SX1 ) @ SX2 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( induct_equal @ SX0 ) @ SX1 ) @ SX2 ) )
                  | ( ( ti @ SX0 @ SX1 )
                    = ( ti @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[207]) ).

thf(231,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
                | ( hBOOL @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( hBOOL @ SX0 )
                | ( hBOOL @ ( ti @ bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[162]) ).

thf(232,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cl_HOL_Oequal @ SX0 )
          | ~ ( ~ ! [SX1: $i,SX2: $i] :
                    ( ( ( ti @ SX0 @ SX1 )
                     != ( ti @ SX0 @ SX2 ) )
                    | ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( equal_equal @ SX0 ) @ SX1 ) @ SX2 ) ) )
              | ~ ! [SX1: $i,SX2: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( equal_equal @ SX0 ) @ SX1 ) @ SX2 ) )
                    | ( ( ti @ SX0 @ SX1 )
                      = ( ti @ SX0 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[184]) ).

thf(233,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ( SX1
             != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ ( sK7_Y_2 @ SX1 @ SX0 ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( sK7_Y_2 @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[194]) ).

thf(234,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
                  | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX2 )
                   != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX1 ) )
                  | ( SX2 = SX1 ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
                  | ( SX2 != SX1 )
                  | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX2 )
                    = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[192]) ).

thf(235,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ( ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX1 )
                   != ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX2 ) )
                  | ( SX1 = SX2 ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ( SX1 != SX2 )
                  | ( ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX1 )
                    = ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[181]) ).

thf(236,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
          ~ ( ~ ! [SX5: $i,SX6: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ SX6 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX2 ) @ SX6 ) )
                  | ( ( hAPP @ SX0 @ SX1 @ SX5 @ SX3 )
                   != ( hAPP @ SX0 @ SX1 @ SX5 @ SX2 ) )
                  | ( ( ti @ SX0 @ SX3 )
                    = ( ti @ SX0 @ SX2 ) ) )
            | ~ ! [SX5: $i,SX6: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ SX6 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX2 ) @ SX6 ) )
                  | ( ( ti @ SX0 @ SX3 )
                   != ( ti @ SX0 @ SX2 ) )
                  | ( ( hAPP @ SX0 @ SX1 @ SX5 @ SX3 )
                    = ( hAPP @ SX0 @ SX1 @ SX5 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[195]) ).

thf(237,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ( SX1 != SX2 )
                  | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( hoare_509422987triple @ SX0 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SX0 ) ) @ SX1 ) @ SX2 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( hoare_509422987triple @ SX0 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SX0 ) ) @ SX1 ) @ SX2 ) )
                  | ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[180]) ).

thf(238,plain,
    ! [SV1: $i] :
      ( ( ~ ( cl_HOL_Oequal @ SV1 )
        | ( ( ti @ ( fun @ SV1 @ ( fun @ SV1 @ bool ) ) @ ( equal_equal @ SV1 ) )
          = ( equal_equal @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(239,plain,
    ! [SV2: $i] :
      ( ( ( ti @ ( fun @ SV2 @ ( fun @ SV2 @ bool ) ) @ ( induct_equal @ SV2 ) )
        = ( induct_equal @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(240,plain,
    ! [SV3: $i] :
      ( ( ( ti @ SV3 @ ( undefined @ SV3 ) )
        = ( undefined @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[168]) ).

thf(241,plain,
    ! [SV4: $i] :
      ( ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV4 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV4 ) ) @ bool ) @ ( hoare_509422987triple @ SV4 ) ) @ ( hoare_244953527triple @ SV4 ) )
        = ( hoare_244953527triple @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[169]) ).

thf(242,plain,
    ! [SV5: $i] :
      ( ( ( ti @ ( fun @ ( hoare_509422987triple @ SV5 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV5 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV5 ) ) @ bool ) ) @ ( hoare_2037801986triple @ SV5 ) )
        = ( hoare_2037801986triple @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[170]) ).

thf(243,plain,
    ! [SV6: $i] :
      ( ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV6 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV6 ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ SV6 ) )
        = ( hoare_1580379338ep_set @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(244,plain,
    ! [SV7: $i] :
      ( ( ( ti @ ( fun @ ( fun @ SV7 @ bool ) @ ( fun @ SV7 @ bool ) ) @ ( collect @ SV7 ) )
        = ( collect @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(245,plain,
    ! [SV8: $i] :
      ( ( ! [SY159: $i] :
            ( ( ti @ ( fun @ ( fun @ SV8 @ SY159 ) @ ( fun @ ( fun @ SY159 @ SV8 ) @ ( fun @ ( fun @ SY159 @ bool ) @ bool ) ) ) @ ( type_definition @ SV8 @ SY159 ) )
            = ( type_definition @ SV8 @ SY159 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[173]) ).

thf(246,plain,
    ! [SV9: $i] :
      ( ( ( ti @ ( fun @ SV9 @ ( fun @ SV9 @ bool ) ) @ ( fequal @ SV9 ) )
        = ( fequal @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[174]) ).

thf(247,plain,
    ! [SV10: $i] :
      ( ( ! [SY160: $i,SY161: $i,SY162: $i] :
            ( ( hAPP @ SV10 @ SY160 @ ( ti @ ( fun @ SV10 @ SY160 ) @ SY161 ) @ SY162 )
            = ( hAPP @ SV10 @ SY160 @ SY161 @ SY162 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[175]) ).

thf(248,plain,
    ! [SV11: $i] :
      ( ( ! [SY163: $i,SY164: $i,SY165: $i] :
            ( ( hAPP @ SV11 @ SY163 @ SY164 @ ( ti @ SV11 @ SY165 ) )
            = ( hAPP @ SV11 @ SY163 @ SY164 @ SY165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[176]) ).

thf(249,plain,
    ! [SV12: $i] :
      ( ( ! [SY166: $i,SY167: $i,SY168: $i] :
            ( ( ti @ SV12 @ ( hAPP @ SY166 @ SV12 @ SY167 @ SY168 ) )
            = ( hAPP @ SY166 @ SV12 @ SY167 @ SY168 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[177]) ).

thf(250,plain,
    ! [SV13: $i] :
      ( ( ( ti @ ( fun @ SV13 @ ( fun @ ( fun @ SV13 @ bool ) @ bool ) ) @ ( member @ SV13 ) )
        = ( member @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[178]) ).

thf(251,plain,
    ! [SV14: $i] :
      ( ( ~ ( cl_HOL_Oequal @ SV14 )
        | ( ( equal_equal @ SV14 )
          = ( fequal @ SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[182]) ).

thf(252,plain,
    ! [SV15: $i] :
      ( ( ~ ( cl_HOL_Oequal @ SV15 )
        | ! [SY169: $i] : ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SY169 ) @ SY169 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[183]) ).

thf(253,plain,
    ! [SV16: $i] :
      ( ( ~ ( cl_HOL_Oequal @ SV16 )
        | ( ( fequal @ SV16 )
          = ( equal_equal @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[185]) ).

thf(254,plain,
    ! [SV17: $i] :
      ( ( ! [SY170: $i] :
            ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_509422987triple @ SV17 ) @ ( hoare_244953527triple @ SV17 ) @ ( hAPP @ ( hoare_509422987triple @ SV17 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_2037801986triple @ SV17 ) @ SY170 ) )
            = SY170 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[186]) ).

thf(255,plain,
    ! [SV18: $i] :
      ( ( ! [SY171: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ SV18 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( hoare_2037801986triple @ SV18 ) @ SY171 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV18 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[187]) ).

thf(256,plain,
    ! [SV19: $i] :
      ( ( ! [SY172: $i,SY173: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SY173 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SY172 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SY173 @ SY172 @ SV19 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SY172 @ SY173 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[188]) ).

thf(257,plain,
    ! [SV20: $i] :
      ( ( ! [SY174: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SY174 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) )
            | ( SY174
              = ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SY174 @ SV20 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[189]) ).

thf(258,plain,
    ! [SV21: $i] :
      ( ( ! [SY175: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SY175 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) )
            | ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SY175 ) )
              = SY175 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[190]) ).

thf(259,plain,
    ! [SV22: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ ( hoare_509422987triple @ SV22 ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ SV22 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ ( hoare_509422987triple @ SV22 ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ SV22 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) ) @ ( hoare_2037801986triple @ SV22 ) ) @ ( hoare_244953527triple @ SV22 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[191]) ).

thf(260,plain,
    ! [SV23: $i] :
      ( ( ! [SY176: $i,SY177: $i,SY178: $i,SY179: $i,SY180: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SY176 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY176 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SY176 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SY176 @ SV23 ) @ SY178 ) @ SY179 ) @ SY180 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SY177 ) @ SY180 ) )
            | ( ( hAPP @ SY176 @ SV23 @ SY178 @ ( hAPP @ SV23 @ SY176 @ SY179 @ SY177 ) )
              = ( ti @ SV23 @ SY177 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[196]) ).

thf(261,plain,
    ! [SV24: $i] :
      ( ( ! [SY181: $i,SY182: $i,SY183: $i,SY184: $i] :
            ( ! [SY185: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SY181 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY181 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SY181 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SY181 @ SV24 ) @ SY183 ) @ SY184 ) @ SY185 ) )
            | ( ( hAPP @ SV24 @ SY181 @ SY184 @ ( hAPP @ SY181 @ SV24 @ SY183 @ SY182 ) )
              = ( ti @ SY181 @ SY182 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[198]) ).

thf(262,plain,
    ! [SV25: $i] :
      ( ( ! [SY186: $i,SY187: $i,SY188: $i,SY189: $i,SY190: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SY186 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY186 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SY186 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SY186 @ SV25 ) @ SY188 ) @ SY189 ) @ SY190 ) )
            | ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SY186 @ SV25 @ SY188 @ SY187 ) ) @ SY190 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[199]) ).

thf(263,plain,
    ( ( hBOOL @ induct_false )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[200]) ).

thf(264,plain,
    ! [SV26: $i] :
      ( ( ! [SY191: $i,SY192: $i,SY193: $i,SY194: $i,SY195: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SY191 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY191 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SY191 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SY191 @ SV26 ) @ SY193 ) @ SY194 ) @ SY195 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SY192 ) @ SY195 ) )
            | ( ( ti @ SV26 @ SY192 )
              = ( hAPP @ SY191 @ SV26 @ SY193 @ ( sK6_X_2 @ SY195 @ SY194 @ SY193 @ SY192 @ SY191 @ SV26 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(265,plain,
    ! [SV27: $i] :
      ( ( ! [SY196: $i,SY197: $i,SY198: $i,SY199: $i,SY200: $i,SY201: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SY196 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY196 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SY196 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SY196 @ SV27 ) @ SY199 ) @ SY200 ) @ SY201 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SY198 ) @ SY201 ) )
            | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SY197 @ ( hAPP @ SY196 @ SV27 @ SY199 @ ( sK3_X_2 @ SY201 @ SY200 @ SY199 @ SY198 @ SY197 @ SY196 @ SV27 ) ) ) )
            | ( hBOOL @ ( hAPP @ SV27 @ bool @ SY197 @ SY198 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[204]) ).

thf(266,plain,
    ! [SV28: $i] :
      ( ( ! [SY202: $i,SY203: $i,SY204: $i] :
            ( ( ( hAPP @ SV28 @ SY202 @ SY203 @ ( sK2_X_2 @ SY204 @ SY203 @ SY202 @ SV28 ) )
             != ( hAPP @ SV28 @ SY202 @ SY204 @ ( sK2_X_2 @ SY204 @ SY203 @ SY202 @ SV28 ) ) )
            | ( ( ti @ ( fun @ SV28 @ SY202 ) @ SY203 )
              = ( ti @ ( fun @ SV28 @ SY202 ) @ SY204 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[208]) ).

thf(267,plain,
    ! [SV29: $i] :
      ( ( ! [SY205: $i] :
            ( ( hAPP @ ( fun @ SV29 @ bool ) @ ( fun @ SV29 @ bool ) @ ( collect @ SV29 ) @ SY205 )
            = ( ti @ ( fun @ SV29 @ bool ) @ SY205 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[210]) ).

thf(268,plain,
    ! [SV30: $i] :
      ( ( ! [SY206: $i] :
            ( ~ ( enum @ SY206 )
            | ~ ( enum @ SV30 )
            | ( enum @ ( sum_sum @ SV30 @ SY206 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[211]) ).

