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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---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 : n002.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 22:21:17 EDT 2024

% Result   : Theorem 120.44s 20.27s
% Output   : Refutation 121.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   50
% Syntax   : Number of formulae    :  598 ( 250 unt;  18 typ;   0 def)
%            Number of atoms       : 1443 ( 773 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 6884 ( 706   ~; 426   |;  51   &;5651   @)
%                                         (   0 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  227 ( 227   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   7 con; 0-4 aty)
%            Number of variables   : 1479 ( 126   ^1338   !;  14   ?;1479   :)
%                                         (   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(31,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
      ( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
      = ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RAND) ).

thf(163,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
      ( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
      = ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(164,plain,
    ! [TA: $tType,TB: $tType,D: TA,C: TA,B: $o,A: TA > TB] :
      ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
      = ( c_2Ebool_2ECOND @ TB @ B @ ( A @ C ) @ ( A @ D ) ) ),
    inference(cnf,[status(esa)],[163]) ).

thf(165,plain,
    ! [TA: $tType,TB: $tType,D: TA,C: TA,B: $o,A: TA > TB] :
      ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
      = ( c_2Ebool_2ECOND @ TB @ B @ ( A @ C ) @ ( A @ D ) ) ),
    inference(lifteq,[status(thm)],[164]) ).

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/sandbox/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(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/sandbox/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/sandbox/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(569,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(574,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( A
       != ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) )
      | ~ ( c_2Earithmetic_2EEVEN @ A ) ),
    inference(cnf,[status(esa)],[569]) ).

thf(575,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( A
       != ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) )
      | ~ ( c_2Earithmetic_2EEVEN @ A ) ),
    inference(lifteq,[status(thm)],[574]) ).

thf(576,plain,
    ! [A: tyop_2Enum_2Enum] :
      ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) ) ),
    inference(simp,[status(thm)],[575]) ).

thf(581,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( 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)],[125,576]) ).

thf(582,plain,
    ! [A: tyop_2Enum_2Enum] :
      ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(1299,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,582]) ).

thf(1959,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(pre_uni,[status(thm)],[1299:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2331,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(simp,[status(thm)],[1959]) ).

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/sandbox/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(1322,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( A @ D ) )
        = ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[157,165]) ).

thf(1578,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1322:[bind(A,$thf( ^ [E: TA] : ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(1976,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[1578]) ).

thf(14140,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(rewrite,[status(thm)],[1976,157]) ).

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/sandbox/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(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(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/sandbox/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(32,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
      = A ),
    file('/export/starexec/sandbox/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(313,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2ESUC @ A )
        = B )
      | ( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2E_2B @ B @ c_2Enum_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[146,168]) ).

thf(316,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2ESUC @ A )
        = B )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 ) ),
    inference(simp,[status(thm)],[313]) ).

thf(318,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2ESUC @ A )
        = A )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 ) ),
    inference(simp,[status(thm)],[316]) ).

thf(23,axiom,
    ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    = ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/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(259,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
     != ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[157,140]) ).

thf(263,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != c_2Enum_2E0 ) ),
    inference(simp,[status(thm)],[259]) ).

thf(588,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 )
      | ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[263,582]) ).

thf(589,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 )
      | ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[588:[]]) ).

thf(6664,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 )
      | ~ ( c_2Earithmetic_2EEVEN @ A )
      | ( ( c_2Enum_2ESUC @ A )
       != ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[318,589]) ).

thf(6665,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 )
      | ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[6664:[bind(A,$thf( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( C ))]]) ).

thf(6687,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 )
      | ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(simp,[status(thm)],[6665]) ).

thf(6830,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
       != ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[985,6687]) ).

thf(6831,plain,
    ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
   != c_2Enum_2E0 ),
    inference(pattern_uni,[status(thm)],[6830:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ))]]) ).

thf(6859,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
       != c_2Enum_2E0 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,6831]) ).

thf(6862,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 ),
    inference(pre_uni,[status(thm)],[6859:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(6865,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 ),
    inference(simp,[status(thm)],[6862]) ).

thf(14151,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,6865]) ).

thf(14278,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[14151]) ).

thf(14358,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[14278]) ).

thf(1454,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
        = ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
      | ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
       != ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[140,165]) ).

thf(1582,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      = ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
    inference(pre_uni,[status(thm)],[1454:[bind(A,$thf( ^ [E: TA] : ( c_2Enum_2ESUC @ c_2Enum_2E0 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(1979,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      = ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
    inference(simp,[status(thm)],[1582]) ).

thf(3069,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(rewrite,[status(thm)],[1979,140]) ).

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(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/sandbox/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(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/sandbox/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(21,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
    file('/export/starexec/sandbox/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(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(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/sandbox/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(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(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(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/sandbox/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(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(9821,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
       != sk1 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[165,9804]) ).

thf(9826,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(pre_uni,[status(thm)],[9821:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(9830,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[9826]) ).

thf(13535,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,9830]) ).

thf(13554,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[13535]) ).

thf(13568,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[13554]) ).

thf(13840,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[13568]) ).

thf(13868,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Earithmetic_2E_2A @ A @ B )
       != ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,13840]) ).

thf(13869,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pattern_uni,[status(thm)],[13868:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

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(491,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 ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ ( 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(paramod_ordered,[status(thm)],[146,390]) ).

thf(498,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 ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ A )
       != sk1 )
      | ( A
       != ( c_2Earithmetic_2E_2A @ B @ ( 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 ) ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[491]) ).

thf(511,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_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( ( 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_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[498]) ).

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(368,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_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[258,133]) ).

thf(369,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Enum_2E0 )),bind(C,$thf( C ))]]) ).

thf(385,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(simp,[status(thm)],[369]) ).

thf(516,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(rewrite,[status(thm)],[385,168]) ).

thf(522,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2E_2A @ A @ B )
       != ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,516]) ).

thf(523,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(595,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[140,582]) ).

thf(597,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 ) ),
    inference(simp,[status(thm)],[595]) ).

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(366,plain,
    ! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ D ) @ C )
        = D )
      | ~ ( c_2Eprim__rec_2E_3C @ D @ C )
      | ( ( c_2Earithmetic_2E_2A @ B @ A )
       != ( c_2Earithmetic_2E_2A @ E @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[125,133]) ).

thf(367,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) @ A )
        = C )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
    inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).

thf(384,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) @ A )
        = C )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
    inference(simp,[status(thm)],[367]) ).

thf(7266,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,6865]) ).

thf(7283,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[7266]) ).

thf(7290,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[7283]) ).

thf(7323,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,7290]) ).

thf(7332,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[7323:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(7338,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[7332]) ).

thf(14231,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,7338]) ).

thf(14274,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14231]) ).

thf(14354,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14274]) ).

thf(4,axiom,
    ! [A: $o] :
      ( c_2Ebool_2EF
     => A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).

thf(42,plain,
    ! [A: $o] :
      ( c_2Ebool_2EF
     => A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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/sandbox/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(282,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ B ) )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) )
      | ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[140,128]) ).

thf(283,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
    inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( c_2Enum_2E0 ))]]) ).

thf(301,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
    inference(simp,[status(thm)],[283]) ).

