TSTP Solution File: ITP003^3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : ITP003^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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  : 300s
% DateTime : Mon May 20 22:27:02 EDT 2024

% Result   : Theorem 155.28s 22.61s
% Output   : Refutation 155.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  140 (  71 unt;  20 typ;   0 def)
%            Number of atoms       :  280 ( 148 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 1010 (  90   ~;  66   |;   5   &; 840   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  18 usr;   8 con; 0-4 aty)
%            Number of variables   :  184 (   0   ^ 167   !;  16   ?; 184   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
    tyop_2Emin_2Ebool: $tType ).

thf(tyop_2Enum_2Enum_type,type,
    tyop_2Enum_2Enum: $tType ).

thf(c_2Earithmetic_2E_2A_type,type,
    c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2E_2B_type,type,
    c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Enum_2E0_type,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

thf(c_2Eprim__rec_2E_3C_type,type,
    c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2EBIT1_type,type,
    c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EBIT2_type,type,
    c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebool_2ECOND_type,type,
    c_2Ebool_2ECOND: 
      !>[TA: $tType] : ( $o > TA > TA > TA ) ).

thf(c_2Earithmetic_2EEVEN_type,type,
    c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $o ).

thf(c_2Ebool_2EF_type,type,
    c_2Ebool_2EF: $o ).

thf(c_2Earithmetic_2EMOD_type,type,
    c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2ENUMERAL_type,type,
    c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EODD_type,type,
    c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o ).

thf(c_2Enum_2ESUC_type,type,
    c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebool_2ET_type,type,
    c_2Ebool_2ET: $o ).

thf(c_2Earithmetic_2EZERO_type,type,
    c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).

thf(sk1_type,type,
    sk1: tyop_2Enum_2Enum ).

thf(sk2_type,type,
    sk2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(sk16_type,type,
    sk16: tyop_2Enum_2Enum ).

thf(24,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EXISTS) ).

thf(141,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(142,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
    inference(cnf,[status(esa)],[141]) ).

thf(143,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
    inference(lifteq,[status(thm)],[142]) ).

thf(28,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EVEN) ).

thf(153,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(154,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
    inference(cnf,[status(esa)],[153]) ).

thf(155,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EODD @ A )
      = ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
    inference(lifteq,[status(thm)],[154]) ).

thf(567,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Earithmetic_2EEVEN @ A ) )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
    inference(rewrite,[status(thm)],[143,155]) ).

thf(568,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ~ ( c_2Earithmetic_2EEVEN @ A )
      | ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
    inference(bool_ext,[status(thm)],[567]) ).

thf(572,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A
        = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( sk2 @ A ) ) ) )
      | ( c_2Earithmetic_2EEVEN @ A ) ),
    inference(cnf,[status(esa)],[568]) ).

thf(573,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( sk2 @ A ) ) )
        = A )
      | ( c_2Earithmetic_2EEVEN @ A ) ),
    inference(lifteq,[status(thm)],[572]) ).

thf(18,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM) ).

thf(123,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(124,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    inference(cnf,[status(esa)],[123]) ).

thf(125,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    inference(lifteq,[status(thm)],[124]) ).

thf(30,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
        = A )
      & ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).

thf(158,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
        = A )
      & ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(159,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
      = B ),
    inference(cnf,[status(esa)],[158]) ).

thf(161,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
      = B ),
    inference(lifteq,[status(thm)],[159]) ).

thf(3,axiom,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
     => ~ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F) ).

thf(37,plain,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
     => ~ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(38,plain,
    ( ( $true
     => c_2Ebool_2EF )
   => ~ $true ),
    inference(instance,[status(thm)],[37]) ).

thf(39,plain,
    ~ c_2Ebool_2EF,
    inference(simp,[status(thm)],[38]) ).

thf(328,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
      = B ),
    inference(rewrite,[status(thm)],[161,39]) ).

thf(20,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ? [D: tyop_2Enum_2Enum] :
          ( ( B
            = ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
          & ( c_2Eprim__rec_2E_3C @ C @ A ) )
     => ( ( c_2Earithmetic_2EMOD @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__UNIQUE) ).

thf(129,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ? [D: tyop_2Enum_2Enum] :
          ( ( B
            = ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
          & ( c_2Eprim__rec_2E_3C @ C @ A ) )
     => ( ( c_2Earithmetic_2EMOD @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(130,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ? [D: tyop_2Enum_2Enum] :
            ( B
            = ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
        & ( c_2Eprim__rec_2E_3C @ C @ A ) )
     => ( ( c_2Earithmetic_2EMOD @ B @ A )
        = C ) ),
    inference(miniscope,[status(thm)],[129]) ).

thf(131,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( B
       != ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ A )
      | ( ( c_2Earithmetic_2EMOD @ B @ A )
        = C ) ),
    inference(cnf,[status(esa)],[130]) ).

