TSTP Solution File: ITP021_3 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP021_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 22:22:01 EDT 2024

% Result   : Theorem 9.95s 3.85s
% Output   : Refutation 9.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   82
% Syntax   : Number of formulae    :  137 (  30 unt;  29 typ;   0 def)
%            Number of atoms       :  593 (  59 equ;   0 cnn)
%            Maximal formula atoms :   32 (   5 avg)
%            Number of connectives : 1742 ( 130   ~; 104   |; 118   &;1177   @)
%                                         (  44 <=>; 169  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  28 usr;  11 con; 0-4 aty)
%            Number of variables   :  237 (   0   ^ 218   !;   3   ?; 237   :)
%                                         (  16  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(tyop_2Eextreal_2Eextreal_type,type,
    tyop_2Eextreal_2Eextreal: $tType ).

thf(tyop_2Emin_2Ebool_type,type,
    tyop_2Emin_2Ebool: $tType ).

thf(app_2E2_type,type,
    app_2E2: 
      !>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ TA ) > TB > TA ) ).

thf(p_type,type,
    p: tyop_2Emin_2Ebool > $o ).

thf(combin_i_2E0_type,type,
    combin_i_2E0: 
      !>[TA: $tType] : ( tyop_2Emin_2Efun @ TA @ TA ) ).

thf(combin_k_2E0_type,type,
    combin_k_2E0: 
      !>[TA: $tType,TB: $tType] : ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) ) ).

thf(combin_s_2E0_type,type,
    combin_s_2E0: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) ) ).

thf(c_2Ebool_2E_21_2E0_type,type,
    c_2Ebool_2E_21_2E0: 
      !>[TA: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ).

thf(c_2Ebool_2E_21_2E1_type,type,
    c_2Ebool_2E_21_2E1: 
      !>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ) ).

thf(c_2Ebool_2E_2F_5C_2E0_type,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).

thf(c_2Ebool_2E_2F_5C_2E2_type,type,
    c_2Ebool_2E_2F_5C_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

thf(c_2Emin_2E_3D_2E0_type,type,
    c_2Emin_2E_3D_2E0: 
      !>[TA: $tType] : ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) ).

thf(c_2Emin_2E_3D_2E2_type,type,
    c_2Emin_2E_3D_2E2: 
      !>[TA: $tType] : ( TA > TA > tyop_2Emin_2Ebool ) ).

thf(c_2Emin_2E_3D_3D_3E_2E0_type,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).

thf(c_2Emin_2E_3D_3D_3E_2E2_type,type,
    c_2Emin_2E_3D_3D_3E_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

thf(c_2Ebool_2E_3F_2E0_type,type,
    c_2Ebool_2E_3F_2E0: 
      !>[TA: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ).

thf(c_2Ebool_2E_3F_2E1_type,type,
    c_2Ebool_2E_3F_2E1: 
      !>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ) ).

thf(c_2Ebool_2ECOND_2E0_type,type,
    c_2Ebool_2ECOND_2E0: 
      !>[TA: $tType] : ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) ) ) ).

thf(c_2Ebool_2ECOND_2E3_type,type,
    c_2Ebool_2ECOND_2E3: 
      !>[TA: $tType] : ( tyop_2Emin_2Ebool > TA > TA > TA ) ).

thf(c_2Ebool_2EF_2E0_type,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

thf(c_2Ebool_2ET_2E0_type,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

thf(c_2Ebool_2E_5C_2F_2E0_type,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).

thf(c_2Ebool_2E_5C_2F_2E2_type,type,
    c_2Ebool_2E_5C_2F_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

thf(c_2Eextreal_2Eextreal__le_2E0_type,type,
    c_2Eextreal_2Eextreal__le_2E0: tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ).

thf(c_2Eextreal_2Eextreal__le_2E2_type,type,
    c_2Eextreal_2Eextreal__le_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Emin_2Ebool ).