thf(269,plain,
    ! [SV31: $i] :
      ( ( ! [SY207: $i] :
            ( ~ ( enum @ SY207 )
            | ~ ( enum @ SV31 )
            | ( enum @ ( fun @ SV31 @ SY207 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[213]) ).

thf(270,plain,
    ! [SV32: $i] :
      ( ( ! [SY208: $i] :
            ( ~ ( cl_HOL_Oequal @ SY208 )
            | ~ ( enum @ SV32 )
            | ( cl_HOL_Oequal @ ( fun @ SV32 @ SY208 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[214]) ).

thf(271,plain,
    ! [SV33: $i] :
      ( ( ! [SY209: $i] : ( cl_HOL_Oequal @ ( sum_sum @ SV33 @ SY209 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[218]) ).

thf(272,plain,
    ! [SV34: $i] :
      ( ( cl_HOL_Oequal @ ( hoare_509422987triple @ SV34 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[219]) ).

thf(273,plain,
    ! [SV35: $i] :
      ( ( ! [SY210: $i] :
            ( ( ti @ SV35 @ ( ti @ SV35 @ SY210 ) )
            = ( ti @ SV35 @ SY210 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[220]) ).

thf(274,plain,
    ! [SV36: $i] :
      ( ( ! [SY211: $i,SY212: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SY211 ) @ SY212 ) )
            | ( ( ti @ SV36 @ SY211 )
              = ( ti @ SV36 @ SY212 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[221]) ).

thf(275,plain,
    ! [SV37: $i] :
      ( ( ! [SY213: $i,SY214: $i] :
            ( ( ( ti @ SV37 @ SY213 )
             != ( ti @ SV37 @ SY214 ) )
            | ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SY213 ) @ SY214 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[222]) ).

thf(276,plain,
    ! [SV38: $i] :
      ( ( ( ti @ state @ SV38 )
        = ( ti @ state @ sK1_T ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[223]) ).

thf(277,plain,
    ! [SV39: $i] :
      ( ( ! [SY215: $i,SY216: $i] :
            ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SY216 @ SY215 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
                | ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY216 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SY216 @ SY215 @ SV39 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY216 @ SY215 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[224]) ).

thf(278,plain,
    ! [SV40: $i] :
      ( ( ! [SY217: $i,SY218: $i,SY219: $i,SY220: $i,SY221: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SY217 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY217 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SY217 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SY217 @ SV40 ) @ SY219 ) @ SY220 ) @ SY221 ) )
            | ~ ( ( ( ti @ SY217 @ SY218 )
                 != ( hAPP @ SV40 @ SY217 @ SY220 @ ( sK5_Y_2 @ SY221 @ SY220 @ SY219 @ SY218 @ SY217 @ SV40 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY221 @ SY220 @ SY219 @ SY218 @ SY217 @ SV40 ) ) @ SY221 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[225]) ).

thf(279,plain,
    ! [SV41: $i] :
      ( ( ! [SY222: $i,SY223: $i,SY224: $i,SY225: $i] :
            ~ ( ~ ( ! [SY226: $i,SY227: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY222 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SY222 @ SV41 ) @ SY225 ) @ SY226 ) @ SY227 ) )
                  | ( ( hAPP @ SY222 @ SV41 @ SY225 @ SY223 )
                   != ( hAPP @ SY222 @ SV41 @ SY225 @ SY224 ) )
                  | ( ( ti @ SY222 @ SY223 )
                    = ( ti @ SY222 @ SY224 ) ) )
              | ~ ( ! [SY228: $i,SY229: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY222 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SY222 @ SV41 ) @ SY225 ) @ SY228 ) @ SY229 ) )
                  | ( ( ti @ SY222 @ SY223 )
                   != ( ti @ SY222 @ SY224 ) )
                  | ( ( hAPP @ SY222 @ SV41 @ SY225 @ SY223 )
                    = ( hAPP @ SY222 @ SV41 @ SY225 @ SY224 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[226]) ).

thf(280,plain,
    ! [SV42: $i] :
      ( ( ! [SY230: $i,SY231: $i,SY232: $i,SY233: $i,SY234: $i,SY235: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SY230 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY230 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SY230 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SY230 @ SV42 ) @ SY233 ) @ SY234 ) @ SY235 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY235 @ SY234 @ SY233 @ SY232 @ SY231 @ SY230 @ SV42 ) ) @ SY235 ) )
                | ~ ~ ( hBOOL @ ( hAPP @ SY230 @ bool @ SY232 @ ( hAPP @ SV42 @ SY230 @ SY234 @ ( sK4_Y_2 @ SY235 @ SY234 @ SY233 @ SY232 @ SY231 @ SY230 @ SV42 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ SY230 @ bool @ SY232 @ SY231 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[227]) ).

thf(281,plain,
    ! [SV43: $i] :
      ( ( ~ ( ~ ! [SY236: $i,SY237: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
                  | ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) )
            | ~ ! [SY238: $i,SY239: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
                  | ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[228]) ).

thf(282,plain,
    ( ( ~ ( ! [SX0: $i,SX1: $i] :
              ( ( ti @ state @ SX0 )
              = ( ti @ state @ SX1 ) )
          | ( hBOOL @ hoare_1883395792gleton ) )
      | ~ ( ~ ( hBOOL @ hoare_1883395792gleton )
          | ( ( ti @ state @ sK11_S )
           != ( ti @ state @ sK12_SY158 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[229]) ).

thf(283,plain,
    ! [SV44: $i] :
      ( ( ~ ( ~ ! [SY240: $i,SY241: $i] :
                  ( ( ( ti @ SV44 @ SY240 )
                   != ( ti @ SV44 @ SY241 ) )
                  | ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) )
            | ~ ! [SY242: $i,SY243: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
                  | ( ( ti @ SV44 @ SY242 )
                    = ( ti @ SV44 @ SY243 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[230]) ).

thf(284,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
            | ( hBOOL @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( hBOOL @ SX0 )
            | ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[231]) ).

thf(285,plain,
    ! [SV45: $i] :
      ( ( ~ ( cl_HOL_Oequal @ SV45 )
        | ~ ( ~ ! [SY244: $i,SY245: $i] :
                  ( ( ( ti @ SV45 @ SY244 )
                   != ( ti @ SV45 @ SY245 ) )
                  | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
            | ~ ! [SY246: $i,SY247: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
                  | ( ( ti @ SV45 @ SY246 )
                    = ( ti @ SV45 @ SY247 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[232]) ).

thf(286,plain,
    ! [SV46: $i] :
      ( ( ! [SY248: $i] :
            ~ ( ( SY248
               != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SY248 @ SV46 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SY248 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[233]) ).

thf(287,plain,
    ! [SV47: $i] :
      ( ( ~ ( ~ ! [SY249: $i,SY250: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
                  | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
                   != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
                  | ( SY250 = SY249 ) )
            | ~ ! [SY251: $i,SY252: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
                  | ( SY252 != SY251 )
                  | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
                    = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[234]) ).

thf(288,plain,
    ! [SV48: $i] :
      ( ( ~ ( ~ ! [SY253: $i,SY254: $i] :
                  ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
                   != ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
                  | ( SY253 = SY254 ) )
            | ~ ! [SY255: $i,SY256: $i] :
                  ( ( SY255 != SY256 )
                  | ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
                    = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[235]) ).

thf(289,plain,
    ! [SV49: $i] :
      ( ( ! [SY257: $i,SY258: $i,SY259: $i,SY260: $i] :
            ~ ( ~ ! [SY261: $i,SY262: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY257 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SY257 @ SV49 ) @ SY260 ) @ SY261 ) @ SY262 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY259 ) @ SY262 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY258 ) @ SY262 ) )
                    | ( ( hAPP @ SV49 @ SY257 @ SY261 @ SY259 )
                     != ( hAPP @ SV49 @ SY257 @ SY261 @ SY258 ) )
                    | ( ( ti @ SV49 @ SY259 )
                      = ( ti @ SV49 @ SY258 ) ) )
              | ~ ! [SY263: $i,SY264: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY257 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SY257 @ SV49 ) @ SY260 ) @ SY263 ) @ SY264 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY259 ) @ SY264 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY258 ) @ SY264 ) )
                    | ( ( ti @ SV49 @ SY259 )
                     != ( ti @ SV49 @ SY258 ) )
                    | ( ( hAPP @ SV49 @ SY257 @ SY263 @ SY259 )
                      = ( hAPP @ SV49 @ SY257 @ SY263 @ SY258 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[236]) ).

thf(290,plain,
    ! [SV50: $i] :
      ( ( ~ ( ~ ! [SY265: $i,SY266: $i] :
                  ( ( SY265 != SY266 )
                  | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) )
            | ~ ! [SY267: $i,SY268: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
                  | ( SY267 = SY268 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[237]) ).

thf(291,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( cl_HOL_Oequal @ SV1 ) )
        = $true )
      | ( ( ( ti @ ( fun @ SV1 @ ( fun @ SV1 @ bool ) ) @ ( equal_equal @ SV1 ) )
          = ( equal_equal @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[238]) ).

thf(292,plain,
    ! [SV51: $i,SV8: $i] :
      ( ( ( ti @ ( fun @ ( fun @ SV8 @ SV51 ) @ ( fun @ ( fun @ SV51 @ SV8 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) ) ) @ ( type_definition @ SV8 @ SV51 ) )
        = ( type_definition @ SV8 @ SV51 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[245]) ).

thf(293,plain,
    ! [SV52: $i,SV10: $i] :
      ( ( ! [SY269: $i,SY270: $i] :
            ( ( hAPP @ SV10 @ SV52 @ ( ti @ ( fun @ SV10 @ SV52 ) @ SY269 ) @ SY270 )
            = ( hAPP @ SV10 @ SV52 @ SY269 @ SY270 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[247]) ).

thf(294,plain,
    ! [SV53: $i,SV11: $i] :
      ( ( ! [SY271: $i,SY272: $i] :
            ( ( hAPP @ SV11 @ SV53 @ SY271 @ ( ti @ SV11 @ SY272 ) )
            = ( hAPP @ SV11 @ SV53 @ SY271 @ SY272 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[248]) ).

thf(295,plain,
    ! [SV54: $i,SV12: $i] :
      ( ( ! [SY273: $i,SY274: $i] :
            ( ( ti @ SV12 @ ( hAPP @ SV54 @ SV12 @ SY273 @ SY274 ) )
            = ( hAPP @ SV54 @ SV12 @ SY273 @ SY274 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[249]) ).

thf(296,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( cl_HOL_Oequal @ SV14 ) )
        = $true )
      | ( ( ( equal_equal @ SV14 )
          = ( fequal @ SV14 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[251]) ).

thf(297,plain,
    ! [SV15: $i] :
      ( ( ( ~ ( cl_HOL_Oequal @ SV15 ) )
        = $true )
      | ( ( ! [SY169: $i] : ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SY169 ) @ SY169 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[252]) ).

thf(298,plain,
    ! [SV16: $i] :
      ( ( ( ~ ( cl_HOL_Oequal @ SV16 ) )
        = $true )
      | ( ( ( fequal @ SV16 )
          = ( equal_equal @ SV16 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[253]) ).

thf(299,plain,
    ! [SV55: $i,SV17: $i] :
      ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_509422987triple @ SV17 ) @ ( hoare_244953527triple @ SV17 ) @ ( hAPP @ ( hoare_509422987triple @ SV17 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_2037801986triple @ SV17 ) @ SV55 ) )
        = SV55 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[254]) ).

thf(300,plain,
    ! [SV56: $i,SV18: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ SV18 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( hoare_2037801986triple @ SV18 ) @ SV56 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV18 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[255]) ).

thf(301,plain,
    ! [SV57: $i,SV19: $i] :
      ( ( ! [SY275: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SY275 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SY275 @ SV57 @ SV19 ) ) ) )
            | ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SY275 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[256]) ).

thf(302,plain,
    ! [SV58: $i,SV20: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SV58 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) )
        | ( SV58
          = ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SV58 @ SV20 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[257]) ).

thf(303,plain,
    ! [SV59: $i,SV21: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SV59 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) )
        | ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SV59 ) )
          = SV59 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[258]) ).