thf(132,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( B
       != ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
      | ( ( c_2Earithmetic_2EMOD @ B @ A )
        = C )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
    inference(lifteq,[status(thm)],[131]) ).

thf(133,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
        = B )
      | ~ ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    inference(simp,[status(thm)],[132]) ).

thf(1,conjecture,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ A ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__2) ).

thf(2,negated_conjecture,
    ~ ! [A: tyop_2Enum_2Enum] :
        ( ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ A ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(34,plain,
    ~ ! [A: tyop_2Enum_2Enum] :
        ( ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ A ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(35,plain,
    ( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
   != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(cnf,[status(esa)],[34]) ).

thf(36,plain,
    ( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
   != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(lifteq,[status(thm)],[35]) ).

thf(370,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ B @ A )
      | ( B
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
       != ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[133,36]) ).

thf(378,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ A )
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( A
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[370]) ).

thf(390,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 ) ),
    inference(simp,[status(thm)],[378]) ).

thf(474,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $false @ A @ B )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[328,390]) ).

thf(497,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( A != c_2Enum_2E0 )
      | ( B
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[474]) ).

thf(510,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( c_2Earithmetic_2EEVEN @ sk1 ) ),
    inference(simp,[status(thm)],[497]) ).

thf(23,axiom,
    ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    = ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EONE) ).

thf(139,plain,
    ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    = ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(140,plain,
    ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
    = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(lifteq,[status(thm)],[139]) ).

thf(29,axiom,
    ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
    = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO) ).

thf(156,plain,
    ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
    = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(157,plain,
    ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(lifteq,[status(thm)],[156]) ).

thf(19,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
      = ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__EQ) ).

thf(126,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
      = ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(127,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
      = ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    inference(cnf,[status(esa)],[126]) ).

thf(128,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
      = ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    inference(lifteq,[status(thm)],[127]) ).

thf(286,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Enum_2ESUC @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[157,128]) ).

thf(287,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).

thf(3926,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[140,287]) ).

thf(3927,plain,
    ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
    = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pattern_uni,[status(thm)],[3926:[bind(A,$thf( c_2Enum_2E0 ))]]) ).

thf(21,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__0) ).

thf(134,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(135,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
    inference(cnf,[status(esa)],[134]) ).

thf(257,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[140,135]) ).

thf(258,plain,
    c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ),
    inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( c_2Enum_2E0 ))]]) ).

thf(4104,plain,
    c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ),
    inference(rewrite,[status(thm)],[3927,258]) ).

thf(15501,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ $true
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( c_2Earithmetic_2EEVEN @ sk1 ) ),
    inference(rewrite,[status(thm)],[510,4104]) ).

thf(15502,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( c_2Earithmetic_2EEVEN @ sk1 ) ),
    inference(simp,[status(thm)],[15501]) ).

thf(15525,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
       != sk1 )
      | ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $false @ A @ B )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[328,15502]) ).

thf(15549,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
       != sk1 )
      | ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( A != c_2Enum_2E0 )
      | ( B
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[15525]) ).

thf(15593,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 ) ),
    inference(simp,[status(thm)],[15549]) ).

thf(25,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2ESUC @ A )
      = ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD1) ).

thf(144,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2ESUC @ A )
      = ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(145,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2ESUC @ A )
      = ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(cnf,[status(esa)],[144]) ).

thf(146,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Enum_2ESUC @ A ) ),
    inference(lifteq,[status(thm)],[145]) ).

thf(18385,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 ) ),
    inference(rewrite,[status(thm)],[15593,146]) ).

thf(18386,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ A ) )
       != sk1 )
      | ( ( c_2Earithmetic_2E_2A @ A @ B )
       != ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,18385]) ).

thf(18387,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
       != sk1 ) ),
    inference(pattern_uni,[status(thm)],[18386:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(21900,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      | ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( A != sk1 )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( sk2 @ A ) ) )
       != ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[573,18387]) ).

thf(21901,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      | ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( A != sk1 ) ),
    inference(pattern_uni,[status(thm)],[21900:[bind(A,$thf( C )),bind(B,$thf( sk2 @ C ))]]) ).

thf(21951,plain,
    ( ( c_2Earithmetic_2EEVEN @ sk1 )
    | ( c_2Earithmetic_2EEVEN @ sk1 ) ),
    inference(simp,[status(thm)],[21901]) ).

thf(22060,plain,
    c_2Earithmetic_2EEVEN @ sk1,
    inference(simp,[status(thm)],[21951]) ).

thf(27,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXISTS) ).

thf(150,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(151,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
    inference(cnf,[status(esa)],[150]) ).

thf(152,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
    inference(lifteq,[status(thm)],[151]) ).

thf(22076,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
      | ( ( c_2Earithmetic_2EEVEN @ sk1 )
       != ( c_2Earithmetic_2EEVEN @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22060,152]) ).