thf(c_2Eextreal_2Eextreal__max_2E0_type,type,
    c_2Eextreal_2Eextreal__max_2E0: tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ).

thf(c_2Eextreal_2Eextreal__max_2E2_type,type,
    c_2Eextreal_2Eextreal__max_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).

thf(c_2Ebool_2E_7E_2E0_type,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ).

thf(c_2Ebool_2E_7E_2E1_type,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

thf(47,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ~ ( ~ ( p @ B )
            | ( p @ A ) )
       => ( p @ c_2Ebool_2EF_2E0 ) )
    <=> ( ( p @ B )
       => ( ~ ( p @ A )
         => ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL3) ).

thf(385,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ~ ( ~ ( p @ B )
              | ( p @ A ) )
         => ( p @ c_2Ebool_2EF_2E0 ) )
       => ( ( p @ B )
         => ( ~ ( p @ A )
           => ( p @ c_2Ebool_2EF_2E0 ) ) ) )
      & ( ( ( p @ B )
         => ( ~ ( p @ A )
           => ( p @ c_2Ebool_2EF_2E0 ) ) )
       => ( ~ ( ~ ( p @ B )
              | ( p @ A ) )
         => ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(29,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( p @ c_2Ebool_2EF_2E0 )
     => ( p @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).

thf(185,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( p @ c_2Ebool_2EF_2E0 )
     => ( p @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(16,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
        | ( p @ B ) )
    <=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).

thf(106,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
          | ( p @ B ) )
       => ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) )
      & ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) )
       => ( ( p @ A )
          | ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2ET_2E0 @ A @ B )
        = A )
      & ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2EF_2E0 @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).

thf(65,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2ET_2E0 @ A @ B )
        = A )
      & ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2EF_2E0 @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(30,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
        | ( p @ B ) )
    <=> ( ( p @ B )
        | ( p @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__SYM) ).

thf(188,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
          | ( p @ B ) )
       => ( ( p @ B )
          | ( p @ A ) ) )
      & ( ( ( p @ B )
          | ( p @ A ) )
       => ( ( p @ A )
          | ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(54,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
        | ( p @ B )
        | ( p @ C ) )
    <=> ( ( p @ A )
        | ( p @ B )
        | ( p @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__ASSOC) ).

thf(471,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(35,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
     => ( ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EF__IMP) ).

thf(264,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
     => ( ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(40,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( p @ C )
      <=> ( ( p @ B )
         => ( p @ A ) ) )
    <=> ( ( ( p @ C )
          | ( p @ B ) )
        & ( ( p @ C )
          | ~ ( p @ A ) )
        & ( ~ ( p @ B )
          | ( p @ A )
          | ~ ( p @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).

thf(313,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( ( ( p @ C )
           => ( ( p @ B )
             => ( p @ A ) ) )
          & ( ( ( p @ B )
             => ( p @ A ) )
           => ( p @ C ) ) )
       => ( ( ( p @ C )
            | ( p @ B ) )
          & ( ( p @ C )
            | ~ ( p @ A ) )
          & ( ~ ( p @ B )
            | ( p @ A )
            | ~ ( p @ C ) ) ) )
      & ( ( ( ( p @ C )
            | ( p @ B ) )
          & ( ( p @ C )
            | ~ ( p @ A ) )
          & ( ~ ( p @ B )
            | ( p @ A )
            | ~ ( p @ C ) ) )
       => ( ( ( p @ C )
           => ( ( p @ B )
             => ( p @ A ) ) )
          & ( ( ( p @ B )
             => ( p @ A ) )
           => ( p @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(7,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ A @ B @ C )
      = ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( c_2Ebool_2ECOND_2E0 @ tyop_2Eextreal_2Eextreal ) @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal) ).