thf(304,plain,
    ! [SV60: $i,SV23: $i] :
      ( ( ! [SY276: $i,SY277: $i,SY278: $i,SY279: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SY277 ) @ SY278 ) @ SY279 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SY276 ) @ SY279 ) )
            | ( ( hAPP @ SV60 @ SV23 @ SY277 @ ( hAPP @ SV23 @ SV60 @ SY278 @ SY276 ) )
              = ( ti @ SV23 @ SY276 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[260]) ).

thf(305,plain,
    ! [SV61: $i,SV24: $i] :
      ( ( ! [SY280: $i,SY281: $i,SY282: $i] :
            ( ! [SY283: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SY281 ) @ SY282 ) @ SY283 ) )
            | ( ( hAPP @ SV24 @ SV61 @ SY282 @ ( hAPP @ SV61 @ SV24 @ SY281 @ SY280 ) )
              = ( ti @ SV61 @ SY280 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[261]) ).

thf(306,plain,
    ! [SV62: $i,SV25: $i] :
      ( ( ! [SY284: $i,SY285: $i,SY286: $i,SY287: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SY285 ) @ SY286 ) @ SY287 ) )
            | ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SY285 @ SY284 ) ) @ SY287 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[262]) ).

thf(307,plain,
    ! [SV63: $i,SV26: $i] :
      ( ( ! [SY288: $i,SY289: $i,SY290: $i,SY291: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SY289 ) @ SY290 ) @ SY291 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SY288 ) @ SY291 ) )
            | ( ( ti @ SV26 @ SY288 )
              = ( hAPP @ SV63 @ SV26 @ SY289 @ ( sK6_X_2 @ SY291 @ SY290 @ SY289 @ SY288 @ SV63 @ SV26 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[264]) ).

thf(308,plain,
    ! [SV64: $i,SV27: $i] :
      ( ( ! [SY292: $i,SY293: $i,SY294: $i,SY295: $i,SY296: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SY294 ) @ SY295 ) @ SY296 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SY293 ) @ SY296 ) )
            | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SY292 @ ( hAPP @ SV64 @ SV27 @ SY294 @ ( sK3_X_2 @ SY296 @ SY295 @ SY294 @ SY293 @ SY292 @ SV64 @ SV27 ) ) ) )
            | ( hBOOL @ ( hAPP @ SV27 @ bool @ SY292 @ SY293 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[265]) ).

thf(309,plain,
    ! [SV65: $i,SV28: $i] :
      ( ( ! [SY297: $i,SY298: $i] :
            ( ( ( hAPP @ SV28 @ SV65 @ SY297 @ ( sK2_X_2 @ SY298 @ SY297 @ SV65 @ SV28 ) )
             != ( hAPP @ SV28 @ SV65 @ SY298 @ ( sK2_X_2 @ SY298 @ SY297 @ SV65 @ SV28 ) ) )
            | ( ( ti @ ( fun @ SV28 @ SV65 ) @ SY297 )
              = ( ti @ ( fun @ SV28 @ SV65 ) @ SY298 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[266]) ).

thf(310,plain,
    ! [SV66: $i,SV29: $i] :
      ( ( ( hAPP @ ( fun @ SV29 @ bool ) @ ( fun @ SV29 @ bool ) @ ( collect @ SV29 ) @ SV66 )
        = ( ti @ ( fun @ SV29 @ bool ) @ SV66 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[267]) ).

thf(311,plain,
    ! [SV30: $i,SV67: $i] :
      ( ( ~ ( enum @ SV67 )
        | ~ ( enum @ SV30 )
        | ( enum @ ( sum_sum @ SV30 @ SV67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[268]) ).

thf(312,plain,
    ! [SV31: $i,SV68: $i] :
      ( ( ~ ( enum @ SV68 )
        | ~ ( enum @ SV31 )
        | ( enum @ ( fun @ SV31 @ SV68 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[269]) ).

thf(313,plain,
    ! [SV32: $i,SV69: $i] :
      ( ( ~ ( cl_HOL_Oequal @ SV69 )
        | ~ ( enum @ SV32 )
        | ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[270]) ).

thf(314,plain,
    ! [SV70: $i,SV33: $i] :
      ( ( cl_HOL_Oequal @ ( sum_sum @ SV33 @ SV70 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[271]) ).

thf(315,plain,
    ! [SV71: $i,SV35: $i] :
      ( ( ( ti @ SV35 @ ( ti @ SV35 @ SV71 ) )
        = ( ti @ SV35 @ SV71 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[273]) ).

thf(316,plain,
    ! [SV72: $i,SV36: $i] :
      ( ( ! [SY299: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SY299 ) )
            | ( ( ti @ SV36 @ SV72 )
              = ( ti @ SV36 @ SY299 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[274]) ).

thf(317,plain,
    ! [SV73: $i,SV37: $i] :
      ( ( ! [SY300: $i] :
            ( ( ( ti @ SV37 @ SV73 )
             != ( ti @ SV37 @ SY300 ) )
            | ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SY300 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[275]) ).

thf(318,plain,
    ! [SV74: $i,SV39: $i] :
      ( ( ! [SY301: $i] :
            ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SY301 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
                | ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY301 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SY301 @ SV74 @ SV39 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY301 @ SV74 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[277]) ).

thf(319,plain,
    ! [SV75: $i,SV40: $i] :
      ( ( ! [SY302: $i,SY303: $i,SY304: $i,SY305: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SY303 ) @ SY304 ) @ SY305 ) )
            | ~ ( ( ( ti @ SV75 @ SY302 )
                 != ( hAPP @ SV40 @ SV75 @ SY304 @ ( sK5_Y_2 @ SY305 @ SY304 @ SY303 @ SY302 @ SV75 @ SV40 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY305 @ SY304 @ SY303 @ SY302 @ SV75 @ SV40 ) ) @ SY305 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[278]) ).

thf(320,plain,
    ! [SV76: $i,SV41: $i] :
      ( ( ! [SY306: $i,SY307: $i,SY308: $i] :
            ~ ( ~ ( ! [SY309: $i,SY310: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY308 ) @ SY309 ) @ SY310 ) )
                  | ( ( hAPP @ SV76 @ SV41 @ SY308 @ SY306 )
                   != ( hAPP @ SV76 @ SV41 @ SY308 @ SY307 ) )
                  | ( ( ti @ SV76 @ SY306 )
                    = ( ti @ SV76 @ SY307 ) ) )
              | ~ ( ! [SY311: $i,SY312: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY308 ) @ SY311 ) @ SY312 ) )
                  | ( ( ti @ SV76 @ SY306 )
                   != ( ti @ SV76 @ SY307 ) )
                  | ( ( hAPP @ SV76 @ SV41 @ SY308 @ SY306 )
                    = ( hAPP @ SV76 @ SV41 @ SY308 @ SY307 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[279]) ).

thf(321,plain,
    ! [SV77: $i,SV42: $i] :
      ( ( ! [SY313: $i,SY314: $i,SY315: $i,SY316: $i,SY317: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SY315 ) @ SY316 ) @ SY317 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY317 @ SY316 @ SY315 @ SY314 @ SY313 @ SV77 @ SV42 ) ) @ SY317 ) )
                | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SY314 @ ( hAPP @ SV42 @ SV77 @ SY316 @ ( sK4_Y_2 @ SY317 @ SY316 @ SY315 @ SY314 @ SY313 @ SV77 @ SV42 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ SV77 @ bool @ SY314 @ SY313 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[280]) ).

thf(322,plain,
    ! [SV43: $i] :
      ( ( ~ ! [SY236: $i,SY237: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
              | ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) )
        | ~ ! [SY238: $i,SY239: $i] :
              ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
              | ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[281]) ).

thf(323,plain,
    ( ( ~ ( ! [SX0: $i,SX1: $i] :
              ( ( ti @ state @ SX0 )
              = ( ti @ state @ SX1 ) )
          | ( hBOOL @ hoare_1883395792gleton ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[282]) ).

thf(324,plain,
    ( ( ~ ( ~ ( hBOOL @ hoare_1883395792gleton )
          | ( ( ti @ state @ sK11_S )
           != ( ti @ state @ sK12_SY158 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[282]) ).

thf(325,plain,
    ! [SV44: $i] :
      ( ( ~ ! [SY240: $i,SY241: $i] :
              ( ( ( ti @ SV44 @ SY240 )
               != ( ti @ SV44 @ SY241 ) )
              | ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) )
        | ~ ! [SY242: $i,SY243: $i] :
              ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
              | ( ( ti @ SV44 @ SY242 )
                = ( ti @ SV44 @ SY243 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[283]) ).

thf(326,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
            | ( hBOOL @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[284]) ).

thf(327,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( hBOOL @ SX0 )
            | ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[284]) ).

thf(328,plain,
    ! [SV45: $i] :
      ( ( ( ~ ( cl_HOL_Oequal @ SV45 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY244: $i,SY245: $i] :
                    ( ( ( ti @ SV45 @ SY244 )
                     != ( ti @ SV45 @ SY245 ) )
                    | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
              | ~ ! [SY246: $i,SY247: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
                    | ( ( ti @ SV45 @ SY246 )
                      = ( ti @ SV45 @ SY247 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[285]) ).

thf(329,plain,
    ! [SV46: $i,SV78: $i] :
      ( ( ~ ( ( SV78
             != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[286]) ).

thf(330,plain,
    ! [SV47: $i] :
      ( ( ~ ! [SY249: $i,SY250: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
               != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
              | ( SY250 = SY249 ) )
        | ~ ! [SY251: $i,SY252: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ( SY252 != SY251 )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
                = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[287]) ).

thf(331,plain,
    ! [SV48: $i] :
      ( ( ~ ! [SY253: $i,SY254: $i] :
              ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
               != ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
              | ( SY253 = SY254 ) )
        | ~ ! [SY255: $i,SY256: $i] :
              ( ( SY255 != SY256 )
              | ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
                = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[288]) ).

thf(332,plain,
    ! [SV79: $i,SV49: $i] :
      ( ( ! [SY318: $i,SY319: $i,SY320: $i] :
            ~ ( ~ ! [SY321: $i,SY322: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY320 ) @ SY321 ) @ SY322 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY319 ) @ SY322 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY318 ) @ SY322 ) )
                    | ( ( hAPP @ SV49 @ SV79 @ SY321 @ SY319 )
                     != ( hAPP @ SV49 @ SV79 @ SY321 @ SY318 ) )
                    | ( ( ti @ SV49 @ SY319 )
                      = ( ti @ SV49 @ SY318 ) ) )
              | ~ ! [SY323: $i,SY324: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY320 ) @ SY323 ) @ SY324 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY319 ) @ SY324 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY318 ) @ SY324 ) )
                    | ( ( ti @ SV49 @ SY319 )
                     != ( ti @ SV49 @ SY318 ) )
                    | ( ( hAPP @ SV49 @ SV79 @ SY323 @ SY319 )
                      = ( hAPP @ SV49 @ SV79 @ SY323 @ SY318 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[289]) ).

thf(333,plain,
    ! [SV50: $i] :
      ( ( ~ ! [SY265: $i,SY266: $i] :
              ( ( SY265 != SY266 )
              | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) )
        | ~ ! [SY267: $i,SY268: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
              | ( SY267 = SY268 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[290]) ).

thf(334,plain,
    ! [SV1: $i] :
      ( ( ( cl_HOL_Oequal @ SV1 )
        = $false )
      | ( ( ( ti @ ( fun @ SV1 @ ( fun @ SV1 @ bool ) ) @ ( equal_equal @ SV1 ) )
          = ( equal_equal @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[291]) ).

thf(335,plain,
    ! [SV80: $i,SV52: $i,SV10: $i] :
      ( ( ! [SY325: $i] :
            ( ( hAPP @ SV10 @ SV52 @ ( ti @ ( fun @ SV10 @ SV52 ) @ SV80 ) @ SY325 )
            = ( hAPP @ SV10 @ SV52 @ SV80 @ SY325 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[293]) ).

thf(336,plain,
    ! [SV81: $i,SV53: $i,SV11: $i] :
      ( ( ! [SY326: $i] :
            ( ( hAPP @ SV11 @ SV53 @ SV81 @ ( ti @ SV11 @ SY326 ) )
            = ( hAPP @ SV11 @ SV53 @ SV81 @ SY326 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[294]) ).

thf(337,plain,
    ! [SV82: $i,SV54: $i,SV12: $i] :
      ( ( ! [SY327: $i] :
            ( ( ti @ SV12 @ ( hAPP @ SV54 @ SV12 @ SV82 @ SY327 ) )
            = ( hAPP @ SV54 @ SV12 @ SV82 @ SY327 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[295]) ).