thf(3,axiom,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
     => ~ A ),
    file('/export/starexec/sandbox/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(377,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_2EMOD @ ( 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 ) ) ) ) @ A )
       != ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(simp,[status(thm)],[370]) ).

thf(389,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_2EMOD @ ( 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 ) ) ) ) @ A )
       != ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(simp,[status(thm)],[377]) ).

thf(26,axiom,
    ! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
      ( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
      = ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RATOR) ).

thf(147,plain,
    ! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
      ( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
      = ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(148,plain,
    ! [TA: $tType,TB: $tType,D: TA,C: TA > TB,B: TA > TB,A: $o] :
      ( ( c_2Ebool_2ECOND @ ( TA > TB ) @ A @ B @ C @ D )
      = ( c_2Ebool_2ECOND @ TB @ A @ ( B @ D ) @ ( C @ D ) ) ),
    inference(cnf,[status(esa)],[147]) ).

thf(149,plain,
    ! [TA: $tType,TB: $tType,D: TA,C: TA > TB,B: TA > TB,A: $o] :
      ( ( c_2Ebool_2ECOND @ ( TA > TB ) @ A @ B @ C @ D )
      = ( c_2Ebool_2ECOND @ TB @ A @ ( B @ D ) @ ( C @ D ) ) ),
    inference(lifteq,[status(thm)],[148]) ).

thf(6860,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
       != c_2Enum_2E0 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,6831]) ).

thf(6863,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 ),
    inference(pre_uni,[status(thm)],[6860:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(6866,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 ),
    inference(simp,[status(thm)],[6863]) ).

thf(7245,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[149,6866]) ).

thf(7255,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Earithmetic_2EBIT1
          @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ A ) ) )
     != c_2Enum_2E0 ),
    inference(pre_uni,[status(thm)],[7245:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(7262,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Earithmetic_2EBIT1
          @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ A ) ) )
     != c_2Enum_2E0 ),
    inference(simp,[status(thm)],[7255]) ).

thf(280,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) )
      | ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
       != ( c_2Enum_2ESUC @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[140,128]) ).

thf(281,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      = ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) ),
    inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( c_2Enum_2E0 ))]]) ).

thf(3341,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[157,281]) ).

thf(3342,plain,
    ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    = ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ),
    inference(pattern_uni,[status(thm)],[3341:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).

thf(15418,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,14358]) ).

thf(15424,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[15418:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(15426,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[15424]) ).

thf(7326,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,7290]) ).

thf(7328,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[7326:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(7334,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[7328]) ).

thf(14214,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,7334]) ).

thf(14311,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14214]) ).

thf(14391,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14311]) ).

thf(1574,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,262]) ).

thf(1805,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1574:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(2185,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[1805]) ).

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(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(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(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(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(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(18194,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,15426]) ).

thf(18221,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[18194]) ).

thf(18236,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[18221]) ).

thf(6252,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        = c_2Enum_2E0 )
      | ( ( 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)],[125,6248]) ).

thf(6253,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      = c_2Enum_2E0 ),
    inference(pattern_uni,[status(thm)],[6252:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(9839,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ E )
       != sk1 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,9818]) ).

thf(9844,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B )
     != sk1 ),
    inference(pre_uni,[status(thm)],[9839:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(9848,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B )
     != sk1 ),
    inference(simp,[status(thm)],[9844]) ).

thf(9959,plain,
    ! [D: tyop_2Enum_2Enum,C: $o,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_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[125,9848]) ).

thf(9960,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[9959:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ G @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( B ))]]) ).

thf(9985,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[9960]) ).

thf(14192,plain,
    ! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,9985]) ).

thf(14252,plain,
    ! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != sk1 )
      | ( A != C )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14192]) ).

thf(14331,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14252]) ).

thf(7237,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,6866]) ).

thf(7250,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[7237]) ).

thf(7258,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[7250]) ).

thf(7303,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
       != c_2Earithmetic_2EZERO )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,7258]) ).

thf(7306,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(pre_uni,[status(thm)],[7303:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(7314,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[7306]) ).

thf(14174,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,7314]) ).

thf(14268,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Earithmetic_2EZERO )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14174]) ).

thf(14346,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Earithmetic_2EZERO )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14268]) ).

thf(9841,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) @ E )
       != sk1 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,9818]) ).

thf(9843,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
     != sk1 ),
    inference(pre_uni,[status(thm)],[9841:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(9847,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
     != sk1 ),
    inference(simp,[status(thm)],[9843]) ).

thf(11755,plain,
    ! [D: tyop_2Enum_2Enum,C: $o,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_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[125,9847]) ).

thf(11756,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[11755:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).

thf(11793,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[11756]) ).

thf(33,axiom,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( ~ A
          | B )
        & ( A
          | C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND) ).

thf(169,plain,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( ~ A
          | B )
        & ( A
          | C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(184,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false )
    = ( ( ~ $true
        | $false )
      & ( $true
        | $false ) ) ),
    inference(instance,[status(thm)],[169]) ).

thf(185,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ),
    inference(simp,[status(thm)],[184]) ).

thf(329,plain,
    ! [B: $o,A: $o] :
      ( ~ B
      | ( ( c_2Ebool_2ECOND @ $o @ $false @ A @ B )
       != ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[328,185]) ).

thf(349,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true )
     != ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ) ),
    inference(simp,[status(thm)],[329]) ).

thf(393,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true ),
    inference(rewrite,[status(thm)],[349,185]) ).

thf(681,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > $o,B: TA > $o,A: $o] :
      ( ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ $o @ $false @ E @ $true ) ) ),
    inference(paramod_ordered,[status(thm)],[149,393]) ).

thf(773,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ A
      @ ^ [C: TA] : $true
      @ B ),
    inference(pre_uni,[status(thm)],[681:[bind(A,$thf( $false )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TA] : $true )),bind(D,$thf( D )),bind(E,$thf( B @ D ))]]) ).

thf(806,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ A
      @ ^ [C: TA] : $true
      @ B ),
    inference(simp,[status(thm)],[773]) ).

thf(1451,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ~ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Ebool_2EF ) ),
    inference(paramod_ordered,[status(thm)],[165,39]) ).

thf(1745,plain,
    ! [A: $o] :
      ~ ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ c_2Ebool_2EF ),
    inference(pre_uni,[status(thm)],[1451:[bind(A,$thf( ^ [E: TA] : c_2Ebool_2EF ))]]) ).

thf(2131,plain,
    ! [A: $o] :
      ~ ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ c_2Ebool_2EF ),
    inference(simp,[status(thm)],[1745]) ).

thf(2410,plain,
    ! [A: $o] :
      ~ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ),
    inference(rewrite,[status(thm)],[2131,39]) ).

thf(2417,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > $o,B: TA > $o,A: $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ $o @ E @ $false @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2410]) ).

thf(2435,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ B
        @ ^ [C: TA] : $false
        @ ^ [C: TA] : $false
        @ A ),
    inference(pre_uni,[status(thm)],[2417:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : $false )),bind(C,$thf( ^ [F: TA] : $false ))]]) ).

thf(2437,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ B
        @ ^ [C: TA] : $false
        @ ^ [C: TA] : $false
        @ A ),
    inference(simp,[status(thm)],[2435]) ).

thf(9,axiom,
    ! [A: $o] :
      ( A
     => ( ~ A
       => c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV__IMP) ).