thf(76,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ A @ B @ C )
      = ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( c_2Ebool_2ECOND_2E0 @ tyop_2Eextreal_2Eextreal ) @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(17,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ~ ( ( p @ A )
            & ( p @ B ) )
      <=> ( ~ ( p @ A )
          | ~ ( p @ B ) ) )
      & ( ~ ( ( p @ A )
            | ( p @ B ) )
      <=> ( ~ ( p @ A )
          & ~ ( p @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDE__MORGAN__THM) ).

thf(112,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ~ ( ( p @ A )
            & ( p @ B ) )
       => ( ~ ( p @ A )
          | ~ ( p @ B ) ) )
      & ( ( ~ ( p @ A )
          | ~ ( p @ B ) )
       => ~ ( ( p @ A )
            & ( p @ B ) ) )
      & ( ~ ( ( p @ A )
            | ( p @ B ) )
       => ( ~ ( p @ A )
          & ~ ( p @ B ) ) )
      & ( ( ~ ( p @ A )
          & ~ ( p @ B ) )
       => ~ ( ( p @ A )
            | ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(23,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
       => ( p @ B ) )
     => ( ( ( p @ B )
         => ( p @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).

thf(146,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
       => ( p @ B ) )
     => ( ( ( p @ B )
         => ( p @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(21,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
    <=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).

thf(138,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ~ ( p @ A )
       => ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) ) )
      & ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
       => ~ ( p @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(14,axiom,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
      = ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).

thf(101,plain,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
      = ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(11,axiom,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2E_21_2E1 @ TA @ A )
      = ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E0 @ TA ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).

thf(88,plain,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2E_21_2E1 @ TA @ A )
      = ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E0 @ TA ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(45,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
    <=> ( ( p @ A )
        & ( p @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).

thf(372,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
       => ( ( p @ A )
          & ( p @ B ) ) )
      & ( ( ( p @ A )
          & ( p @ B ) )
       => ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(31,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
      <=> ( p @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).

thf(196,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
         => ( p @ B ) )
        & ( ( p @ B )
         => ( p @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(25,axiom,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B )
      = ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ c_2Eextreal_2Eextreal__le_2E0 @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eextreal_2Eextreal__le_2E2) ).

thf(157,plain,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B )
      = ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ c_2Eextreal_2Eextreal__le_2E0 @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(53,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ( ( p @ c_2Ebool_2ET_2E0 )
         => ( p @ A ) )
      <=> ( p @ A ) )
      & ( ( ( p @ A )
         => ( p @ c_2Ebool_2ET_2E0 ) )
      <=> ( p @ c_2Ebool_2ET_2E0 ) )
      & ( ( ( p @ c_2Ebool_2EF_2E0 )
         => ( p @ A ) )
      <=> ( p @ c_2Ebool_2ET_2E0 ) )
      & ( ( ( p @ A )
         => ( p @ A ) )
      <=> ( p @ c_2Ebool_2ET_2E0 ) )
      & ( ( ( p @ A )
         => ( p @ c_2Ebool_2EF_2E0 ) )
      <=> ~ ( p @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).

thf(448,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ( ( p @ c_2Ebool_2ET_2E0 )
         => ( p @ A ) )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( ( p @ c_2Ebool_2ET_2E0 )
         => ( p @ A ) ) )
      & ( ( ( p @ A )
         => ( p @ c_2Ebool_2ET_2E0 ) )
       => ( p @ c_2Ebool_2ET_2E0 ) )
      & ( ( p @ c_2Ebool_2ET_2E0 )
       => ( ( p @ A )
         => ( p @ c_2Ebool_2ET_2E0 ) ) )
      & ( ( ( p @ c_2Ebool_2EF_2E0 )
         => ( p @ A ) )
       => ( p @ c_2Ebool_2ET_2E0 ) )
      & ( ( p @ c_2Ebool_2ET_2E0 )
       => ( ( p @ c_2Ebool_2EF_2E0 )
         => ( p @ A ) ) )
      & ( p @ c_2Ebool_2ET_2E0 )
      & ( ( ( p @ A )
         => ( p @ c_2Ebool_2EF_2E0 ) )
       => ~ ( p @ A ) )
      & ( ~ ( p @ A )
       => ( ( p @ A )
         => ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(34,axiom,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) )
    <=> ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_3F) ).