thf(338,plain,
    ! [SV14: $i] :
      ( ( ( cl_HOL_Oequal @ SV14 )
        = $false )
      | ( ( ( equal_equal @ SV14 )
          = ( fequal @ SV14 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[296]) ).

thf(339,plain,
    ! [SV15: $i] :
      ( ( ( cl_HOL_Oequal @ SV15 )
        = $false )
      | ( ( ! [SY169: $i] : ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SY169 ) @ SY169 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[297]) ).

thf(340,plain,
    ! [SV16: $i] :
      ( ( ( cl_HOL_Oequal @ SV16 )
        = $false )
      | ( ( ( fequal @ SV16 )
          = ( equal_equal @ SV16 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[298]) ).

thf(341,plain,
    ! [SV57: $i,SV83: $i,SV19: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
        | ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[301]) ).

thf(342,plain,
    ! [SV58: $i,SV20: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SV58 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) ) )
        = $true )
      | ( ( SV58
          = ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SV58 @ SV20 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[302]) ).

thf(343,plain,
    ! [SV59: $i,SV21: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SV59 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) ) )
        = $true )
      | ( ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SV59 ) )
          = SV59 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[303]) ).

thf(344,plain,
    ! [SV84: $i,SV60: $i,SV23: $i] :
      ( ( ! [SY328: $i,SY329: $i,SY330: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SY328 ) @ SY329 ) @ SY330 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SY330 ) )
            | ( ( hAPP @ SV60 @ SV23 @ SY328 @ ( hAPP @ SV23 @ SV60 @ SY329 @ SV84 ) )
              = ( ti @ SV23 @ SV84 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[304]) ).

thf(345,plain,
    ! [SV85: $i,SV61: $i,SV24: $i] :
      ( ( ! [SY331: $i,SY332: $i] :
            ( ! [SY283: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SY331 ) @ SY332 ) @ SY283 ) )
            | ( ( hAPP @ SV24 @ SV61 @ SY332 @ ( hAPP @ SV61 @ SV24 @ SY331 @ SV85 ) )
              = ( ti @ SV61 @ SV85 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[305]) ).

thf(346,plain,
    ! [SV86: $i,SV62: $i,SV25: $i] :
      ( ( ! [SY334: $i,SY335: $i,SY336: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SY334 ) @ SY335 ) @ SY336 ) )
            | ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SY334 @ SV86 ) ) @ SY336 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[306]) ).

thf(347,plain,
    ! [SV87: $i,SV63: $i,SV26: $i] :
      ( ( ! [SY337: $i,SY338: $i,SY339: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SY337 ) @ SY338 ) @ SY339 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SY339 ) )
            | ( ( ti @ SV26 @ SV87 )
              = ( hAPP @ SV63 @ SV26 @ SY337 @ ( sK6_X_2 @ SY339 @ SY338 @ SY337 @ SV87 @ SV63 @ SV26 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[307]) ).

thf(348,plain,
    ! [SV88: $i,SV64: $i,SV27: $i] :
      ( ( ! [SY340: $i,SY341: $i,SY342: $i,SY343: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SY341 ) @ SY342 ) @ SY343 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SY340 ) @ SY343 ) )
            | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SY341 @ ( sK3_X_2 @ SY343 @ SY342 @ SY341 @ SY340 @ SV88 @ SV64 @ SV27 ) ) ) )
            | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SY340 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[308]) ).

thf(349,plain,
    ! [SV89: $i,SV65: $i,SV28: $i] :
      ( ( ! [SY344: $i] :
            ( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SY344 @ SV89 @ SV65 @ SV28 ) )
             != ( hAPP @ SV28 @ SV65 @ SY344 @ ( sK2_X_2 @ SY344 @ SV89 @ SV65 @ SV28 ) ) )
            | ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
              = ( ti @ ( fun @ SV28 @ SV65 ) @ SY344 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[309]) ).

thf(350,plain,
    ! [SV30: $i,SV67: $i] :
      ( ( ( ~ ( enum @ SV67 )
          | ~ ( enum @ SV30 ) )
        = $true )
      | ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[311]) ).

thf(351,plain,
    ! [SV31: $i,SV68: $i] :
      ( ( ( ~ ( enum @ SV68 )
          | ~ ( enum @ SV31 ) )
        = $true )
      | ( ( enum @ ( fun @ SV31 @ SV68 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[312]) ).

thf(352,plain,
    ! [SV32: $i,SV69: $i] :
      ( ( ( ~ ( cl_HOL_Oequal @ SV69 )
          | ~ ( enum @ SV32 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[313]) ).

thf(353,plain,
    ! [SV90: $i,SV72: $i,SV36: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SV90 ) )
        | ( ( ti @ SV36 @ SV72 )
          = ( ti @ SV36 @ SV90 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[316]) ).

thf(354,plain,
    ! [SV91: $i,SV73: $i,SV37: $i] :
      ( ( ( ( ti @ SV37 @ SV73 )
         != ( ti @ SV37 @ SV91 ) )
        | ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SV91 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[317]) ).

thf(355,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
            | ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
        | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[318]) ).

thf(356,plain,
    ! [SV93: $i,SV75: $i,SV40: $i] :
      ( ( ! [SY345: $i,SY346: $i,SY347: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SY345 ) @ SY346 ) @ SY347 ) )
            | ~ ( ( ( ti @ SV75 @ SV93 )
                 != ( hAPP @ SV40 @ SV75 @ SY346 @ ( sK5_Y_2 @ SY347 @ SY346 @ SY345 @ SV93 @ SV75 @ SV40 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY347 @ SY346 @ SY345 @ SV93 @ SV75 @ SV40 ) ) @ SY347 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[319]) ).

thf(357,plain,
    ! [SV94: $i,SV76: $i,SV41: $i] :
      ( ( ! [SY348: $i,SY349: $i] :
            ~ ( ~ ( ! [SY309: $i,SY310: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY349 ) @ SY309 ) @ SY310 ) )
                  | ( ( hAPP @ SV76 @ SV41 @ SY349 @ SV94 )
                   != ( hAPP @ SV76 @ SV41 @ SY349 @ SY348 ) )
                  | ( ( ti @ SV76 @ SV94 )
                    = ( ti @ SV76 @ SY348 ) ) )
              | ~ ( ! [SY311: $i,SY312: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY349 ) @ SY311 ) @ SY312 ) )
                  | ( ( ti @ SV76 @ SV94 )
                   != ( ti @ SV76 @ SY348 ) )
                  | ( ( hAPP @ SV76 @ SV41 @ SY349 @ SV94 )
                    = ( hAPP @ SV76 @ SV41 @ SY349 @ SY348 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[320]) ).

thf(358,plain,
    ! [SV95: $i,SV77: $i,SV42: $i] :
      ( ( ! [SY354: $i,SY355: $i,SY356: $i,SY357: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SY355 ) @ SY356 ) @ SY357 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY357 @ SY356 @ SY355 @ SY354 @ SV95 @ SV77 @ SV42 ) ) @ SY357 ) )
                | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SY354 @ ( hAPP @ SV42 @ SV77 @ SY356 @ ( sK4_Y_2 @ SY357 @ SY356 @ SY355 @ SY354 @ SV95 @ SV77 @ SV42 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ SV77 @ bool @ SY354 @ SV95 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[321]) ).

thf(359,plain,
    ! [SV43: $i] :
      ( ( ~ ! [SY236: $i,SY237: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
              | ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[322]) ).

thf(360,plain,
    ! [SV43: $i] :
      ( ( ~ ! [SY238: $i,SY239: $i] :
              ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
              | ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[322]) ).

thf(361,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ti @ state @ SX0 )
          = ( ti @ state @ SX1 ) )
      | ( hBOOL @ hoare_1883395792gleton ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[323]) ).

thf(362,plain,
    ( ( ~ ( hBOOL @ hoare_1883395792gleton )
      | ( ( ti @ state @ sK11_S )
       != ( ti @ state @ sK12_SY158 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[324]) ).

thf(363,plain,
    ! [SV44: $i] :
      ( ( ~ ! [SY240: $i,SY241: $i] :
              ( ( ( ti @ SV44 @ SY240 )
               != ( ti @ SV44 @ SY241 ) )
              | ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[325]) ).

thf(364,plain,
    ! [SV44: $i] :
      ( ( ~ ! [SY242: $i,SY243: $i] :
              ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
              | ( ( ti @ SV44 @ SY242 )
                = ( ti @ SV44 @ SY243 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[325]) ).

thf(365,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
          | ( hBOOL @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[326]) ).

thf(366,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( hBOOL @ SX0 )
          | ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[327]) ).

thf(367,plain,
    ! [SV45: $i] :
      ( ( ( cl_HOL_Oequal @ SV45 )
        = $false )
      | ( ( ~ ( ~ ! [SY244: $i,SY245: $i] :
                    ( ( ( ti @ SV45 @ SY244 )
                     != ( ti @ SV45 @ SY245 ) )
                    | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
              | ~ ! [SY246: $i,SY247: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
                    | ( ( ti @ SV45 @ SY246 )
                      = ( ti @ SV45 @ SY247 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[328]) ).

thf(368,plain,
    ! [SV46: $i,SV78: $i] :
      ( ( ( SV78
         != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[329]) ).

thf(369,plain,
    ! [SV47: $i] :
      ( ( ~ ! [SY249: $i,SY250: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
               != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
              | ( SY250 = SY249 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[330]) ).

thf(370,plain,
    ! [SV47: $i] :
      ( ( ~ ! [SY251: $i,SY252: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
              | ( SY252 != SY251 )
              | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
                = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[330]) ).

thf(371,plain,
    ! [SV48: $i] :
      ( ( ~ ! [SY253: $i,SY254: $i] :
              ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
               != ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
              | ( SY253 = SY254 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[331]) ).

thf(372,plain,
    ! [SV48: $i] :
      ( ( ~ ! [SY255: $i,SY256: $i] :
              ( ( SY255 != SY256 )
              | ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
                = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[331]) ).

thf(373,plain,
    ! [SV96: $i,SV79: $i,SV49: $i] :
      ( ( ! [SY358: $i,SY359: $i] :
            ~ ( ~ ! [SY360: $i,SY361: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY359 ) @ SY360 ) @ SY361 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY358 ) @ SY361 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY361 ) )
                    | ( ( hAPP @ SV49 @ SV79 @ SY360 @ SY358 )
                     != ( hAPP @ SV49 @ SV79 @ SY360 @ SV96 ) )
                    | ( ( ti @ SV49 @ SY358 )
                      = ( ti @ SV49 @ SV96 ) ) )
              | ~ ! [SY362: $i,SY363: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY359 ) @ SY362 ) @ SY363 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY358 ) @ SY363 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY363 ) )
                    | ( ( ti @ SV49 @ SY358 )
                     != ( ti @ SV49 @ SV96 ) )
                    | ( ( hAPP @ SV49 @ SV79 @ SY362 @ SY358 )
                      = ( hAPP @ SV49 @ SV79 @ SY362 @ SV96 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[332]) ).

thf(374,plain,
    ! [SV50: $i] :
      ( ( ~ ! [SY265: $i,SY266: $i] :
              ( ( SY265 != SY266 )
              | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[333]) ).

thf(375,plain,
    ! [SV50: $i] :
      ( ( ~ ! [SY267: $i,SY268: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
              | ( SY267 = SY268 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[333]) ).

thf(376,plain,
    ! [SV97: $i,SV80: $i,SV52: $i,SV10: $i] :
      ( ( ( hAPP @ SV10 @ SV52 @ ( ti @ ( fun @ SV10 @ SV52 ) @ SV80 ) @ SV97 )
        = ( hAPP @ SV10 @ SV52 @ SV80 @ SV97 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[335]) ).

thf(377,plain,
    ! [SV98: $i,SV81: $i,SV53: $i,SV11: $i] :
      ( ( ( hAPP @ SV11 @ SV53 @ SV81 @ ( ti @ SV11 @ SV98 ) )
        = ( hAPP @ SV11 @ SV53 @ SV81 @ SV98 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[336]) ).

thf(378,plain,
    ! [SV99: $i,SV82: $i,SV54: $i,SV12: $i] :
      ( ( ( ti @ SV12 @ ( hAPP @ SV54 @ SV12 @ SV82 @ SV99 ) )
        = ( hAPP @ SV54 @ SV12 @ SV82 @ SV99 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[337]) ).

