TSTP Solution File: SWW469+5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWW469+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 06:49:46 EDT 2024

% Result   : Theorem 6.27s 2.41s
% Output   : Refutation 6.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  153 (  64 unt;  25 typ;   0 def)
%            Number of atoms       :  250 ( 103 equ;   0 cnn)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives : 4730 (  30   ~;   4   |;  16   &;4578   @)
%                                         (  10 <=>;  92  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  25 usr;   7 con; 0-4 aty)
%            Number of variables   :  318 (   0   ^ 312   !;   6   ?; 318   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ti_type,type,
    ti: $i > $i > $i ).

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

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

thf(hoare_1883395792gleton_type,type,
    hoare_1883395792gleton: $i ).

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

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

thf(bool_type,type,
    bool: $i ).

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

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

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

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

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

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

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

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

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

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

thf(hoare_509422987triple_type,type,
    hoare_509422987triple: $i > $i ).

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

thf(hoare_2037801986triple_type,type,
    hoare_2037801986triple: $i > $i ).

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

thf(hoare_1580379338ep_set_type,type,
    hoare_1580379338ep_set: $i > $i ).

thf(hoare_244953527triple_type,type,
    hoare_244953527triple: $i > $i ).

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

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

thf(53,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Rep__triple__inverse) ).

thf(217,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(32,axiom,
    cl_HOL_Oequal @ state,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).

thf(142,plain,
    cl_HOL_Oequal @ state,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(42,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
       => ~ ! [G: $i] :
              ( ( ti @ A @ C )
             != ( hAPP @ B @ A @ D @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_type__definition_ORep__cases) ).

thf(174,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
       => ~ ! [G: $i] :
              ( ( ti @ A @ C )
             != ( hAPP @ B @ A @ D @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( induct_equal @ A ) )
      = ( induct_equal @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__equal_res) ).

thf(184,plain,
    ! [A: $i] :
      ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( induct_equal @ A ) )
      = ( induct_equal @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(28,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
      | ( ( ti @ A @ B )
        = ( ti @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

thf(129,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
      | ( ( ti @ A @ B )
        = ( ti @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ( ( fequal @ A )
        = ( equal_equal @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_eq__equal) ).

thf(73,plain,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ( ( fequal @ A )
        = ( equal_equal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(50,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B )
        = ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).

thf(204,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B )
          = ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) )
       => ( B = C ) )
      & ( ( B = C )
       => ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B )
          = ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(22,axiom,
    ! [A: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal) ).

thf(112,plain,
    ! [A: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ~ ! [G: $i] :
            ( ( ( ti @ B @ C )
              = ( hAPP @ A @ B @ E @ G ) )
           => ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ G ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_type__definition_OAbs__cases) ).

thf(143,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ~ ! [G: $i] :
            ( ( ( ti @ B @ C )
              = ( hAPP @ A @ B @ E @ G ) )
           => ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ G ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
      = ( member @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).

thf(178,plain,
    ! [A: $i] :
      ( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
      = ( member @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ A ) ) @ B ) @ C ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).

thf(100,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ A ) ) @ B ) @ C ) )
       => ( B = C ) )
      & ( ( B = C )
       => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ A ) ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(3,axiom,
    hBOOL @ hoare_1883395792gleton,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(69,plain,
    hBOOL @ hoare_1883395792gleton,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( induct_equal @ A ) @ B ) @ C ) )
    <=> ( ( ti @ A @ B )
        = ( ti @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_induct__equal__def) ).

thf(249,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( induct_equal @ A ) @ B ) @ C ) )
       => ( ( ti @ A @ B )
          = ( ti @ A @ C ) ) )
      & ( ( ( ti @ A @ B )
          = ( ti @ A @ C ) )
       => ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( induct_equal @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(12,axiom,
    cl_HOL_Oequal @ com,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).

thf(88,plain,
    cl_HOL_Oequal @ com,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(16,axiom,
    cl_HOL_Oequal @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).

thf(93,plain,
    cl_HOL_Oequal @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ( ( hAPP @ B @ A @ E @ C )
          = ( hAPP @ B @ A @ E @ D ) )
      <=> ( ( ti @ B @ C )
          = ( ti @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_type__definition_ORep__inject) ).

thf(152,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ( ( ( hAPP @ B @ A @ E @ C )
            = ( hAPP @ B @ A @ E @ D ) )
         => ( ( ti @ B @ C )
            = ( ti @ B @ D ) ) )
        & ( ( ( ti @ B @ C )
            = ( ti @ B @ D ) )
         => ( ( hAPP @ B @ A @ E @ C )
            = ( hAPP @ B @ A @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(38,axiom,
    ( ( ti @ bool @ induct_false )
    = induct_false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__false_res) ).