thf(61,plain,
    ! [A: $o] :
      ( A
     => ( ~ A
       => c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(18213,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,15426]) ).

thf(18229,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[18213]) ).

thf(18241,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[18229]) ).

thf(1453,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
        = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Enum_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[165,140]) ).

thf(1903,plain,
    ! [A: $o] :
      ( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[1453:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).

thf(2278,plain,
    ! [A: $o] :
      ( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[1903]) ).

thf(2854,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) )
        = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2278]) ).

thf(2869,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( ( c_2Enum_2ESUC
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : c_2Enum_2E0
          @ ^ [C: TA] : c_2Enum_2E0
          @ A ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[2854:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).

thf(2884,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( ( c_2Enum_2ESUC
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : c_2Enum_2E0
          @ ^ [C: TA] : c_2Enum_2E0
          @ A ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[2869]) ).

thf(174,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false )
    = ( ( ~ $false
        | $true )
      & ( $false
        | $false ) ) ),
    inference(instance,[status(thm)],[169]) ).

thf(175,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ),
    inference(simp,[status(thm)],[174]) ).

thf(419,plain,
    ! [B: $o,A: $o] :
      ( ~ A
      | ( ( c_2Ebool_2ECOND @ $o @ $true @ A @ B )
       != ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[413,175]) ).

thf(434,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
     != ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ),
    inference(simp,[status(thm)],[419]) ).

thf(442,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
     != ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ),
    inference(simp,[status(thm)],[434]) ).

thf(448,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A ),
    inference(rewrite,[status(thm)],[442,175]) ).

thf(668,plain,
    ! [TA: $tType,E: TA,D: TA > $o,C: TA > $o,B: $o,A: $o] :
      ( ( c_2Ebool_2ECOND @ ( TA > $o ) @ B @ C @ D @ E )
      | ( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
       != ( c_2Ebool_2ECOND @ $o @ B @ ( C @ E ) @ ( D @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[448,149]) ).

thf(777,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
      @ ^ [C: TA] : $true
      @ A
      @ B ),
    inference(pre_uni,[status(thm)],[668:[bind(A,$thf( D @ E )),bind(B,$thf( $true )),bind(C,$thf( ^ [F: TA] : $true ))]]) ).

thf(810,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
      @ ^ [C: TA] : $true
      @ A
      @ B ),
    inference(simp,[status(thm)],[777]) ).

thf(360,plain,
    ! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ E @ C ) @ D ) @ C )
        = D )
      | ~ ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
       != ( c_2Eprim__rec_2E_3C @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[128,133]) ).

thf(361,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ C ) ) @ ( c_2Enum_2ESUC @ B ) ) @ ( c_2Enum_2ESUC @ C ) )
        = ( c_2Enum_2ESUC @ B ) )
      | ~ ( c_2Eprim__rec_2E_3C @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( c_2Enum_2ESUC @ G )),bind(D,$thf( c_2Enum_2ESUC @ F ))]]) ).

thf(381,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ C ) ) @ ( c_2Enum_2ESUC @ B ) ) @ ( c_2Enum_2ESUC @ C ) )
        = ( c_2Enum_2ESUC @ B ) )
      | ~ ( c_2Eprim__rec_2E_3C @ B @ C ) ),
    inference(simp,[status(thm)],[361]) ).

thf(7296,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,7258]) ).

thf(7310,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(pre_uni,[status(thm)],[7296:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(7318,plain,
    ! [A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[7310]) ).

thf(12095,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,7318]) ).

thf(12119,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[12095]) ).

thf(12132,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[12119]) ).

thf(176,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false )
    = ( ( ~ $false
        | $false )
      & ( $false
        | $false ) ) ),
    inference(instance,[status(thm)],[169]) ).

thf(177,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ),
    inference(simp,[status(thm)],[176]) ).

thf(725,plain,
    ! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[149,177]) ).

thf(756,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $false
        @ A ),
    inference(pre_uni,[status(thm)],[725:[bind(A,$thf( $false )),bind(B,$thf( ^ [E: TA] : $false )),bind(C,$thf( ^ [E: TA] : $false ))]]) ).

thf(847,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $false
        @ A ),
    inference(simp,[status(thm)],[756]) ).

thf(1394,plain,
    ! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $false
          @ ^ [F: TC] : ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
          @ ^ [F: TC] : $false
          @ E )
      | ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[165,847]) ).

thf(1674,plain,
    ! [TC: $tType,B: TC,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $false
        @ ^ [C: TC] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
        @ ^ [C: TC] : $false
        @ B ),
    inference(pre_uni,[status(thm)],[1394:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).

thf(2061,plain,
    ! [TA: $tType,B: TA,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
        @ ^ [C: TA] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
        @ ^ [C: TA] : $false
        @ B ),
    inference(simp,[status(thm)],[1674]) ).

thf(2424,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ~ ( c_2Ebool_2ECOND @ $o @ E @ $false @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) )
      | ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[165,2410]) ).

thf(2430,plain,
    ! [B: $o,A: $o] :
      ~ ( c_2Ebool_2ECOND @ $o @ B @ $false @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) ),
    inference(pre_uni,[status(thm)],[2424:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).

thf(2439,plain,
    ! [B: $o,A: $o] :
      ~ ( c_2Ebool_2ECOND @ $o @ B @ $false @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) ),
    inference(simp,[status(thm)],[2430]) ).

thf(4069,plain,
    ! [A: $o] :
      ~ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ),
    inference(rewrite,[status(thm)],[2439,2410]) ).

thf(5334,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $false
        @ A ),
    inference(rewrite,[status(thm)],[2061,4069]) ).

thf(4121,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,4104]) ).

thf(4151,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[4121:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(4172,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[4151]) ).

thf(1305,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
      | ( c_2Ebool_2ET
       != ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[52,165]) ).

thf(1601,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ c_2Ebool_2ET ),
    inference(pre_uni,[status(thm)],[1305:[bind(A,$thf( ^ [E: TA] : c_2Ebool_2ET ))]]) ).

thf(1996,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ c_2Ebool_2ET ),
    inference(simp,[status(thm)],[1601]) ).

thf(2346,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
    inference(rewrite,[status(thm)],[1996,52]) ).

thf(2364,plain,
    ! [TB: $tType,E: $o,D: $o,C: $o,B: $o > TB,A: $o] :
      ( ( ( B @ $true )
        = ( c_2Ebool_2ECOND @ TB @ C @ ( B @ D ) @ ( B @ E ) ) )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true )
       != ( c_2Ebool_2ECOND @ $o @ C @ D @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[2346,165]) ).

thf(2365,plain,
    ! [TB: $tType,B: $o > TB,A: $o] :
      ( ( c_2Ebool_2ECOND @ TB @ A @ ( B @ $true ) @ ( B @ $true ) )
      = ( B @ $true ) ),
    inference(pattern_uni,[status(thm)],[2364:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( $true )),bind(E,$thf( $true ))]]) ).

thf(2409,plain,
    ! [TA: $tType,B: $o > TA,A: $o] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ ( B @ $true ) @ ( B @ $true ) )
      = ( B @ $true ) ),
    inference(simp,[status(thm)],[2365]) ).

thf(284,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
       != ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[128,135]) ).