thf(261,plain,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) )
       => ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) )
      & ( ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) )
       => ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(49,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ~ ~ ( p @ A )
    <=> ( p @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2ENOT__NOT) ).

thf(397,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(20,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D) ).

thf(132,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(48,axiom,
    p @ c_2Ebool_2ET_2E0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).

thf(396,plain,
    p @ c_2Ebool_2ET_2E0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(10,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ TA,B: tyop_2Emin_2Efun @ TB @ TA] :
      ( ! [C: TB] :
          ( ( app_2E2 @ TB @ TA @ A @ C )
          = ( app_2E2 @ TB @ TA @ B @ C ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).

thf(85,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ TA,B: tyop_2Emin_2Efun @ TB @ TA] :
      ( ! [C: TB] :
          ( ( app_2E2 @ TB @ TA @ A @ C )
          = ( app_2E2 @ TB @ TA @ B @ C ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(44,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( A = B )
    <=> ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).

thf(366,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( A = B )
       => ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) ) )
      & ( ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(26,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ~ ( ( p @ B )
            | ( p @ A ) )
       => ( p @ c_2Ebool_2EF_2E0 ) )
    <=> ( ( ( p @ B )
         => ( p @ c_2Ebool_2EF_2E0 ) )
       => ( ~ ( p @ A )
         => ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).

thf(160,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ~ ( ( p @ B )
              | ( p @ A ) )
         => ( p @ c_2Ebool_2EF_2E0 ) )
       => ( ( ( p @ B )
           => ( p @ c_2Ebool_2EF_2E0 ) )
         => ( ~ ( p @ A )
           => ( p @ c_2Ebool_2EF_2E0 ) ) ) )
      & ( ( ( ( p @ B )
           => ( p @ c_2Ebool_2EF_2E0 ) )
         => ( ~ ( p @ A )
           => ( p @ c_2Ebool_2EF_2E0 ) ) )
       => ( ~ ( ( p @ B )
              | ( p @ A ) )
         => ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(5,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( A = c_2Ebool_2ET_2E0 )
      | ( A = c_2Ebool_2EF_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).

thf(70,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( A = c_2Ebool_2ET_2E0 )
      | ( A = c_2Ebool_2EF_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA] :
      ( ( app_2E2 @ TA @ TA @ ( combin_i_2E0 @ TA ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).

thf(73,plain,
    ! [TA: $tType,A: TA] :
      ( ( app_2E2 @ TA @ TA @ ( combin_i_2E0 @ TA ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(36,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ~ ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) )
     => ( ( ( p @ A )
         => ( p @ c_2Ebool_2EF_2E0 ) )
       => ( p @ c_2Ebool_2EF_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV2) ).

thf(266,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ~ ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) )
     => ( ( ( p @ A )
         => ( p @ c_2Ebool_2EF_2E0 ) )
       => ( p @ c_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(32,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ( c_2Ebool_2ET_2E0 = A )
      <=> ( p @ A ) )
      & ( ( A = c_2Ebool_2ET_2E0 )
      <=> ( p @ A ) )
      & ( ( c_2Ebool_2EF_2E0 = A )
      <=> ~ ( p @ A ) )
      & ( ( A = c_2Ebool_2EF_2E0 )
      <=> ~ ( p @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).

thf(205,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ( c_2Ebool_2ET_2E0 = A )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( c_2Ebool_2ET_2E0 = A ) )
      & ( ( A = c_2Ebool_2ET_2E0 )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( A = c_2Ebool_2ET_2E0 ) )
      & ( ( c_2Ebool_2EF_2E0 = A )
       => ~ ( p @ A ) )
      & ( ~ ( p @ A )
       => ( c_2Ebool_2EF_2E0 = A ) )
      & ( ( A = c_2Ebool_2EF_2E0 )
       => ~ ( p @ A ) )
      & ( ~ ( p @ A )
       => ( A = c_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(50,axiom,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) )
    <=> ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_21) ).