thf(379,plain,
    ! [SV100: $i,SV15: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SV100 ) @ SV100 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV15 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[339]) ).

thf(380,plain,
    ! [SV57: $i,SV83: $i,SV19: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
          | ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[341]) ).

thf(381,plain,
    ! [SV58: $i,SV20: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SV58 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) )
        = $false )
      | ( ( SV58
          = ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SV58 @ SV20 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[342]) ).

thf(382,plain,
    ! [SV59: $i,SV21: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SV59 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) )
        = $false )
      | ( ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SV59 ) )
          = SV59 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[343]) ).

thf(383,plain,
    ! [SV84: $i,SV101: $i,SV60: $i,SV23: $i] :
      ( ( ! [SY364: $i,SY365: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SY364 ) @ SY365 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SY365 ) )
            | ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SY364 @ SV84 ) )
              = ( ti @ SV23 @ SV84 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[344]) ).

thf(384,plain,
    ! [SV85: $i,SV102: $i,SV61: $i,SV24: $i] :
      ( ( ! [SY366: $i] :
            ( ! [SY367: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SY366 ) @ SY367 ) )
            | ( ( hAPP @ SV24 @ SV61 @ SY366 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
              = ( ti @ SV61 @ SV85 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[345]) ).

thf(385,plain,
    ! [SV86: $i,SV103: $i,SV62: $i,SV25: $i] :
      ( ( ! [SY368: $i,SY369: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SY368 ) @ SY369 ) )
            | ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SY369 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[346]) ).

thf(386,plain,
    ! [SV87: $i,SV104: $i,SV63: $i,SV26: $i] :
      ( ( ! [SY370: $i,SY371: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SY370 ) @ SY371 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SY371 ) )
            | ( ( ti @ SV26 @ SV87 )
              = ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SY371 @ SY370 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[347]) ).

thf(387,plain,
    ! [SV88: $i,SV105: $i,SV64: $i,SV27: $i] :
      ( ( ! [SY372: $i,SY373: $i,SY374: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SY372 ) @ SY373 ) @ SY374 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SY374 ) )
            | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SY372 @ ( sK3_X_2 @ SY374 @ SY373 @ SY372 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
            | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[348]) ).

thf(388,plain,
    ! [SV106: $i,SV89: $i,SV65: $i,SV28: $i] :
      ( ( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) )
         != ( hAPP @ SV28 @ SV65 @ SV106 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) ) )
        | ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
          = ( ti @ ( fun @ SV28 @ SV65 ) @ SV106 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[349]) ).

thf(389,plain,
    ! [SV30: $i,SV67: $i] :
      ( ( ( ~ ( enum @ SV67 ) )
        = $true )
      | ( ( ~ ( enum @ SV30 ) )
        = $true )
      | ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[350]) ).

thf(390,plain,
    ! [SV31: $i,SV68: $i] :
      ( ( ( ~ ( enum @ SV68 ) )
        = $true )
      | ( ( ~ ( enum @ SV31 ) )
        = $true )
      | ( ( enum @ ( fun @ SV31 @ SV68 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[351]) ).

thf(391,plain,
    ! [SV32: $i,SV69: $i] :
      ( ( ( ~ ( cl_HOL_Oequal @ SV69 ) )
        = $true )
      | ( ( ~ ( enum @ SV32 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[352]) ).

thf(392,plain,
    ! [SV90: $i,SV72: $i,SV36: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SV90 ) ) )
        = $true )
      | ( ( ( ti @ SV36 @ SV72 )
          = ( ti @ SV36 @ SV90 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[353]) ).

thf(393,plain,
    ! [SV91: $i,SV73: $i,SV37: $i] :
      ( ( ( ( ( ti @ SV37 @ SV73 )
           != ( ti @ SV37 @ SV91 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SV91 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[354]) ).

thf(394,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
              | ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[355]) ).

thf(395,plain,
    ! [SV93: $i,SV107: $i,SV75: $i,SV40: $i] :
      ( ( ! [SY375: $i,SY376: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SY375 ) @ SY376 ) )
            | ~ ( ( ( ti @ SV75 @ SV93 )
                 != ( hAPP @ SV40 @ SV75 @ SY375 @ ( sK5_Y_2 @ SY376 @ SY375 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY376 @ SY375 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SY376 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[356]) ).

thf(396,plain,
    ! [SV108: $i,SV94: $i,SV76: $i,SV41: $i] :
      ( ( ! [SY377: $i] :
            ~ ( ~ ( ! [SY309: $i,SY310: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY377 ) @ SY309 ) @ SY310 ) )
                  | ( ( hAPP @ SV76 @ SV41 @ SY377 @ SV94 )
                   != ( hAPP @ SV76 @ SV41 @ SY377 @ SV108 ) )
                  | ( ( ti @ SV76 @ SV94 )
                    = ( ti @ SV76 @ SV108 ) ) )
              | ~ ( ! [SY311: $i,SY312: $i] :
                      ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY377 ) @ SY311 ) @ SY312 ) )
                  | ( ( ti @ SV76 @ SV94 )
                   != ( ti @ SV76 @ SV108 ) )
                  | ( ( hAPP @ SV76 @ SV41 @ SY377 @ SV94 )
                    = ( hAPP @ SV76 @ SV41 @ SY377 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[357]) ).

thf(397,plain,
    ! [SV95: $i,SV109: $i,SV77: $i,SV42: $i] :
      ( ( ! [SY382: $i,SY383: $i,SY384: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SY382 ) @ SY383 ) @ SY384 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY384 @ SY383 @ SY382 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SY384 ) )
                | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SY383 @ ( sK4_Y_2 @ SY384 @ SY383 @ SY382 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[358]) ).

thf(398,plain,
    ! [SV43: $i] :
      ( ( ! [SY236: $i,SY237: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
            | ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[359]) ).

thf(399,plain,
    ! [SV43: $i] :
      ( ( ! [SY238: $i,SY239: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
            | ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[360]) ).

thf(400,plain,
    ( ( ( ! [SX0: $i,SX1: $i] :
            ( ( ti @ state @ SX0 )
            = ( ti @ state @ SX1 ) ) )
      = $true )
    | ( ( hBOOL @ hoare_1883395792gleton )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[361]) ).

thf(401,plain,
    ( ( ( ~ ( hBOOL @ hoare_1883395792gleton ) )
      = $true )
    | ( ( ( ( ti @ state @ sK11_S )
         != ( ti @ state @ sK12_SY158 ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[362]) ).

thf(402,plain,
    ! [SV44: $i] :
      ( ( ! [SY240: $i,SY241: $i] :
            ( ( ( ti @ SV44 @ SY240 )
             != ( ti @ SV44 @ SY241 ) )
            | ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[363]) ).

thf(403,plain,
    ! [SV44: $i] :
      ( ( ! [SY242: $i,SY243: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
            | ( ( ti @ SV44 @ SY242 )
              = ( ti @ SV44 @ SY243 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[364]) ).

thf(404,plain,
    ! [SV110: $i] :
      ( ( ~ ( hBOOL @ ( ti @ bool @ SV110 ) )
        | ( hBOOL @ SV110 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[365]) ).

thf(405,plain,
    ! [SV111: $i] :
      ( ( ~ ( hBOOL @ SV111 )
        | ( hBOOL @ ( ti @ bool @ SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[366]) ).

thf(406,plain,
    ! [SV45: $i] :
      ( ( ( ~ ! [SY244: $i,SY245: $i] :
                ( ( ( ti @ SV45 @ SY244 )
                 != ( ti @ SV45 @ SY245 ) )
                | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
          | ~ ! [SY246: $i,SY247: $i] :
                ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
                | ( ( ti @ SV45 @ SY246 )
                  = ( ti @ SV45 @ SY247 ) ) ) )
        = $false )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[367]) ).

thf(407,plain,
    ! [SV46: $i,SV78: $i] :
      ( ( ( SV78
         != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[368]) ).

thf(408,plain,
    ! [SV78: $i,SV46: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[368]) ).

thf(409,plain,
    ! [SV47: $i] :
      ( ( ! [SY249: $i,SY250: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
             != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
            | ( SY250 = SY249 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[369]) ).

thf(410,plain,
    ! [SV47: $i] :
      ( ( ! [SY251: $i,SY252: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ( SY252 != SY251 )
            | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
              = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[370]) ).

thf(411,plain,
    ! [SV48: $i] :
      ( ( ! [SY253: $i,SY254: $i] :
            ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
             != ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
            | ( SY253 = SY254 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[371]) ).

thf(412,plain,
    ! [SV48: $i] :
      ( ( ! [SY255: $i,SY256: $i] :
            ( ( SY255 != SY256 )
            | ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
              = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[372]) ).

thf(413,plain,
    ! [SV96: $i,SV112: $i,SV79: $i,SV49: $i] :
      ( ( ! [SY385: $i] :
            ~ ( ~ ! [SY386: $i,SY387: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY385 ) @ SY386 ) @ SY387 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY387 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY387 ) )
                    | ( ( hAPP @ SV49 @ SV79 @ SY386 @ SV112 )
                     != ( hAPP @ SV49 @ SV79 @ SY386 @ SV96 ) )
                    | ( ( ti @ SV49 @ SV112 )
                      = ( ti @ SV49 @ SV96 ) ) )
              | ~ ! [SY388: $i,SY389: $i] :
                    ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY385 ) @ SY388 ) @ SY389 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY389 ) )
                    | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY389 ) )
                    | ( ( ti @ SV49 @ SV112 )
                     != ( ti @ SV49 @ SV96 ) )
                    | ( ( hAPP @ SV49 @ SV79 @ SY388 @ SV112 )
                      = ( hAPP @ SV49 @ SV79 @ SY388 @ SV96 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[373]) ).

thf(414,plain,
    ! [SV50: $i] :
      ( ( ! [SY265: $i,SY266: $i] :
            ( ( SY265 != SY266 )
            | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[374]) ).

thf(415,plain,
    ! [SV50: $i] :
      ( ( ! [SY267: $i,SY268: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
            | ( SY267 = SY268 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[375]) ).

thf(416,plain,
    ! [SV57: $i,SV83: $i,SV19: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
          | ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[380]) ).

thf(417,plain,
    ! [SV84: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
      ( ( ! [SY390: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SY390 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SY390 ) )
            | ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
              = ( ti @ SV23 @ SV84 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[383]) ).

thf(418,plain,
    ! [SV85: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
      ( ( ! [SY391: $i] :
            ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SY391 ) )
        | ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
          = ( ti @ SV61 @ SV85 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[384]) ).

thf(419,plain,
    ! [SV86: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
      ( ( ! [SY392: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SY392 ) )
            | ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SY392 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[385]) ).

thf(420,plain,
    ! [SV87: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
      ( ( ! [SY393: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SY393 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SY393 ) )
            | ( ( ti @ SV26 @ SV87 )
              = ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SY393 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[386]) ).

thf(421,plain,
    ! [SV88: $i,SV105: $i,SV117: $i,SV64: $i,SV27: $i] :
      ( ( ! [SY394: $i,SY395: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SY394 ) @ SY395 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SY395 ) )
            | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SY395 @ SY394 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
            | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[387]) ).

thf(422,plain,
    ! [SV106: $i,SV89: $i,SV65: $i,SV28: $i] :
      ( ( ( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) )
           != ( hAPP @ SV28 @ SV65 @ SV106 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) ) ) )
        = $true )
      | ( ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
          = ( ti @ ( fun @ SV28 @ SV65 ) @ SV106 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[388]) ).

thf(423,plain,
    ! [SV30: $i,SV67: $i] :
      ( ( ( enum @ SV67 )
        = $false )
      | ( ( ~ ( enum @ SV30 ) )
        = $true )
      | ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[389]) ).

thf(424,plain,
    ! [SV31: $i,SV68: $i] :
      ( ( ( enum @ SV68 )
        = $false )
      | ( ( ~ ( enum @ SV31 ) )
        = $true )
      | ( ( enum @ ( fun @ SV31 @ SV68 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[390]) ).

thf(425,plain,
    ! [SV32: $i,SV69: $i] :
      ( ( ( cl_HOL_Oequal @ SV69 )
        = $false )
      | ( ( ~ ( enum @ SV32 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[391]) ).