thf(297,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( c_2Enum_2ESUC @ A )
       != c_2Enum_2E0 )
      | ( ( c_2Enum_2ESUC @ B )
       != ( c_2Enum_2ESUC @ C ) ) ),
    inference(simp,[status(thm)],[284]) ).

thf(4119,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,4104]) ).

thf(4136,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[4119:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(4160,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[4136]) ).

thf(9963,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,9848]) ).

thf(9980,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
       != sk1 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[9963]) ).

thf(9993,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[9980]) ).

thf(1564,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( 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 ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[165,36]) ).

thf(1681,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ sk1 @ sk1 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
     != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1564:[bind(A,$thf( ^ [E: TA] : sk1 ))]]) ).

thf(2068,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ sk1 @ 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(simp,[status(thm)],[1681]) ).

thf(3076,plain,
    ! [TB: $tType,E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum > TB,A: $o] :
      ( ( ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ebool_2ECOND @ TB @ C @ ( B @ D ) @ ( B @ E ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ D @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,165]) ).

thf(3077,plain,
    ! [TB: $tType,B: tyop_2Enum_2Enum > TB,A: $o] :
      ( ( c_2Ebool_2ECOND @ TB @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pattern_uni,[status(thm)],[3076:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(E,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).

thf(3144,plain,
    ! [TA: $tType,B: tyop_2Enum_2Enum > TA,A: $o] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[3077]) ).

thf(9822,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
       != sk1 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,9804]) ).

thf(9825,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(pre_uni,[status(thm)],[9822:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(9829,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[9825]) ).

thf(1512,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,258]) ).

thf(1927,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1512:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(2300,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[1927]) ).

thf(7,axiom,
    c_2Ebool_2ET,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).

thf(53,plain,
    c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1508,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,258]) ).

thf(1910,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1508:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2284,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[1910]) ).

thf(3030,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2284]) ).

thf(3050,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Earithmetic_2EBIT1
          @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ A ) ) ) ),
    inference(pre_uni,[status(thm)],[3030:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(3060,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Earithmetic_2EBIT1
          @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ A ) ) ) ),
    inference(simp,[status(thm)],[3050]) ).

thf(3308,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2300]) ).

thf(3312,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ A ) ) ),
    inference(pre_uni,[status(thm)],[3308:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(3326,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ A ) ) ),
    inference(simp,[status(thm)],[3312]) ).

thf(13486,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,7338]) ).

thf(13515,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[13486]) ).

thf(13527,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[13515]) ).

thf(9919,plain,
    ! [D: tyop_2Enum_2Enum,C: $o,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 @ D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,9829]) ).

thf(9920,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ A )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[9919:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ G @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )),bind(C,$thf( G )),bind(D,$thf( A ))]]) ).

thf(9944,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ A )
     != sk1 ),
    inference(simp,[status(thm)],[9920]) ).

thf(10081,plain,
    ! [TA: $tType,F: $o,E: tyop_2Enum_2Enum,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) @ E )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[149,9944]) ).

thf(10084,plain,
    ! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
      ( ( c_2Earithmetic_2E_2A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) )
        @ B )
     != sk1 ),
    inference(pre_uni,[status(thm)],[10081:[bind(A,$thf( F )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(10094,plain,
    ! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
      ( ( c_2Earithmetic_2E_2A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) )
        @ B )
     != sk1 ),
    inference(simp,[status(thm)],[10084]) ).

thf(16,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          & A )
        = A )
      & ( ( A
          & c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF
          & A )
        = c_2Ebool_2EF )
      & ( ( A
          & c_2Ebool_2EF )
        = c_2Ebool_2EF )
      & ( ( A
          & A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).

thf(109,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          & A )
        = A )
      & ( ( A
          & c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF
          & A )
        = c_2Ebool_2EF )
      & ( ( A
          & c_2Ebool_2EF )
        = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(493,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_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_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[262,390]) ).

thf(504,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_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_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[493]) ).

thf(515,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_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 ) ),
    inference(simp,[status(thm)],[504]) ).

thf(14160,plain,
    ! [TB: $tType,E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: $o,B: tyop_2Enum_2Enum > TB,A: $o] :
      ( ( ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Ebool_2ECOND @ TB @ C @ ( B @ D ) @ ( B @ E ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ D @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,165]) ).

thf(14161,plain,
    ! [TB: $tType,B: tyop_2Enum_2Enum > TB,A: $o] :
      ( ( c_2Ebool_2ECOND @ TB @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pattern_uni,[status(thm)],[14160:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(E,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ))]]) ).

thf(14369,plain,
    ! [TA: $tType,B: tyop_2Enum_2Enum > TA,A: $o] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[14161]) ).

thf(3363,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        = ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) )
      | ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[140,281]) ).

thf(3364,plain,
    ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
    = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) ),
    inference(pattern_uni,[status(thm)],[3363:[bind(A,$thf( c_2Enum_2E0 ))]]) ).

thf(9824,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
       != sk1 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,9804]) ).

thf(9827,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(pre_uni,[status(thm)],[9824:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(9831,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[9827]) ).

thf(10787,plain,
    ! [D: tyop_2Enum_2Enum,C: $o,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 @ D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,9831]) ).

thf(10788,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[10787:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )),bind(C,$thf( F )),bind(D,$thf( A ))]]) ).

thf(10815,plain,
    ! [B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
     != sk1 ),
    inference(simp,[status(thm)],[10788]) ).

thf(1319,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
        = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,157]) ).

thf(1652,plain,
    ! [A: $o] :
      ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[1319:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2043,plain,
    ! [A: $o] :
      ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[1652]) ).

thf(9972,plain,
    ! [TA: $tType,F: tyop_2Enum_2Enum,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) @ F )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[149,9848]) ).

thf(9983,plain,
    ! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
      ( ( c_2Earithmetic_2E_2A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) )
        @ C )
     != sk1 ),
    inference(pre_uni,[status(thm)],[9972:[bind(A,$thf( E )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(9996,plain,
    ! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
      ( ( c_2Earithmetic_2E_2A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) )
        @ C )
     != sk1 ),
    inference(simp,[status(thm)],[9983]) ).

thf(14395,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: $o,C: TA,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_2Earithmetic_2ENUMERAL
            @ ( c_2Earithmetic_2EBIT2
              @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ D
                @ ^ [F: TA] : c_2Earithmetic_2EZERO
                @ ^ [F: TA] : c_2Earithmetic_2EZERO
                @ C ) ) )
          @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[125,9996]) ).

thf(14396,plain,
    ! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ C ) ) ) )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[14395:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ H @ ^ [H: TA] : c_2Earithmetic_2EZERO @ ^ [H: TA] : c_2Earithmetic_2EZERO @ K ) ) )),bind(B,$thf( B )),bind(C,$thf( K )),bind(D,$thf( H )),bind(E,$thf( B ))]]) ).

thf(14433,plain,
    ! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ C ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[14396]) ).

thf(584,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
       != ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[140,576]) ).

thf(586,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
       != c_2Enum_2E0 ) ),
    inference(simp,[status(thm)],[584]) ).

thf(14232,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,9848]) ).

thf(14257,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ C )
       != sk1 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14232]) ).

thf(14335,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14257]) ).

thf(1318,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
        = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,157]) ).