thf(164,plain,
    ( ( ti @ bool @ induct_false )
    = induct_false ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ A ) )
      = ( hoare_1580379338ep_set @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res) ).

thf(211,plain,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ A ) )
      = ( hoare_1580379338ep_set @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( ti @ bool @ A ) )
    <=> ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).

thf(121,plain,
    ! [A: $i] :
      ( ( ( hBOOL @ ( ti @ bool @ A ) )
       => ( hBOOL @ A ) )
      & ( ( hBOOL @ A )
       => ( hBOOL @ ( ti @ bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

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

thf(84,plain,
    ! [A: $i,B: $i] :
      ( ( ( enum @ B )
        & ( enum @ A ) )
     => ( enum @ ( fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ~ ! [C: $i] :
          ( ( B
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Abs__triple__cases) ).

thf(147,plain,
    ! [A: $i,B: $i] :
      ~ ! [C: $i] :
          ( ( B
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(29,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( ( hAPP @ A @ B @ E @ ( hAPP @ B @ A @ D @ C ) )
        = ( ti @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_type__definition_ORep__inverse) ).

thf(132,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( ( hAPP @ A @ B @ E @ ( hAPP @ B @ A @ D @ C ) )
        = ( ti @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( ( enum @ B )
        & ( enum @ A ) )
     => ( enum @ ( sum_sum @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).

thf(89,plain,
    ! [A: $i,B: $i] :
      ( ( ( enum @ B )
        & ( enum @ A ) )
     => ( enum @ ( sum_sum @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(58,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Abs__triple__inverse) ).

thf(233,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(24,axiom,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Rep__triple) ).

thf(117,plain,
    ! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(54,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ D ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
         => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ D ) ) ) )
     => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Abs__triple__induct) ).

thf(220,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ D ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
         => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ D ) ) ) )
     => ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( equal_equal @ A ) )
        = ( equal_equal @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oequal__class_Oequal_res) ).

thf(260,plain,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( equal_equal @ A ) )
        = ( equal_equal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ! [H: $i] :
            ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ H ) @ G ) )
           => ( hBOOL @ ( hAPP @ B @ bool @ D @ ( hAPP @ A @ B @ F @ H ) ) ) )
       => ( hBOOL @ ( hAPP @ B @ bool @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_type__definition_OAbs__induct) ).

thf(70,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ! [H: $i] :
            ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ H ) @ G ) )
           => ( hBOOL @ ( hAPP @ B @ bool @ D @ ( hAPP @ A @ B @ F @ H ) ) ) )
       => ( hBOOL @ ( hAPP @ B @ bool @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(48,axiom,
    ( ( hBOOL @ hoare_1883395792gleton )
  <=> ? [A: $i,B: $i] :
        ( ( ti @ state @ A )
       != ( ti @ state @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).

thf(192,plain,
    ( ( ( hBOOL @ hoare_1883395792gleton )
     => ? [A: $i,B: $i] :
          ( ( ti @ state @ A )
         != ( ti @ state @ B ) ) )
    & ( ? [A: $i,B: $i] :
          ( ( ti @ state @ A )
         != ( ti @ state @ B ) )
     => ( hBOOL @ hoare_1883395792gleton ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(15,axiom,
    hBOOL @ induct_true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_induct__trueI) ).

thf(92,plain,
    hBOOL @ induct_true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1,conjecture,
    ! [A: $i] :
      ~ ! [B: $i] :
          ( ( ti @ state @ B )
          = ( ti @ state @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ~ ! [B: $i] :
            ( ( ti @ state @ B )
            = ( ti @ state @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(65,plain,
    ~ ! [A: $i] :
        ~ ! [B: $i] :
            ( ( ti @ state @ B )
            = ( ti @ state @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(63,axiom,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ~ ! [C: $i] :
            ( B
           != ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Rep__triple__cases) ).

thf(256,plain,
    ! [A: $i,B: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ~ ! [C: $i] :
            ( B
           != ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(56,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
       => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ G ) )
         => ( ( ( hAPP @ A @ B @ F @ D )
              = ( hAPP @ A @ B @ F @ C ) )
          <=> ( ( ti @ A @ D )
              = ( ti @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_type__definition_OAbs__inject) ).

thf(225,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
       => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ G ) )
         => ( ( ( ( hAPP @ A @ B @ F @ D )
                = ( hAPP @ A @ B @ F @ C ) )
             => ( ( ti @ A @ D )
                = ( ti @ A @ C ) ) )
            & ( ( ( ti @ A @ D )
                = ( ti @ A @ C ) )
             => ( ( hAPP @ A @ B @ F @ D )
                = ( hAPP @ A @ B @ F @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
       => ( ! [H: $i] : ( hBOOL @ ( hAPP @ A @ bool @ C @ ( hAPP @ B @ A @ E @ H ) ) )
         => ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_type__definition_ORep__induct) ).