thf(426,plain,
    ! [SV90: $i,SV72: $i,SV36: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SV90 ) )
        = $false )
      | ( ( ( ti @ SV36 @ SV72 )
          = ( ti @ SV36 @ SV90 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[392]) ).

thf(427,plain,
    ! [SV91: $i,SV73: $i,SV37: $i] :
      ( ( ( ( ti @ SV37 @ SV73 )
          = ( ti @ SV37 @ SV91 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SV91 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[393]) ).

thf(428,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
          | ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[394]) ).

thf(429,plain,
    ! [SV93: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
      ( ( ! [SY396: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SY396 ) )
            | ~ ( ( ( ti @ SV75 @ SV93 )
                 != ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SY396 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
                | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY396 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SY396 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[395]) ).

thf(430,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ~ ( ~ ( ! [SY397: $i,SY398: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
                | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
                 != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
                | ( ( ti @ SV76 @ SV94 )
                  = ( ti @ SV76 @ SV108 ) ) )
            | ~ ( ! [SY399: $i,SY400: $i] :
                    ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
                | ( ( ti @ SV76 @ SV94 )
                 != ( ti @ SV76 @ SV108 ) )
                | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
                  = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[396]) ).

thf(431,plain,
    ! [SV95: $i,SV109: $i,SV120: $i,SV77: $i,SV42: $i] :
      ( ( ! [SY401: $i,SY402: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SY401 ) @ SY402 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY402 @ SY401 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SY402 ) )
                | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SY401 @ ( sK4_Y_2 @ SY402 @ SY401 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[397]) ).

thf(432,plain,
    ! [SV121: $i,SV43: $i] :
      ( ( ! [SY403: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SY403 ) )
            | ( hBOOL @ ( hAPP @ SV43 @ bool @ SY403 @ SV121 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[398]) ).

thf(433,plain,
    ! [SV122: $i,SV43: $i] :
      ( ( ! [SY404: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY404 @ SV122 ) )
            | ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SY404 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[399]) ).

thf(434,plain,
    ! [SV123: $i] :
      ( ( ( ! [SY405: $i] :
              ( ( ti @ state @ SV123 )
              = ( ti @ state @ SY405 ) ) )
        = $true )
      | ( ( hBOOL @ hoare_1883395792gleton )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[400]) ).

thf(435,plain,
    ( ( ( hBOOL @ hoare_1883395792gleton )
      = $false )
    | ( ( ( ( ti @ state @ sK11_S )
         != ( ti @ state @ sK12_SY158 ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[401]) ).

thf(436,plain,
    ! [SV124: $i,SV44: $i] :
      ( ( ! [SY406: $i] :
            ( ( ( ti @ SV44 @ SV124 )
             != ( ti @ SV44 @ SY406 ) )
            | ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SY406 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[402]) ).

thf(437,plain,
    ! [SV125: $i,SV44: $i] :
      ( ( ! [SY407: $i] :
            ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SY407 ) )
            | ( ( ti @ SV44 @ SV125 )
              = ( ti @ SV44 @ SY407 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[403]) ).

thf(438,plain,
    ! [SV110: $i] :
      ( ( ( ~ ( hBOOL @ ( ti @ bool @ SV110 ) ) )
        = $true )
      | ( ( hBOOL @ SV110 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[404]) ).

thf(439,plain,
    ! [SV111: $i] :
      ( ( ( ~ ( hBOOL @ SV111 ) )
        = $true )
      | ( ( hBOOL @ ( ti @ bool @ SV111 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[405]) ).

thf(440,plain,
    ! [SV45: $i] :
      ( ( ( ~ ! [SY244: $i,SY245: $i] :
                ( ( ( ti @ SV45 @ SY244 )
                 != ( ti @ SV45 @ SY245 ) )
                | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) ) )
        = $false )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[406]) ).

thf(441,plain,
    ! [SV45: $i] :
      ( ( ( ~ ! [SY246: $i,SY247: $i] :
                ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
                | ( ( ti @ SV45 @ SY246 )
                  = ( ti @ SV45 @ SY247 ) ) ) )
        = $false )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[406]) ).

thf(442,plain,
    ! [SV46: $i,SV78: $i] :
      ( ( SV78
        = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[407]) ).

thf(443,plain,
    ! [SV78: $i,SV46: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[408]) ).

thf(444,plain,
    ! [SV126: $i,SV47: $i] :
      ( ( ! [SY408: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY408 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY408 )
             != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
            | ( SY408 = SV126 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[409]) ).

thf(445,plain,
    ! [SV127: $i,SV47: $i] :
      ( ( ! [SY409: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY409 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
            | ( SY409 != SV127 )
            | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY409 )
              = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[410]) ).

thf(446,plain,
    ! [SV128: $i,SV48: $i] :
      ( ( ! [SY410: $i] :
            ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
             != ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY410 ) )
            | ( SV128 = SY410 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[411]) ).

thf(447,plain,
    ! [SV48: $i,SV129: $i] :
      ( ( ! [SY411: $i] :
            ( ( SV129 != SY411 )
            | ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
              = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY411 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[412]) ).

thf(448,plain,
    ! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ~ ( ~ ! [SY412: $i,SY413: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
                  | ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
                   != ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
                  | ( ( ti @ SV49 @ SV112 )
                    = ( ti @ SV49 @ SV96 ) ) )
            | ~ ! [SY414: $i,SY415: $i] :
                  ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
                  | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
                  | ( ( ti @ SV49 @ SV112 )
                   != ( ti @ SV49 @ SV96 ) )
                  | ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
                    = ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[413]) ).

thf(449,plain,
    ! [SV50: $i,SV131: $i] :
      ( ( ! [SY416: $i] :
            ( ( SV131 != SY416 )
            | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SY416 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[414]) ).

thf(450,plain,
    ! [SV132: $i,SV50: $i] :
      ( ( ! [SY417: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SY417 ) )
            | ( SV132 = SY417 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[415]) ).

thf(451,plain,
    ! [SV83: $i,SV57: $i,SV19: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[416]) ).

thf(452,plain,
    ! [SV84: $i,SV133: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
        | ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
          = ( ti @ SV23 @ SV84 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[417]) ).

thf(453,plain,
    ! [SV85: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
      ( ( ( ! [SY391: $i] :
              ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SY391 ) ) )
        = $true )
      | ( ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
          = ( ti @ SV61 @ SV85 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[418]) ).

thf(454,plain,
    ! [SV86: $i,SV134: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SV134 ) )
        | ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SV134 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[419]) ).

thf(455,plain,
    ! [SV87: $i,SV135: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
        | ( ( ti @ SV26 @ SV87 )
          = ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[420]) ).

thf(456,plain,
    ! [SV88: $i,SV105: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
      ( ( ! [SY418: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SY418 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SY418 ) )
            | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SY418 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
            | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[421]) ).

thf(457,plain,
    ! [SV106: $i,SV89: $i,SV65: $i,SV28: $i] :
      ( ( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) )
          = ( hAPP @ SV28 @ SV65 @ SV106 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) ) )
        = $false )
      | ( ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
          = ( ti @ ( fun @ SV28 @ SV65 ) @ SV106 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[422]) ).

thf(458,plain,
    ! [SV67: $i,SV30: $i] :
      ( ( ( enum @ SV30 )
        = $false )
      | ( ( enum @ SV67 )
        = $false )
      | ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[423]) ).

thf(459,plain,
    ! [SV68: $i,SV31: $i] :
      ( ( ( enum @ SV31 )
        = $false )
      | ( ( enum @ SV68 )
        = $false )
      | ( ( enum @ ( fun @ SV31 @ SV68 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[424]) ).

thf(460,plain,
    ! [SV69: $i,SV32: $i] :
      ( ( ( enum @ SV32 )
        = $false )
      | ( ( cl_HOL_Oequal @ SV69 )
        = $false )
      | ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[425]) ).

thf(461,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[428]) ).

thf(462,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[428]) ).

thf(463,plain,
    ! [SV93: $i,SV137: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
        | ~ ( ( ( ti @ SV75 @ SV93 )
             != ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[429]) ).

thf(464,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ~ ( ! [SY397: $i,SY398: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
            | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
             != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
            | ( ( ti @ SV76 @ SV94 )
              = ( ti @ SV76 @ SV108 ) ) )
        | ~ ( ! [SY399: $i,SY400: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
            | ( ( ti @ SV76 @ SV94 )
             != ( ti @ SV76 @ SV108 ) )
            | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
              = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[430]) ).

thf(465,plain,
    ! [SV95: $i,SV109: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
      ( ( ! [SY419: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SY419 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY419 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SY419 ) )
                | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SY419 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
            | ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[431]) ).

thf(466,plain,
    ! [SV139: $i,SV121: $i,SV43: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SV139 ) )
        | ( hBOOL @ ( hAPP @ SV43 @ bool @ SV139 @ SV121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[432]) ).

thf(467,plain,
    ! [SV122: $i,SV140: $i,SV43: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SV140 @ SV122 ) )
        | ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SV140 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[433]) ).

thf(468,plain,
    ! [SV141: $i,SV123: $i] :
      ( ( ( ( ti @ state @ SV123 )
          = ( ti @ state @ SV141 ) )
        = $true )
      | ( ( hBOOL @ hoare_1883395792gleton )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[434]) ).

thf(469,plain,
    ( ( ( ( ti @ state @ sK11_S )
        = ( ti @ state @ sK12_SY158 ) )
      = $false )
    | ( ( hBOOL @ hoare_1883395792gleton )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[435]) ).

thf(470,plain,
    ! [SV142: $i,SV124: $i,SV44: $i] :
      ( ( ( ( ti @ SV44 @ SV124 )
         != ( ti @ SV44 @ SV142 ) )
        | ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SV142 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[436]) ).

thf(471,plain,
    ! [SV143: $i,SV125: $i,SV44: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SV143 ) )
        | ( ( ti @ SV44 @ SV125 )
          = ( ti @ SV44 @ SV143 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[437]) ).

thf(472,plain,
    ! [SV110: $i] :
      ( ( ( hBOOL @ ( ti @ bool @ SV110 ) )
        = $false )
      | ( ( hBOOL @ SV110 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[438]) ).

thf(473,plain,
    ! [SV111: $i] :
      ( ( ( hBOOL @ SV111 )
        = $false )
      | ( ( hBOOL @ ( ti @ bool @ SV111 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[439]) ).

thf(474,plain,
    ! [SV45: $i] :
      ( ( ( ! [SY244: $i,SY245: $i] :
              ( ( ( ti @ SV45 @ SY244 )
               != ( ti @ SV45 @ SY245 ) )
              | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[440]) ).

thf(475,plain,
    ! [SV45: $i] :
      ( ( ( ! [SY246: $i,SY247: $i] :
              ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
              | ( ( ti @ SV45 @ SY246 )
                = ( ti @ SV45 @ SY247 ) ) ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[441]) ).

thf(476,plain,
    ! [SV126: $i,SV144: $i,SV47: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
         != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
        | ( SV144 = SV126 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[444]) ).

thf(477,plain,
    ! [SV127: $i,SV145: $i,SV47: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        | ( SV145 != SV127 )
        | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
          = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[445]) ).

thf(478,plain,
    ! [SV146: $i,SV128: $i,SV48: $i] :
      ( ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
         != ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV146 ) )
        | ( SV128 = SV146 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[446]) ).

thf(479,plain,
    ! [SV48: $i,SV147: $i,SV129: $i] :
      ( ( ( SV129 != SV147 )
        | ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
          = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV147 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[447]) ).

thf(480,plain,
    ! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ~ ! [SY412: $i,SY413: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
              | ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
               != ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
              | ( ( ti @ SV49 @ SV112 )
                = ( ti @ SV49 @ SV96 ) ) )
        | ~ ! [SY414: $i,SY415: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
              | ( ( ti @ SV49 @ SV112 )
               != ( ti @ SV49 @ SV96 ) )
              | ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
                = ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[448]) ).

thf(481,plain,
    ! [SV50: $i,SV148: $i,SV131: $i] :
      ( ( ( SV131 != SV148 )
        | ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SV148 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[449]) ).

thf(482,plain,
    ! [SV149: $i,SV132: $i,SV50: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SV149 ) )
        | ( SV132 = SV149 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[450]) ).

thf(483,plain,
    ! [SV83: $i,SV57: $i,SV19: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[451]) ).