thf(1761,plain,
    ! [A: $o] :
      ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[1318:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(2144,plain,
    ! [A: $o] :
      ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[1761]) ).

thf(291,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
       != ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[258,128]) ).

thf(298,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( c_2Enum_2ESUC @ A )
       != c_2Enum_2E0 )
      | ( ( c_2Enum_2ESUC @ B )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[291]) ).

thf(362,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) @ B )
        = C )
      | ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) )
       != ( c_2Eprim__rec_2E_3C @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[135,133]) ).

thf(363,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ B ) ) @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) )
      = c_2Enum_2E0 ),
    inference(pattern_uni,[status(thm)],[362:[bind(A,$thf( E )),bind(B,$thf( c_2Enum_2ESUC @ E )),bind(C,$thf( c_2Enum_2E0 ))]]) ).

thf(382,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ B ) ) @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) )
      = c_2Enum_2E0 ),
    inference(simp,[status(thm)],[363]) ).

thf(7459,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ B ) ) @ ( c_2Enum_2ESUC @ B ) )
      = c_2Enum_2E0 ),
    inference(rewrite,[status(thm)],[382,168]) ).

thf(1337,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) @ E )
      | ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[165,448]) ).

thf(1580,plain,
    ! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ B ),
    inference(pre_uni,[status(thm)],[1337:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).

thf(1977,plain,
    ! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ B ),
    inference(simp,[status(thm)],[1580]) ).

thf(3523,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A ),
    inference(rewrite,[status(thm)],[1977,2346]) ).

thf(285,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ B @ C )
      | ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) )
       != ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ B ) @ ( c_2Enum_2ESUC @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[135,128]) ).

thf(296,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ B @ C )
      | ( ( c_2Enum_2ESUC @ B )
       != c_2Enum_2E0 )
      | ( ( c_2Enum_2ESUC @ A )
       != ( c_2Enum_2ESUC @ C ) ) ),
    inference(simp,[status(thm)],[285]) ).

thf(3254,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2185]) ).

thf(3268,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
          @ A ) ) ),
    inference(pre_uni,[status(thm)],[3254:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(3274,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
          @ A ) ) ),
    inference(simp,[status(thm)],[3268]) ).

thf(1572,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Enum_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[165,262]) ).

thf(1657,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[1572:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).

thf(2048,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[1657]) ).

thf(1571,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,262]) ).

thf(1811,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1571:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2191,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[1811]) ).

thf(2757,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2191]) ).

thf(2775,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Earithmetic_2EBIT2
          @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ A ) ) ) ),
    inference(pre_uni,[status(thm)],[2757:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2791,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
      @ ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Earithmetic_2EBIT2
          @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ ^ [C: TA] : c_2Earithmetic_2EZERO
            @ A ) ) ) ),
    inference(simp,[status(thm)],[2775]) ).

thf(2354,plain,
    ! [TA: $tType,E: TA,D: TA > $o,C: TA > $o,B: $o,A: $o] :
      ( ( c_2Ebool_2ECOND @ ( TA > $o ) @ B @ C @ D @ E )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true )
       != ( c_2Ebool_2ECOND @ $o @ B @ ( C @ E ) @ ( D @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2346,149]) ).

thf(2383,plain,
    ! [TA: $tType,B: TA,A: $o] :
      ( c_2Ebool_2ECOND @ ( TA > $o ) @ A
      @ ^ [C: TA] : $true
      @ ^ [C: TA] : $true
      @ B ),
    inference(pre_uni,[status(thm)],[2354:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TA] : $true )),bind(D,$thf( ^ [F: TA] : $true ))]]) ).

thf(2398,plain,
    ! [TA: $tType,B: TA,A: $o] :
      ( c_2Ebool_2ECOND @ ( TA > $o ) @ A
      @ ^ [C: TA] : $true
      @ ^ [C: TA] : $true
      @ B ),
    inference(simp,[status(thm)],[2383]) ).

thf(11,axiom,
    ! [A: $o,B: $o] :
      ( ( ~ ( ~ B
            | A )
       => c_2Ebool_2EF )
      = ( B
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL3) ).

thf(71,plain,
    ! [A: $o,B: $o] :
      ( ( ~ ( ~ B
            | A )
       => c_2Ebool_2EF )
      = ( B
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1248,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,1014]) ).

thf(1936,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(pre_uni,[status(thm)],[1248:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2308,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(simp,[status(thm)],[1936]) ).

thf(3900,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ 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_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[157,287]) ).

thf(3901,plain,
    ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
    = ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pattern_uni,[status(thm)],[3900:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).

thf(5033,plain,
    ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
    = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) ),
    inference(rewrite,[status(thm)],[3901,3364]) ).

thf(8,axiom,
    ! [A: $o] :
      ( ( A = c_2Ebool_2ET )
      | ( A = c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__CASES__AX) ).

thf(54,plain,
    ! [A: $o] :
      ( ( A = c_2Ebool_2ET )
      | ( A = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1420,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) @ E ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,985]) ).

thf(1842,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
    inference(pre_uni,[status(thm)],[1420:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(2220,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
    inference(simp,[status(thm)],[1842]) ).

thf(1510,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Enum_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[165,258]) ).

thf(1772,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[1510:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).

thf(2155,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[1772]) ).

thf(2693,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2155]) ).

thf(2703,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C
      @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
        @ ^ [C: TA] : c_2Enum_2E0
        @ ^ [C: TA] : c_2Enum_2E0
        @ A )
      @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[2693:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).

thf(2721,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C
      @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
        @ ^ [C: TA] : c_2Enum_2E0
        @ ^ [C: TA] : c_2Enum_2E0
        @ A )
      @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[2703]) ).

thf(14218,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ C )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,9847]) ).

thf(14284,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ C )
       != sk1 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[14218]) ).

thf(14364,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[14284]) ).

thf(4118,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,4104]) ).

thf(4156,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[4118:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(4176,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[4156]) ).

thf(373,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ A @ B )
        = C )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ B )
      | ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
       != ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[168,133]) ).

thf(374,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ B )
        = c_2Enum_2E0 )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ),
    inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( c_2Earithmetic_2E_2A @ E @ F )),bind(B,$thf( F )),bind(C,$thf( c_2Enum_2E0 )),bind(D,$thf( E ))]]) ).

thf(387,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ B )
        = c_2Enum_2E0 )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ),
    inference(simp,[status(thm)],[374]) ).

thf(1417,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ E ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,985]) ).

thf(1973,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
    inference(pre_uni,[status(thm)],[1417:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2343,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
    inference(simp,[status(thm)],[1973]) ).

thf(10,axiom,
    ( ! [A: $o] :
        ( ( ~ ~ A )
        = A )
    & ( ~ c_2Ebool_2ET = c_2Ebool_2EF )
    & ( ~ c_2Ebool_2EF = c_2Ebool_2ET ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).

thf(66,plain,
    ( ( ~ c_2Ebool_2ET = c_2Ebool_2EF )
    & ( ~ c_2Ebool_2EF = c_2Ebool_2ET ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(1503,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) @ E ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,576]) ).

thf(1789,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ) ),
    inference(pre_uni,[status(thm)],[1503:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2171,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ) ),
    inference(simp,[status(thm)],[1789]) ).

thf(1560,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,36]) ).