thf(96,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
       => ( ! [H: $i] : ( hBOOL @ ( hAPP @ A @ bool @ C @ ( hAPP @ B @ A @ E @ H ) ) )
         => ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(39,axiom,
    ( ( ti @ bool @ induct_true )
    = induct_true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__true_res) ).

thf(166,plain,
    ( ( ti @ bool @ induct_true )
    = induct_true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) )
      = ( hoare_2037801986triple @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res) ).

thf(161,plain,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) )
      = ( hoare_2037801986triple @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
      = ( fequal @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).

thf(236,plain,
    ! [A: $i] :
      ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
      = ( fequal @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ti @ A @ B )
       != ( ti @ A @ C ) )
      | ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

thf(181,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ti @ A @ B )
       != ( ti @ A @ C ) )
      | ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ D @ C ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_type__definition_ORep) ).

thf(86,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ D @ C ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(46,axiom,
    ! [A: $i,B: $i] :
      ( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ bool ) ) ) @ ( type_definition @ A @ B ) )
      = ( type_definition @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Typedef_Otype__definition_res) ).

thf(187,plain,
    ! [A: $i,B: $i] :
      ( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ bool ) ) ) @ ( type_definition @ A @ B ) )
      = ( type_definition @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
      = ( collect @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).

thf(230,plain,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
      = ( collect @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ( ( equal_equal @ A )
        = ( fequal @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_equal) ).

thf(76,plain,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ( ( equal_equal @ A )
        = ( fequal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_equal__refl) ).

thf(98,plain,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(14,axiom,
    hBOOL @ induct_true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_induct__true__def) ).

thf(91,plain,
    hBOOL @ induct_true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
       => ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C )
            = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
        <=> ( C = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Abs__triple__inject) ).

thf(198,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
       => ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C )
              = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
           => ( C = B ) )
          & ( ( C = B )
           => ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C )
              = ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(55,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ D ) ) )
       => ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Rep__triple__induct) ).

thf(223,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
     => ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ D ) ) )
       => ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(8,axiom,
    ~ ( hBOOL @ induct_false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_induct__false__def) ).

thf(80,plain,
    ~ ( hBOOL @ induct_false ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
      = ( ti @ ( fun @ A @ bool ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Collect__def) ).

thf(158,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
      = ( ti @ ( fun @ A @ bool ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( ti @ A @ ( ti @ A @ B ) )
      = ( ti @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).

thf(114,plain,
    ! [A: $i,B: $i] :
      ( ( ti @ A @ ( ti @ A @ B ) )
      = ( ti @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( ti @ A @ ( undefined @ A ) )
      = ( undefined @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).

thf(171,plain,
    ! [A: $i] :
      ( ( ti @ A @ ( undefined @ A ) )
      = ( undefined @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(31,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
      = ( hAPP @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).

thf(139,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
      = ( hAPP @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(25,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) ) @ ( hoare_244953527triple @ A ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_type__definition__triple) ).

thf(119,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) ) @ ( hoare_244953527triple @ A ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
       => ( ( hAPP @ B @ A @ D @ ( hAPP @ A @ B @ E @ C ) )
          = ( ti @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_type__definition_OAbs__inverse) ).

thf(246,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
     => ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
       => ( ( hAPP @ B @ A @ D @ ( hAPP @ A @ B @ E @ C ) )
          = ( ti @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

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

thf(82,plain,
    ! [A: $i,B: $i] :
      ( ( ( cl_HOL_Oequal @ B )
        & ( enum @ A ) )
     => ( cl_HOL_Oequal @ ( fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(52,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
      = ( hAPP @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).

thf(214,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
      = ( hAPP @ B @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( hAPP @ A @ B @ C @ E )
          = ( hAPP @ A @ B @ D @ E ) )
     => ( ( ti @ ( fun @ A @ B ) @ C )
        = ( ti @ ( fun @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ext) ).

thf(168,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( hAPP @ A @ B @ C @ E )
          = ( hAPP @ A @ B @ D @ E ) )
     => ( ( ti @ ( fun @ A @ B ) @ C )
        = ( ti @ ( fun @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(47,axiom,
    ( ( ti @ bool @ hoare_1883395792gleton )
    = hoare_1883395792gleton ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res) ).

thf(190,plain,
    ( ( ti @ bool @ hoare_1883395792gleton )
    = hoare_1883395792gleton ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
    <=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_mem__def) ).

thf(107,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) )
      & ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
       => ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ! [B: $i,C: $i] :
          ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ C ) )
        <=> ( ( ti @ A @ B )
            = ( ti @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_equal__eq) ).