thf(484,plain,
    ! [SV84: $i,SV133: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
          | ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
            = ( ti @ SV23 @ SV84 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[452]) ).

thf(485,plain,
    ! [SV85: $i,SV150: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SV150 ) ) )
        = $true )
      | ( ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
          = ( ti @ SV61 @ SV85 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[453]) ).

thf(486,plain,
    ! [SV86: $i,SV134: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SV134 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SV134 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[454]) ).

thf(487,plain,
    ! [SV87: $i,SV135: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
          | ( ( ti @ SV26 @ SV87 )
            = ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[455]) ).

thf(488,plain,
    ! [SV88: $i,SV105: $i,SV151: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
        | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
        | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[456]) ).

thf(489,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[461]) ).

thf(490,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[462]) ).

thf(491,plain,
    ! [SV93: $i,SV137: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) ) )
        = $true )
      | ( ( ~ ( ( ( ti @ SV75 @ SV93 )
               != ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[463]) ).

thf(492,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ~ ( ! [SY397: $i,SY398: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
            | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
             != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
            | ( ( ti @ SV76 @ SV94 )
              = ( ti @ SV76 @ SV108 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[464]) ).

thf(493,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ~ ( ! [SY399: $i,SY400: $i] :
                ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
            | ( ( ti @ SV76 @ SV94 )
             != ( ti @ SV76 @ SV108 ) )
            | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
              = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[464]) ).

thf(494,plain,
    ! [SV95: $i,SV109: $i,SV152: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        | ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
            | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
        | ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[465]) ).

thf(495,plain,
    ! [SV139: $i,SV121: $i,SV43: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SV139 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV43 @ bool @ SV139 @ SV121 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[466]) ).

thf(496,plain,
    ! [SV122: $i,SV140: $i,SV43: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SV140 @ SV122 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SV140 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[467]) ).

thf(497,plain,
    ! [SV142: $i,SV124: $i,SV44: $i] :
      ( ( ( ( ( ti @ SV44 @ SV124 )
           != ( ti @ SV44 @ SV142 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SV142 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[470]) ).

thf(498,plain,
    ! [SV143: $i,SV125: $i,SV44: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SV143 ) ) )
        = $true )
      | ( ( ( ti @ SV44 @ SV125 )
          = ( ti @ SV44 @ SV143 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[471]) ).

thf(499,plain,
    ! [SV153: $i,SV45: $i] :
      ( ( ( ! [SY420: $i] :
              ( ( ( ti @ SV45 @ SV153 )
               != ( ti @ SV45 @ SY420 ) )
              | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SY420 ) ) ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[474]) ).

thf(500,plain,
    ! [SV154: $i,SV45: $i] :
      ( ( ( ! [SY421: $i] :
              ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SY421 ) )
              | ( ( ti @ SV45 @ SV154 )
                = ( ti @ SV45 @ SY421 ) ) ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[475]) ).

thf(501,plain,
    ! [SV126: $i,SV144: $i,SV47: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
          | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
           != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
          | ( SV144 = SV126 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[476]) ).

thf(502,plain,
    ! [SV127: $i,SV145: $i,SV47: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
          | ( SV145 != SV127 )
          | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[477]) ).

thf(503,plain,
    ! [SV146: $i,SV128: $i,SV48: $i] :
      ( ( ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
           != ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV146 ) ) )
        = $true )
      | ( ( SV128 = SV146 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[478]) ).

thf(504,plain,
    ! [SV48: $i,SV147: $i,SV129: $i] :
      ( ( ( ( SV129 != SV147 ) )
        = $true )
      | ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
          = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[479]) ).

thf(505,plain,
    ! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ~ ! [SY412: $i,SY413: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
              | ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
               != ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
              | ( ( ti @ SV49 @ SV112 )
                = ( ti @ SV49 @ SV96 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[480]) ).

thf(506,plain,
    ! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ~ ! [SY414: $i,SY415: $i] :
              ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
              | ( ( ti @ SV49 @ SV112 )
               != ( ti @ SV49 @ SV96 ) )
              | ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
                = ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[480]) ).

thf(507,plain,
    ! [SV50: $i,SV148: $i,SV131: $i] :
      ( ( ( ( SV131 != SV148 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SV148 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[481]) ).

thf(508,plain,
    ! [SV149: $i,SV132: $i,SV50: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SV149 ) ) )
        = $true )
      | ( ( SV132 = SV149 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[482]) ).

thf(509,plain,
    ! [SV84: $i,SV133: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
          | ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
            = ( ti @ SV23 @ SV84 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[484]) ).

thf(510,plain,
    ! [SV85: $i,SV150: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SV150 ) )
        = $false )
      | ( ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
          = ( ti @ SV61 @ SV85 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[485]) ).

thf(511,plain,
    ! [SV86: $i,SV134: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SV134 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SV134 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[486]) ).

thf(512,plain,
    ! [SV87: $i,SV135: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
          | ( ( ti @ SV26 @ SV87 )
            = ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[487]) ).

thf(513,plain,
    ! [SV88: $i,SV105: $i,SV151: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
          | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
          | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[488]) ).

thf(514,plain,
    ! [SV74: $i,SV92: $i,SV39: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[490]) ).

thf(515,plain,
    ! [SV93: $i,SV137: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
        = $false )
      | ( ( ~ ( ( ( ti @ SV75 @ SV93 )
               != ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
              | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[491]) ).

thf(516,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ! [SY397: $i,SY398: $i] :
            ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
        | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
         != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
        | ( ( ti @ SV76 @ SV94 )
          = ( ti @ SV76 @ SV108 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[492]) ).

thf(517,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ! [SY399: $i,SY400: $i] :
            ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
        | ( ( ti @ SV76 @ SV94 )
         != ( ti @ SV76 @ SV108 ) )
        | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
          = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[493]) ).

thf(518,plain,
    ! [SV95: $i,SV109: $i,SV152: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
              | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
          | ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[494]) ).

thf(519,plain,
    ! [SV139: $i,SV121: $i,SV43: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SV139 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV43 @ bool @ SV139 @ SV121 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[495]) ).

thf(520,plain,
    ! [SV122: $i,SV140: $i,SV43: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV43 @ bool @ SV140 @ SV122 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[496]) ).

thf(521,plain,
    ! [SV142: $i,SV124: $i,SV44: $i] :
      ( ( ( ( ti @ SV44 @ SV124 )
          = ( ti @ SV44 @ SV142 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SV142 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[497]) ).

thf(522,plain,
    ! [SV143: $i,SV125: $i,SV44: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SV143 ) )
        = $false )
      | ( ( ( ti @ SV44 @ SV125 )
          = ( ti @ SV44 @ SV143 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[498]) ).

thf(523,plain,
    ! [SV155: $i,SV153: $i,SV45: $i] :
      ( ( ( ( ( ti @ SV45 @ SV153 )
           != ( ti @ SV45 @ SV155 ) )
          | ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SV155 ) ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[499]) ).

thf(524,plain,
    ! [SV156: $i,SV154: $i,SV45: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SV156 ) )
          | ( ( ti @ SV45 @ SV154 )
            = ( ti @ SV45 @ SV156 ) ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[500]) ).

thf(525,plain,
    ! [SV126: $i,SV144: $i,SV47: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
          | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
           != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
          | ( SV144 = SV126 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[501]) ).

thf(526,plain,
    ! [SV127: $i,SV145: $i,SV47: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
          | ( SV145 != SV127 )
          | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[502]) ).

thf(527,plain,
    ! [SV146: $i,SV128: $i,SV48: $i] :
      ( ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
          = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV146 ) )
        = $false )
      | ( ( SV128 = SV146 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[503]) ).

thf(528,plain,
    ! [SV48: $i,SV147: $i,SV129: $i] :
      ( ( ( SV129 = SV147 )
        = $false )
      | ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
          = ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[504]) ).

thf(529,plain,
    ! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ! [SY412: $i,SY413: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
            | ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
             != ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
            | ( ( ti @ SV49 @ SV112 )
              = ( ti @ SV49 @ SV96 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[505]) ).

thf(530,plain,
    ! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ! [SY414: $i,SY415: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
            | ( ( ti @ SV49 @ SV112 )
             != ( ti @ SV49 @ SV96 ) )
            | ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
              = ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[506]) ).

thf(531,plain,
    ! [SV50: $i,SV148: $i,SV131: $i] :
      ( ( ( SV131 = SV148 )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SV148 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[507]) ).

thf(532,plain,
    ! [SV149: $i,SV132: $i,SV50: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SV149 ) )
        = $false )
      | ( ( SV132 = SV149 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[508]) ).

thf(533,plain,
    ! [SV113: $i,SV101: $i,SV60: $i,SV133: $i,SV84: $i,SV23: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) ) )
        = $true )
      | ( ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
          = ( ti @ SV23 @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[509]) ).

thf(534,plain,
    ! [SV116: $i,SV104: $i,SV63: $i,SV135: $i,SV87: $i,SV26: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) ) )
        = $true )
      | ( ( ( ti @ SV26 @ SV87 )
          = ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[512]) ).

thf(535,plain,
    ! [SV88: $i,SV105: $i,SV151: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
          | ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
          | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[513]) ).

thf(536,plain,
    ! [SV107: $i,SV137: $i,SV118: $i,SV40: $i,SV93: $i,SV75: $i] :
      ( ( ( ( ( ti @ SV75 @ SV93 )
           != ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[515]) ).

thf(537,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( ! [SY397: $i,SY398: $i] :
              ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) ) )
        = $true )
      | ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
           != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
          | ( ( ti @ SV76 @ SV94 )
            = ( ti @ SV76 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[516]) ).

thf(538,plain,
    ! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( ! [SY399: $i,SY400: $i] :
              ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) ) )
        = $true )
      | ( ( ( ( ti @ SV76 @ SV94 )
           != ( ti @ SV76 @ SV108 ) )
          | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
            = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[517]) ).

thf(539,plain,
    ! [SV95: $i,SV109: $i,SV152: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
              | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
          | ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[518]) ).

thf(540,plain,
    ! [SV155: $i,SV153: $i,SV45: $i] :
      ( ( ( ( ( ti @ SV45 @ SV153 )
           != ( ti @ SV45 @ SV155 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SV155 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[523]) ).

thf(541,plain,
    ! [SV156: $i,SV154: $i,SV45: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SV156 ) ) )
        = $true )
      | ( ( ( ti @ SV45 @ SV154 )
          = ( ti @ SV45 @ SV156 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[524]) ).

thf(542,plain,
    ! [SV144: $i,SV126: $i,SV47: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
        = $true )
      | ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
           != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
          | ( SV144 = SV126 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[525]) ).

thf(543,plain,
    ! [SV145: $i,SV127: $i,SV47: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
        = $true )
      | ( ( ( SV145 != SV127 )
          | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[526]) ).

thf(544,plain,
    ! [SV96: $i,SV112: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ! [SY422: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SY422 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY422 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY422 ) )
            | ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
             != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
            | ( ( ti @ SV49 @ SV112 )
              = ( ti @ SV49 @ SV96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[529]) ).

thf(545,plain,
    ! [SV96: $i,SV112: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ! [SY423: $i] :
            ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SY423 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY423 ) )
            | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY423 ) )
            | ( ( ti @ SV49 @ SV112 )
             != ( ti @ SV49 @ SV96 ) )
            | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
              = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[530]) ).

thf(546,plain,
    ! [SV113: $i,SV101: $i,SV60: $i,SV133: $i,SV84: $i,SV23: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
        = $false )
      | ( ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
          = ( ti @ SV23 @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[533]) ).

thf(547,plain,
    ! [SV116: $i,SV104: $i,SV63: $i,SV135: $i,SV87: $i,SV26: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
        = $false )
      | ( ( ( ti @ SV26 @ SV87 )
          = ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[534]) ).

thf(548,plain,
    ! [SV136: $i,SV117: $i,SV64: $i,SV88: $i,SV151: $i,SV105: $i,SV27: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
          | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[535]) ).

thf(549,plain,
    ! [SV107: $i,SV137: $i,SV118: $i,SV40: $i,SV93: $i,SV75: $i] :
      ( ( ( ( ( ti @ SV75 @ SV93 )
           != ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[536]) ).

thf(550,plain,
    ! [SV75: $i,SV93: $i,SV107: $i,SV118: $i,SV137: $i,SV40: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[536]) ).