thf(22077,plain,
    ? [A: tyop_2Enum_2Enum] :
      ( sk1
      = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[22076:[bind(A,$thf( sk1 ))]]) ).

thf(22137,plain,
    ( sk1
    = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ sk16 ) ),
    inference(cnf,[status(esa)],[22077]) ).

thf(22138,plain,
    ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ sk16 )
    = sk1 ),
    inference(lifteq,[status(thm)],[22137]) ).

thf(938,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      | ~ ? [B: tyop_2Enum_2Enum] :
            ( A
            = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
    inference(bool_ext,[status(thm)],[152]) ).

thf(983,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( A
       != ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
      | ( c_2Earithmetic_2EEVEN @ A ) ),
    inference(cnf,[status(esa)],[938]) ).

thf(984,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( A
       != ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
      | ( c_2Earithmetic_2EEVEN @ A ) ),
    inference(lifteq,[status(thm)],[983]) ).

thf(985,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
    inference(simp,[status(thm)],[984]) ).

thf(1013,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ B ) )
      | ( ( c_2Earithmetic_2E_2A @ B @ A )
       != ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[125,985]) ).

thf(1014,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pattern_uni,[status(thm)],[1013:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(160,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
      = A ),
    inference(cnf,[status(esa)],[158]) ).

thf(162,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
      = A ),
    inference(lifteq,[status(thm)],[160]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA] :
      ( ( A = A )
      = c_2Ebool_2ET ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).

thf(52,plain,
    c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(413,plain,
    ! [TA: $tType,B: TA,A: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ $true @ A @ B )
      = A ),
    inference(rewrite,[status(thm)],[162,52]) ).

thf(261,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[157,135]) ).

thf(262,plain,
    c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ),
    inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).

thf(375,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
        = B )
      | ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[262,133]) ).

thf(376,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Enum_2E0 )),bind(C,$thf( C ))]]) ).

thf(388,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(simp,[status(thm)],[376]) ).

thf(32,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__0) ).

thf(166,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(167,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
      = A ),
    inference(cnf,[status(esa)],[166]) ).

thf(168,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
      = A ),
    inference(lifteq,[status(thm)],[167]) ).

thf(6248,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(rewrite,[status(thm)],[388,168]) ).

thf(6279,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6248,36]) ).

thf(6290,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[6279]) ).

thf(6303,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 ) ),
    inference(simp,[status(thm)],[6290]) ).

thf(6328,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( A != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $true @ A @ B )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[413,6303]) ).

thf(6337,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ~ ( c_2Earithmetic_2EEVEN @ sk1 )
      | ( c_2Enum_2E0 != c_2Enum_2E0 )
      | ( A
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[6328]) ).

thf(6355,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
    inference(simp,[status(thm)],[6337]) ).

thf(6455,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EEVEN @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[1014,6355]) ).

thf(6457,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 ) ),
    inference(simp,[status(thm)],[6455]) ).

thf(9795,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( sk1 != sk1 ) ),
    inference(eqfactor_ordered,[status(thm)],[6457]) ).

thf(9804,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[9795:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(9817,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2E_2A @ A @ B )
       != ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,9804]) ).

thf(9818,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[9817:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(22247,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[22138,9818]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : ITP003^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n023.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sat May 18 17:32:54 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.97/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.40/1.07  % [INFO] 	 Parsing done (170ms). 
% 1.40/1.08  % [INFO] 	 Running in sequential loop mode. 
% 2.06/1.32  % [INFO] 	 nitpick registered as external prover. 
% 2.06/1.33  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ... 
% 2.32/1.46  % [INFO] 	 Axiom selection finished. Selected 31 axioms (removed 33 axioms). 
% 2.56/1.50  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.56/1.50  % [INFO] 	 Type checking passed. 
% 2.56/1.51  % [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 ... 
% 155.00/22.59  % [INFO] 	 Killing All external provers ... 
% 155.28/22.60  % Time passed: 22048ms (effective reasoning time: 21505ms)
% 155.28/22.60  % 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)>
% 155.28/22.60  % Axioms used in derivation (14): thm_2Ebool_2EREFL__CLAUSE, thm_2Earithmetic_2EEVEN__EXISTS, thm_2Ebool_2ECOND__CLAUSES, thm_2Earithmetic_2EODD__EVEN, thm_2Earithmetic_2ETWO, thm_2Earithmetic_2EADD__0, thm_2Earithmetic_2ELESS__MONO__EQ, thm_2Ebool_2EIMP__F, thm_2Earithmetic_2EODD__EXISTS, thm_2Eprim__rec_2ELESS__0, thm_2Earithmetic_2EONE, thm_2Earithmetic_2EMOD__UNIQUE, thm_2Earithmetic_2EMULT__COMM, thm_2Earithmetic_2EADD1
% 155.28/22.60  % No. of inferences in proof: 120
% 155.28/22.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22048 ms resp. 21505 ms w/o parsing
% 155.30/22.68  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 155.30/22.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------