thf(1700,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
     != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1560:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(2086,plain,
    ! [A: $o] :
      ( ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ 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(simp,[status(thm)],[1700]) ).

thf(13075,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,7334]) ).

thf(13098,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[13075]) ).

thf(13112,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     != ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[13098]) ).

thf(12,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
         => A )
        = A )
      & ( ( A
         => c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
         => A )
        = c_2Ebool_2ET )
      & ( ( A
         => A )
        = c_2Ebool_2ET )
      & ( ( A
         => c_2Ebool_2EF )
        = ~ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).

thf(80,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
         => A )
        = A )
      & ( ( A
         => c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
         => A )
        = c_2Ebool_2ET )
      & c_2Ebool_2ET
      & ( ( A
         => c_2Ebool_2EF )
        = ~ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(476,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( 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_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
       != ( 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 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[128,390]) ).

thf(505,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( 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_2Enum_2ESUC @ A )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      | ( ( c_2Enum_2ESUC @ B )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[476]) ).

thf(1251,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,1014]) ).

thf(1773,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(pre_uni,[status(thm)],[1251:[bind(A,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(2156,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(simp,[status(thm)],[1773]) ).

thf(7239,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,6866]) ).

thf(7253,plain,
    ! [B: $o,A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Enum_2E0 ),
    inference(pre_uni,[status(thm)],[7239:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(7260,plain,
    ! [B: $o,A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Enum_2E0 ),
    inference(simp,[status(thm)],[7253]) ).

thf(486,plain,
    ! [C: tyop_2Enum_2Enum,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 ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( 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 )
      | ( ( 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)],[125,390]) ).

thf(487,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 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 ) ),
    inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(14,axiom,
    ! [A: $o,B: $o] :
      ( ( ~ ( B
            | A )
       => c_2Ebool_2EF )
      = ( ( B
         => c_2Ebool_2EF )
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).

thf(95,plain,
    ! [A: $o,B: $o] :
      ( ( ~ ( B
            | A )
       => c_2Ebool_2EF )
      = ( ( B
         => c_2Ebool_2EF )
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(9932,plain,
    ! [TA: $tType,F: tyop_2Enum_2Enum,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ F @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[149,9829]) ).

thf(9936,plain,
    ! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
      ( ( c_2Earithmetic_2E_2A @ C
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) ) )
     != sk1 ),
    inference(pre_uni,[status(thm)],[9932:[bind(A,$thf( E )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(9948,plain,
    ! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
      ( ( c_2Earithmetic_2E_2A @ C
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[9936]) ).

thf(10503,plain,
    ! [TA: $tType,F: $o,E: tyop_2Enum_2Enum,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ F @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[149,9985]) ).

thf(10511,plain,
    ! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
      ( ( c_2Earithmetic_2E_2A @ B
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) ) )
     != sk1 ),
    inference(pre_uni,[status(thm)],[10503:[bind(A,$thf( F )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(10521,plain,
    ! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
      ( ( c_2Earithmetic_2E_2A @ B
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ A ) ) ) )
     != sk1 ),
    inference(simp,[status(thm)],[10511]) ).

thf(701,plain,
    ! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[149,175]) ).

thf(761,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
        @ ^ [B: TA] : $true
        @ ^ [B: TA] : $false
        @ A ),
    inference(pre_uni,[status(thm)],[701:[bind(A,$thf( $false )),bind(B,$thf( ^ [E: TA] : $true )),bind(C,$thf( ^ [E: TA] : $false ))]]) ).

thf(852,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
        @ ^ [B: TA] : $true
        @ ^ [B: TA] : $false
        @ A ),
    inference(simp,[status(thm)],[761]) ).

thf(1401,plain,
    ! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
          @ ^ [F: TC] : $true
          @ ^ [F: TC] : $false
          @ E )
      | ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[165,852]) ).

thf(1598,plain,
    ! [TC: $tType,B: TC,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
        @ ^ [C: TC] : $true
        @ ^ [C: TC] : $false
        @ B ),
    inference(pre_uni,[status(thm)],[1401:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).

thf(1993,plain,
    ! [TA: $tType,B: TA,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
        @ ^ [C: TA] : $true
        @ ^ [C: TA] : $false
        @ B ),
    inference(simp,[status(thm)],[1598]) ).

thf(4961,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
        @ ^ [B: TA] : $true
        @ ^ [B: TA] : $false
        @ A ),
    inference(rewrite,[status(thm)],[1993,4069]) ).

thf(10791,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,9831]) ).

thf(10806,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[10791]) ).

thf(10820,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[10806]) ).

thf(583,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
       != ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,576]) ).

thf(585,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[583]) ).

thf(1237,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ ( c_2Enum_2ESUC @ E ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Enum_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[165,135]) ).

thf(1583,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) ),
    inference(pre_uni,[status(thm)],[1237:[bind(A,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).

thf(1980,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) ),
    inference(simp,[status(thm)],[1583]) ).

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(14208,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,6866]) ).

thf(14309,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != c_2Enum_2E0 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14208]) ).

thf(14389,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14309]) ).

thf(16761,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
     != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
    | ( c_2Earithmetic_2EZERO != c_2Earithmetic_2EZERO ) ),
    inference(eqfactor_ordered,[status(thm)],[14346]) ).

thf(16766,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO )
    | ( ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
     != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[16761]) ).

thf(371,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Enum_2ESUC @ A ) @ B )
        = C )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ B )
      | ( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[146,133]) ).

thf(372,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ B ) ) @ B )
        = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ~ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ B ) ),
    inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( c_2Earithmetic_2E_2A @ E @ F )),bind(B,$thf( F )),bind(C,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( E ))]]) ).

thf(386,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ B ) ) @ B )
        = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ~ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ B ) ),
    inference(simp,[status(thm)],[372]) ).

thf(4123,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) ) )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[165,4104]) ).

thf(4143,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[4123:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(4165,plain,
    ! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[4143]) ).

thf(663,plain,
    ! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ) ) ),
    inference(paramod_ordered,[status(thm)],[149,185]) ).

thf(782,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $false
        @ A ),
    inference(pre_uni,[status(thm)],[663:[bind(A,$thf( $true )),bind(B,$thf( ^ [E: TA] : $false )),bind(C,$thf( ^ [E: TA] : $false ))]]) ).

thf(815,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $false
        @ A ),
    inference(simp,[status(thm)],[782]) ).

thf(1386,plain,
    ! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > TC > $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
          @ ^ [F: TC] : $false
          @ ( c_2Ebool_2ECOND @ ( TC > $o ) @ B @ ( A @ C ) @ ( A @ D ) )
          @ E )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != ( ^ [F: TC] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[165,815]) ).

thf(1624,plain,
    ! [TC: $tType,B: TC,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
        @ ^ [C: TC] : $false
        @ ( c_2Ebool_2ECOND @ ( TC > $o ) @ A
          @ ^ [C: TC] : $false
          @ ^ [C: TC] : $false )
        @ B ),
    inference(pre_uni,[status(thm)],[1386:[bind(A,$thf( ^ [F: TA] : ^ [G: TC] : $false ))]]) ).

thf(2016,plain,
    ! [TA: $tType,B: TA,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [C: TA] : $false
        @ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A
          @ ^ [C: TA] : $false
          @ ^ [C: TA] : $false )
        @ B ),
    inference(simp,[status(thm)],[1624]) ).