thf(551,plain,
    ! [SV108: $i,SV94: $i,SV159: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( ! [SY424: $i] :
              ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SY424 ) ) )
        = $true )
      | ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
           != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
          | ( ( ti @ SV76 @ SV94 )
            = ( ti @ SV76 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[537]) ).

thf(552,plain,
    ! [SV108: $i,SV94: $i,SV160: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( ! [SY425: $i] :
              ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SY425 ) ) )
        = $true )
      | ( ( ( ( ti @ SV76 @ SV94 )
           != ( ti @ SV76 @ SV108 ) )
          | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
            = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[538]) ).

thf(553,plain,
    ! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
              | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[539]) ).

thf(554,plain,
    ! [SV155: $i,SV153: $i,SV45: $i] :
      ( ( ( ( ti @ SV45 @ SV153 )
          = ( ti @ SV45 @ SV155 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SV155 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[540]) ).

thf(555,plain,
    ! [SV156: $i,SV154: $i,SV45: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SV156 ) )
        = $false )
      | ( ( ( ti @ SV45 @ SV154 )
          = ( ti @ SV45 @ SV156 ) )
        = $true )
      | ( ( cl_HOL_Oequal @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[541]) ).

thf(556,plain,
    ! [SV144: $i,SV126: $i,SV47: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
           != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
          | ( SV144 = SV126 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[542]) ).

thf(557,plain,
    ! [SV145: $i,SV127: $i,SV47: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( ( SV145 != SV127 )
          | ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[543]) ).

thf(558,plain,
    ! [SV96: $i,SV112: $i,SV161: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
        | ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
         != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
        | ( ( ti @ SV49 @ SV112 )
          = ( ti @ SV49 @ SV96 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[544]) ).

thf(559,plain,
    ! [SV96: $i,SV112: $i,SV162: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
        | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
        | ( ( ti @ SV49 @ SV112 )
         != ( ti @ SV49 @ SV96 ) )
        | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
          = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[545]) ).

thf(560,plain,
    ! [SV136: $i,SV117: $i,SV64: $i,SV88: $i,SV151: $i,SV105: $i,SV27: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
          | ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[548]) ).

thf(561,plain,
    ! [SV107: $i,SV137: $i,SV118: $i,SV40: $i,SV93: $i,SV75: $i] :
      ( ( ( ( ti @ SV75 @ SV93 )
          = ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[549]) ).

thf(562,plain,
    ! [SV75: $i,SV93: $i,SV107: $i,SV118: $i,SV137: $i,SV40: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[550]) ).

thf(563,plain,
    ! [SV108: $i,SV94: $i,SV163: $i,SV159: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) ) )
        = $true )
      | ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
           != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
          | ( ( ti @ SV76 @ SV94 )
            = ( ti @ SV76 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[551]) ).

thf(564,plain,
    ! [SV108: $i,SV94: $i,SV164: $i,SV160: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) ) )
        = $true )
      | ( ( ( ( ti @ SV76 @ SV94 )
           != ( ti @ SV76 @ SV108 ) )
          | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
            = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[552]) ).

thf(565,plain,
    ! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
          | ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[553]) ).

thf(566,plain,
    ! [SV126: $i,SV144: $i,SV47: $i] :
      ( ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
           != ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) ) )
        = $true )
      | ( ( SV144 = SV126 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[556]) ).

thf(567,plain,
    ! [SV47: $i,SV127: $i,SV145: $i] :
      ( ( ( ( SV145 != SV127 ) )
        = $true )
      | ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
          = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[557]) ).

thf(568,plain,
    ! [SV96: $i,SV112: $i,SV161: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
           != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
          | ( ( ti @ SV49 @ SV112 )
            = ( ti @ SV49 @ SV96 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[558]) ).

thf(569,plain,
    ! [SV96: $i,SV112: $i,SV162: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
          | ( ( ti @ SV49 @ SV112 )
           != ( ti @ SV49 @ SV96 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
            = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[559]) ).

thf(570,plain,
    ! [SV105: $i,SV136: $i,SV151: $i,SV117: $i,SV64: $i,SV88: $i,SV27: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[560]) ).

thf(571,plain,
    ! [SV108: $i,SV94: $i,SV163: $i,SV159: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) )
        = $false )
      | ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
           != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
          | ( ( ti @ SV76 @ SV94 )
            = ( ti @ SV76 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[563]) ).

thf(572,plain,
    ! [SV108: $i,SV94: $i,SV164: $i,SV160: $i,SV119: $i,SV76: $i,SV41: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) )
        = $false )
      | ( ( ( ( ti @ SV76 @ SV94 )
           != ( ti @ SV76 @ SV108 ) )
          | ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
            = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[564]) ).

thf(573,plain,
    ! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[565]) ).

thf(574,plain,
    ! [SV95: $i,SV120: $i,SV152: $i,SV138: $i,SV42: $i,SV109: $i,SV77: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[565]) ).

thf(575,plain,
    ! [SV126: $i,SV144: $i,SV47: $i] :
      ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
          = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
        = $false )
      | ( ( SV144 = SV126 )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[566]) ).

thf(576,plain,
    ! [SV47: $i,SV127: $i,SV145: $i] :
      ( ( ( SV145 = SV127 )
        = $false )
      | ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
          = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[567]) ).

thf(577,plain,
    ! [SV96: $i,SV112: $i,SV161: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
           != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
          | ( ( ti @ SV49 @ SV112 )
            = ( ti @ SV49 @ SV96 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[568]) ).

thf(578,plain,
    ! [SV96: $i,SV112: $i,SV162: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
          | ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
          | ( ( ti @ SV49 @ SV112 )
           != ( ti @ SV49 @ SV96 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
            = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[569]) ).

thf(579,plain,
    ! [SV105: $i,SV136: $i,SV151: $i,SV117: $i,SV64: $i,SV88: $i,SV27: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[570]) ).

thf(580,plain,
    ! [SV163: $i,SV159: $i,SV108: $i,SV94: $i,SV119: $i,SV41: $i,SV76: $i] :
      ( ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
           != ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
        = $true )
      | ( ( ( ti @ SV76 @ SV94 )
          = ( ti @ SV76 @ SV108 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[571]) ).

thf(581,plain,
    ! [SV164: $i,SV160: $i,SV119: $i,SV41: $i,SV108: $i,SV94: $i,SV76: $i] :
      ( ( ( ( ( ti @ SV76 @ SV94 )
           != ( ti @ SV76 @ SV108 ) ) )
        = $true )
      | ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
          = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[572]) ).

thf(582,plain,
    ! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[573]) ).

thf(583,plain,
    ! [SV95: $i,SV120: $i,SV152: $i,SV138: $i,SV42: $i,SV109: $i,SV77: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[574]) ).

thf(584,plain,
    ! [SV130: $i,SV157: $i,SV79: $i,SV96: $i,SV161: $i,SV112: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
           != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
          | ( ( ti @ SV49 @ SV112 )
            = ( ti @ SV49 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[577]) ).

thf(585,plain,
    ! [SV130: $i,SV158: $i,SV79: $i,SV96: $i,SV162: $i,SV112: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
          | ( ( ti @ SV49 @ SV112 )
           != ( ti @ SV49 @ SV96 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
            = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[578]) ).

thf(586,plain,
    ! [SV163: $i,SV159: $i,SV108: $i,SV94: $i,SV119: $i,SV41: $i,SV76: $i] :
      ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
          = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
        = $false )
      | ( ( ( ti @ SV76 @ SV94 )
          = ( ti @ SV76 @ SV108 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[580]) ).

thf(587,plain,
    ! [SV164: $i,SV160: $i,SV119: $i,SV41: $i,SV108: $i,SV94: $i,SV76: $i] :
      ( ( ( ( ti @ SV76 @ SV94 )
          = ( ti @ SV76 @ SV108 ) )
        = $false )
      | ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
          = ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[581]) ).

thf(588,plain,
    ! [SV95: $i,SV120: $i,SV152: $i,SV138: $i,SV42: $i,SV109: $i,SV77: $i] :
      ( ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[583]) ).

thf(589,plain,
    ! [SV130: $i,SV157: $i,SV79: $i,SV96: $i,SV161: $i,SV112: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
           != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
          | ( ( ti @ SV49 @ SV112 )
            = ( ti @ SV49 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[584]) ).

thf(590,plain,
    ! [SV130: $i,SV158: $i,SV79: $i,SV96: $i,SV162: $i,SV112: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
          | ( ( ti @ SV49 @ SV112 )
           != ( ti @ SV49 @ SV96 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
            = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[585]) ).

thf(591,plain,
    ! [SV130: $i,SV112: $i,SV157: $i,SV79: $i,SV161: $i,SV96: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) ) )
        = $true )
      | ( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
           != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
          | ( ( ti @ SV49 @ SV112 )
            = ( ti @ SV49 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[589]) ).

thf(592,plain,
    ! [SV130: $i,SV158: $i,SV79: $i,SV112: $i,SV162: $i,SV96: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) ) )
        = $true )
      | ( ( ( ( ti @ SV49 @ SV112 )
           != ( ti @ SV49 @ SV96 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
            = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[590]) ).

thf(593,plain,
    ! [SV130: $i,SV112: $i,SV157: $i,SV79: $i,SV161: $i,SV96: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
        = $false )
      | ( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
           != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
          | ( ( ti @ SV49 @ SV112 )
            = ( ti @ SV49 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[591]) ).

thf(594,plain,
    ! [SV130: $i,SV158: $i,SV79: $i,SV112: $i,SV162: $i,SV96: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
        = $false )
      | ( ( ( ( ti @ SV49 @ SV112 )
           != ( ti @ SV49 @ SV96 ) )
          | ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
            = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[592]) ).

thf(595,plain,
    ! [SV130: $i,SV161: $i,SV96: $i,SV112: $i,SV157: $i,SV79: $i,SV49: $i] :
      ( ( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
           != ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) ) )
        = $true )
      | ( ( ( ti @ SV49 @ SV112 )
          = ( ti @ SV49 @ SV96 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[593]) ).

thf(596,plain,
    ! [SV130: $i,SV162: $i,SV158: $i,SV79: $i,SV96: $i,SV112: $i,SV49: $i] :
      ( ( ( ( ( ti @ SV49 @ SV112 )
           != ( ti @ SV49 @ SV96 ) ) )
        = $true )
      | ( ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
          = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[594]) ).

thf(597,plain,
    ! [SV130: $i,SV161: $i,SV96: $i,SV112: $i,SV157: $i,SV79: $i,SV49: $i] :
      ( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
          = ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
        = $false )
      | ( ( ( ti @ SV49 @ SV112 )
          = ( ti @ SV49 @ SV96 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[595]) ).

thf(598,plain,
    ! [SV130: $i,SV162: $i,SV158: $i,SV79: $i,SV96: $i,SV112: $i,SV49: $i] :
      ( ( ( ( ti @ SV49 @ SV112 )
          = ( ti @ SV49 @ SV96 ) )
        = $false )
      | ( ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
          = ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[596]) ).

thf(599,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[161,598,597,588,587,586,582,579,576,575,562,561,555,554,547,546,532,531,528,527,522,521,520,519,514,511,510,489,483,473,472,469,468,460,459,458,457,443,442,427,426,382,381,379,378,377,376,340,338,334,315,314,310,300,299,292,276,272,263,259,250,246,244,243,242,241,240,239,217,216,215,212,206,205,167,166,163]) ).

thf(600,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[599]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun  4 21:24:24 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.40  .
% 0.47/0.67  
% 0.47/0.67   No.of.Axioms: 62
% 0.47/0.67  
% 0.47/0.67   Length.of.Defs: 0
% 0.47/0.67  
% 0.47/0.67   Contains.Choice.Funs: false
% 0.52/0.72  ..
% 0.69/0.92  (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:0,translation:fof_full)...................................................................................
% 2.31/2.54  
% 2.31/2.54  ********************************
% 2.31/2.54  *   All subproblems solved!    *
% 2.31/2.54  ********************************
% 2.31/2.54  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:599,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.49/2.71  
% 2.49/2.71  %**** Beginning of derivation protocol ****
% 2.49/2.71  % SZS output start CNFRefutation
% See solution above
% 2.49/2.72  
% 2.49/2.72  %**** End of derivation protocol ****
% 2.49/2.72  %**** no. of clauses in derivation: 600 ****
% 2.49/2.72  %**** clause counter: 599 ****
% 2.49/2.72  
% 2.49/2.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:599,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------