thf(239,plain,
    ! [A: $i] :
      ( ( cl_HOL_Oequal @ A )
     => ! [B: $i,C: $i] :
          ( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ C ) )
           => ( ( ti @ A @ B )
              = ( ti @ A @ C ) ) )
          & ( ( ( ti @ A @ B )
              = ( ti @ A @ C ) )
           => ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(7,axiom,
    enum @ bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).

thf(79,plain,
    enum @ bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(17,axiom,
    ! [A: $i,B: $i] : ( cl_HOL_Oequal @ ( sum_sum @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).

thf(94,plain,
    ! [A: $i,B: $i] : ( cl_HOL_Oequal @ ( sum_sum @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
      = ( hAPP @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).

thf(126,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
      = ( hAPP @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( hoare_244953527triple @ A ) )
      = ( hoare_244953527triple @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res) ).

thf(136,plain,
    ! [A: $i] :
      ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( hoare_244953527triple @ A ) )
      = ( hoare_244953527triple @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(263,plain,
    $false,
    inference(e,[status(thm)],[217,142,174,184,129,73,204,112,143,178,100,69,249,88,93,152,164,211,121,84,147,132,89,233,117,220,260,70,192,92,65,256,225,96,166,161,236,181,86,187,230,76,98,91,198,223,80,158,114,171,139,119,246,82,214,168,190,107,239,79,94,126,136]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11  % Problem  : SWW469+5 : TPTP v8.2.0. Released v5.3.0.
% 0.12/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.32  % Computer : n032.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Sat May 18 19:33:08 EDT 2024
% 0.13/0.32  % CPUTime  : 
% 0.73/0.76  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.34/0.94  % [INFO] 	 Parsing done (179ms). 
% 1.34/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.58/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.58/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.58/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 62 axioms. Running axiom selection ... 
% 2.25/1.33  % [INFO] 	 Axiom selection finished. Selected 62 axioms (removed 0 axioms). 
% 2.55/1.44  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.55/1.45  % [INFO] 	 Type checking passed. 
% 2.55/1.46  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 6.27/2.40  % External prover 'e' found a proof!
% 6.27/2.40  % [INFO] 	 Killing All external provers ... 
% 6.27/2.40  % Time passed: 1973ms (effective reasoning time: 1453ms)
% 6.27/2.41  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.27/2.41  % Axioms used in derivation (62): fact_3_equal, fact_7_Rep__triple__inverse, fact_21_induct__false__def, fact_0_state__not__singleton__def, tsy_c_HOL_Oundefined_res, tsy_c_HOL_Oequal__class_Oequal_res, fact_12_type__definition__triple, tsy_c_HOL_Oinduct__equal_res, fact_14_Abs__triple__induct, fact_11_Abs__triple__inverse, fact_24_type__definition_OAbs__induct, tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res, fact_28_induct__equal__def, fact_8_Rep__triple, arity_fun___HOL_Oequal, tsy_c_member_res, fact_19_type__definition_ORep__inverse, fact_22_type__definition_ORep__cases, fact_27_induct__true__def, tsy_c_HOL_Oinduct__false_res, tsy_c_Typedef_Otype__definition_res, fact_26_induct__trueI, tsy_c_hAPP_res, fact_2_Rep__triple__inject, tsy_c_Set_OCollect_res, tsy_c_hAPP_arg1, arity_HOL_Obool___HOL_Oequal, tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res, arity_fun___Enum_Oenum, tsy_c_hBOOL_arg1, fact_23_type__definition_OAbs__cases, fact_6_eq__equal, arity_sum___HOL_Oequal, arity_Com_Ocom___HOL_Oequal, arity_sum___Enum_Oenum, fact_31_Collect__def, arity_HOL_Obool___Enum_Oenum, tsy_c_hAPP_arg2, fact_13_Abs__triple__inject, help_ti_idem, help_fequal_1_1_T, fact_18_type__definition_ORep__inject, fact_10_Rep__triple__cases, tsy_c_fequal_res, arity_Com_Ostate___HOL_Oequal, fact_25_type__definition_ORep__induct, tsy_c_HOL_Oinduct__true_res, fact_20_type__definition_ORep, fact_16_type__definition_OAbs__inject, arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal, help_fequal_2_1_T, fact_15_Abs__triple__cases, fact_1_equal__triple__def, fact_29_ext, tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res, fact_17_type__definition_OAbs__inverse, fact_30_mem__def, fact_4_equal__refl, tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res, fact_9_Rep__triple__induct, fact_5_equal__eq, conj_0
% 6.27/2.41  % No. of inferences in proof: 128
% 6.27/2.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1973 ms resp. 1453 ms w/o parsing
% 6.69/2.50  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.69/2.50  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------