thf(4997,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $false
        @ A ),
    inference(rewrite,[status(thm)],[2016,2437]) ).

thf(7275,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) )
       != c_2Enum_2E0 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[149,6865]) ).

thf(7281,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ A ) )
     != c_2Enum_2E0 ),
    inference(pre_uni,[status(thm)],[7275:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( ^ [F: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).

thf(7288,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( ( c_2Earithmetic_2ENUMERAL
        @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
          @ A ) )
     != c_2Enum_2E0 ),
    inference(simp,[status(thm)],[7281]) ).

thf(15,axiom,
    ! [A: $o] :
      ( ( ~ A
       => c_2Ebool_2EF )
     => ( ( A
         => c_2Ebool_2EF )
       => c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV2) ).

thf(104,plain,
    ! [A: $o] :
      ( ( ~ A
       => c_2Ebool_2EF )
     => ( ( A
         => c_2Ebool_2EF )
       => c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(13992,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: $o,C: TA,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 @ E
          @ ( c_2Earithmetic_2ENUMERAL
            @ ( c_2Earithmetic_2EBIT2
              @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ D
                @ ^ [F: TA] : c_2Earithmetic_2EZERO
                @ ^ [F: TA] : c_2Earithmetic_2EZERO
                @ C ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,9948]) ).

thf(13993,plain,
    ! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ C ) ) )
        @ A )
     != sk1 ),
    inference(pattern_uni,[status(thm)],[13992:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ H @ ^ [H: TA] : c_2Earithmetic_2EZERO @ ^ [H: TA] : c_2Earithmetic_2EZERO @ K ) ) )),bind(C,$thf( K )),bind(D,$thf( H )),bind(E,$thf( A ))]]) ).

thf(14026,plain,
    ! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A
        @ ( c_2Earithmetic_2ENUMERAL
          @ ( c_2Earithmetic_2EBIT2
            @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ ^ [D: TA] : c_2Earithmetic_2EZERO
              @ C ) ) )
        @ A )
     != sk1 ),
    inference(simp,[status(thm)],[13993]) ).

thf(17,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET = A )
        = A )
      & ( ( A = c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF = A )
        = ~ A )
      & ( ( A = c_2Ebool_2EF )
        = ~ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).

thf(114,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET = A )
        = A )
      & ( ( A = c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF = A )
        = ~ A )
      & ( ( A = c_2Ebool_2EF )
        = ~ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1407,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) @ E @ $true )
      | ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[165,393]) ).

thf(1713,plain,
    ! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) @ B @ $true ),
    inference(pre_uni,[status(thm)],[1407:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).

thf(2098,plain,
    ! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) @ B @ $true ),
    inference(simp,[status(thm)],[1713]) ).

thf(3662,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true ),
    inference(rewrite,[status(thm)],[2098,2410]) ).

thf(9923,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[3069,9829]) ).

thf(9943,plain,
    ! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != sk1 )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[9923]) ).

thf(9955,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[9943]) ).

thf(364,plain,
    ! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ D ) @ C )
        = D )
      | ~ ( c_2Eprim__rec_2E_3C @ D @ C )
      | ( ( c_2Earithmetic_2E_2A @ A @ B )
       != ( c_2Earithmetic_2E_2A @ E @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[125,133]) ).

thf(365,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ B )
        = C )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ B ) ),
    inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).

thf(383,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ B )
        = C )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ B ) ),
    inference(simp,[status(thm)],[365]) ).

thf(1566,plain,
    ! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2B @ E @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) )
        = E )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Enum_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[165,168]) ).

thf(1852,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2B @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
      = B ),
    inference(pre_uni,[status(thm)],[1566:[bind(A,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).

thf(2230,plain,
    ! [B: tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Earithmetic_2E_2B @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
      = B ),
    inference(simp,[status(thm)],[1852]) ).

thf(288,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ B ) )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Enum_2ESUC @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[157,128]) ).

thf(289,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
      = ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B ))]]) ).

thf(300,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
      = ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
    inference(simp,[status(thm)],[289]) ).

thf(7238,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ c_2Earithmetic_2EZERO ) ) )
       != c_2Enum_2E0 )
      | ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(paramod_ordered,[status(thm)],[165,6866]) ).

thf(7251,plain,
    ! [B: $o,A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 ),
    inference(pre_uni,[status(thm)],[7238:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).

thf(7259,plain,
    ! [B: $o,A: $o] :
      ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) @ c_2Earithmetic_2EZERO ) ) )
     != c_2Enum_2E0 ),
    inference(simp,[status(thm)],[7251]) ).

thf(182,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true )
    = ( ( ~ $true
        | $false )
      & ( $true
        | $true ) ) ),
    inference(instance,[status(thm)],[169]) ).

thf(183,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ),
    inference(simp,[status(thm)],[182]) ).

thf(735,plain,
    ! [TA: $tType,D: TA,C: TA > $o,B: TA > $o,A: $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A @ B @ C @ D )
      | ( ( c_2Ebool_2ECOND @ $o @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ) ) ),
    inference(paramod_ordered,[status(thm)],[149,183]) ).

thf(741,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $true
        @ A ),
    inference(pre_uni,[status(thm)],[735:[bind(A,$thf( $true )),bind(B,$thf( ^ [E: TA] : $false )),bind(C,$thf( ^ [E: TA] : $true ))]]) ).

thf(833,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $true
        @ A ),
    inference(simp,[status(thm)],[741]) ).

thf(1555,plain,
    ! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
          @ ^ [F: TC] : ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
          @ ^ [F: TC] : $true
          @ E )
      | ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[165,833]) ).

thf(1705,plain,
    ! [TC: $tType,B: TC,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
        @ ^ [C: TC] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
        @ ^ [C: TC] : $true
        @ B ),
    inference(pre_uni,[status(thm)],[1555:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).

thf(2091,plain,
    ! [TA: $tType,B: TA,A: $o] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [C: TA] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
        @ ^ [C: TA] : $true
        @ B ),
    inference(simp,[status(thm)],[1705]) ).

thf(5371,plain,
    ! [TA: $tType,A: TA] :
      ~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
        @ ^ [B: TA] : $false
        @ ^ [B: TA] : $true
        @ A ),
    inference(rewrite,[status(thm)],[2091,4069]) ).

thf(11694,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Earithmetic_2E_2A @ A @ B )
       != ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,10820]) ).

thf(11695,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pattern_uni,[status(thm)],[11694:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )),bind(C,$thf( A ))]]) ).

thf(1515,plain,
    ! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ( ( c_2Ebool_2ECOND @ $o @ B @ $true @ ( A @ D ) )
        = ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) )
      | ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
       != ( A @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[258,165]) ).

thf(1769,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ $true @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pre_uni,[status(thm)],[1515:[bind(A,$thf( ^ [E: TA] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).

thf(2152,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ $true @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[1769]) ).

thf(18278,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
    inference(rewrite,[status(thm)],[2152,258]) ).

thf(18293,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
      ( ( c_2Ebool_2ECOND @ $o @ E @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) @ $true )
      | ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[165,18278]) ).

thf(18335,plain,
    ! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ $true ),
    inference(pre_uni,[status(thm)],[18293:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).

thf(18370,plain,
    ! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ $true ),
    inference(simp,[status(thm)],[18335]) ).

thf(18453,plain,
    ! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
    inference(rewrite,[status(thm)],[18370,18278]) ).

thf(14149,plain,
    ! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,11793]) ).

thf(14236,plain,
    ! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( A != C )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[14149]) ).

thf(14315,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[14236]) ).

thf(13841,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2A @ A @ B )
       != ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[125,13568]) ).

thf(13842,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A )
       != sk1 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(pattern_uni,[status(thm)],[13841:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).

thf(2627,plain,
    ! [TA: $tType,E: $o,D: TA,C: TA > tyop_2Enum_2Enum,B: TA > tyop_2Enum_2Enum,A: $o] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ A @ B @ C @ D ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( B @ D ) @ ( C @ D ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ E @ c_2Enum_2E0 @ c_2Enum_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[149,2048]) ).

thf(2635,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C
      @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
        @ ^ [C: TA] : c_2Enum_2E0
        @ ^ [C: TA] : c_2Enum_2E0
        @ A )
      @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(pre_uni,[status(thm)],[2627:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).

thf(2651,plain,
    ! [TA: $tType,B: $o,A: TA] :
      ( c_2Eprim__rec_2E_3C
      @ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
        @ ^ [C: TA] : c_2Enum_2E0
        @ ^ [C: TA] : c_2Enum_2E0
        @ A )
      @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
    inference(simp,[status(thm)],[2635]) ).

thf(293,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
       != ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[262,128]) ).

thf(294,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( ( c_2Enum_2ESUC @ A )
       != c_2Enum_2E0 )
      | ( ( c_2Enum_2ESUC @ B )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[293]) ).

thf(22,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      = ( ~ ( c_2Earithmetic_2EODD @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__ODD) ).

thf(136,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EEVEN @ A )
      = ( ~ ( c_2Earithmetic_2EODD @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(594,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
       != ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,582]) ).

thf(596,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
      | ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
    inference(simp,[status(thm)],[594]) ).

thf(5,axiom,
    ! [A: $o] :
      ( ~ A
     => ( A
       => c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__IMP) ).

thf(47,plain,
    ! [A: $o] :
      ( ~ A
     => ( A
       => c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(13,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          | A )
        = c_2Ebool_2ET )
      & ( ( A
          | c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
          | A )
        = A )
      & ( ( A
          | c_2Ebool_2EF )
        = A )
      & ( ( A
          | A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).

thf(90,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          | A )
        = c_2Ebool_2ET )
      & ( ( A
          | c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
          | A )
        = A )
      & ( ( A
          | c_2Ebool_2EF )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(14189,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
       != ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ),
    inference(paramod_ordered,[status(thm)],[14140,7318]) ).

thf(14267,plain,
    ! [B: $o,A: $o] :
      ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
       != c_2Enum_2E0 )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( A != B )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO )
      | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
       != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14189]) ).

thf(14345,plain,
    ( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
     != c_2Enum_2E0 )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO )
    | ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
     != c_2Earithmetic_2EZERO ) ),
    inference(simp,[status(thm)],[14267]) ).

thf(477,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ A @ ( 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 @ $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)],[413,390]) ).

thf(494,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ A @ ( 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)],[477]) ).

thf(508,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( 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)],[494]) ).

thf(14032,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)],[508,262]) ).

thf(14033,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)],[14032]) ).

thf(22141,plain,
    $false,
    inference(e,[status(thm)],[2331,14358,13869,511,523,582,597,9818,384,153,14354,42,301,37,389,52,7262,3342,15426,125,14391,2185,18385,157,18236,6253,14331,152,7258,7290,14346,11793,806,147,2437,61,18241,133,2884,810,381,6865,12132,5334,4172,2409,297,3069,165,4160,9993,7314,13568,2068,3144,4104,9829,2300,9804,156,53,169,141,3060,3326,7318,13527,10094,109,328,985,515,14369,129,4069,3364,134,128,10815,2043,14433,9985,586,14335,2144,298,7459,166,34,3523,149,296,3274,2048,2791,9996,281,413,15502,2398,71,2308,144,6248,5033,54,2220,2721,14364,6866,2284,567,39,4176,387,2343,140,66,2278,155,2171,2086,7334,13112,135,80,13840,505,2156,7260,487,516,123,9847,150,95,9948,10521,4961,10820,585,1980,576,18387,14389,16766,175,386,4165,4997,7288,104,6831,14026,258,158,390,114,139,3662,14140,9955,383,2230,287,300,2155,146,7259,183,5371,9944,11695,18453,36,168,262,14315,13842,2651,294,126,136,7338,596,47,163,9848,90,14345,14033,2191,9831,1014]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ITP003^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat May 18 17:32:54 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.89/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.43/1.15  % [INFO] 	 Parsing done (236ms). 
% 1.43/1.16  % [INFO] 	 Running in sequential loop mode. 
% 1.87/1.42  % [INFO] 	 eprover registered as external prover. 
% 1.87/1.42  % [INFO] 	 cvc4 registered as external prover. 
% 2.02/1.43  % [INFO] 	 Scanning for conjecture ... 
% 2.09/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ... 
% 2.31/1.59  % [INFO] 	 Axiom selection finished. Selected 31 axioms (removed 33 axioms). 
% 2.53/1.65  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.53/1.66  % [INFO] 	 Type checking passed. 
% 2.53/1.66  % [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 ... 
% 120.44/20.26  % External prover 'e' found a proof!
% 120.44/20.27  % [INFO] 	 Killing All external provers ... 
% 120.44/20.27  % Time passed: 19781ms (effective reasoning time: 19100ms)
% 120.44/20.27  % 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)>
% 120.44/20.27  % Axioms used in derivation (31): thm_2Ebool_2EBOOL__CASES__AX, thm_2Ebool_2ENOT__CLAUSES, thm_2Ebool_2ECOND__CLAUSES, thm_2Earithmetic_2ETWO, thm_2Ebool_2EOR__CLAUSES, thm_2Earithmetic_2EADD__0, thm_2Ebool_2EAND__CLAUSES, thm_2Esat_2EOR__DUAL2, thm_2Earithmetic_2ELESS__MONO__EQ, thm_2Esat_2EAND__INV__IMP, thm_2Esat_2EOR__DUAL3, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2ECOND__RAND, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EIMP__F, thm_2Earithmetic_2EODD__EXISTS, thm_2Earithmetic_2EEVEN__EXISTS, thm_2Ebool_2EFALSITY, thm_2Eprim__rec_2ELESS__0, thm_2Earithmetic_2EONE, thm_2Ebool_2ECOND__EXPAND, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, thm_2Earithmetic_2EODD__EVEN, thm_2Ebool_2EF__IMP, thm_2Earithmetic_2EMOD__UNIQUE, thm_2Esat_2EAND__INV2, thm_2Earithmetic_2EMULT__COMM, thm_2Earithmetic_2EADD1, thm_2Ebool_2ECOND__RATOR, thm_2Earithmetic_2EEVEN__ODD
% 120.44/20.27  % No. of inferences in proof: 580
% 120.44/20.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19781 ms resp. 19100 ms w/o parsing
% 121.07/20.52  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 121.07/20.52  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------