thf(398,plain,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) )
       => ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) )
      & ( ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) )
       => ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(18,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) )
     => ~ ( p @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F) ).

thf(128,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) )
     => ~ ( p @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(41,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( p @ A )
     => ( ~ ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV__IMP) ).

thf(343,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( p @ A )
     => ( ~ ( p @ A )
       => ( p @ c_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(42,axiom,
    p @ c_2Ebool_2ET_2E0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).

thf(345,plain,
    p @ c_2Ebool_2ET_2E0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(12,axiom,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2E_3F_2E1 @ TA @ A )
      = ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E0 @ TA ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).

thf(91,plain,
    ! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
      ( ( c_2Ebool_2E_3F_2E1 @ TA @ A )
      = ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E0 @ TA ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(24,axiom,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
      | ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).

thf(155,plain,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
      | ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(27,axiom,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
      = ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ c_2Eextreal_2Eextreal__max_2E0 @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eextreal_2Eextreal__max_2E2) ).

thf(175,plain,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
      ( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
      = ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ c_2Eextreal_2Eextreal__max_2E0 @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(52,axiom,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
      ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
        & ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
     => ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).

thf(446,plain,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
      ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
        & ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
     => ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(22,axiom,
    ( ! [A: tyop_2Emin_2Ebool] :
        ( ~ ~ ( p @ A )
      <=> ( p @ A ) )
    & ( ~ ( p @ c_2Ebool_2ET_2E0 )
    <=> ( p @ c_2Ebool_2EF_2E0 ) )
    & ( ~ ( p @ c_2Ebool_2EF_2E0 )
    <=> ( p @ c_2Ebool_2ET_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).

thf(143,plain,
    ( ( ~ ( p @ c_2Ebool_2ET_2E0 )
     => ( p @ c_2Ebool_2EF_2E0 ) )
    & ( ( p @ c_2Ebool_2EF_2E0 )
     => ~ ( p @ c_2Ebool_2ET_2E0 ) )
    & ( ~ ( p @ c_2Ebool_2EF_2E0 )
     => ( p @ c_2Ebool_2ET_2E0 ) )
    & ( ( p @ c_2Ebool_2ET_2E0 )
     => ~ ( p @ c_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(33,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( p @ C )
      <=> ( ( p @ B )
          | ( p @ A ) ) )
    <=> ( ( ( p @ C )
          | ~ ( p @ B ) )
        & ( ( p @ C )
          | ~ ( p @ A ) )
        & ( ( p @ B )
          | ( p @ A )
          | ~ ( p @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).

thf(231,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( ( ( p @ C )
           => ( ( p @ B )
              | ( p @ A ) ) )
          & ( ( ( p @ B )
              | ( p @ A ) )
           => ( p @ C ) ) )
       => ( ( ( p @ C )
            | ~ ( p @ B ) )
          & ( ( p @ C )
            | ~ ( p @ A ) )
          & ( ( p @ B )
            | ( p @ A )
            | ~ ( p @ C ) ) ) )
      & ( ( ( ( p @ C )
            | ~ ( p @ B ) )
          & ( ( p @ C )
            | ~ ( p @ A ) )
          & ( ( p @ B )
            | ( p @ A )
            | ~ ( p @ C ) ) )
       => ( ( ( p @ C )
           => ( ( p @ B )
              | ( p @ A ) ) )
          & ( ( ( p @ B )
              | ( p @ A ) )
           => ( p @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(15,axiom,
    ~ ( p @ c_2Ebool_2EF_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).

thf(104,plain,
    ~ ( p @ c_2Ebool_2EF_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1,conjecture,
    ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
      ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
    <=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
        & ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).

thf(2,negated_conjecture,
    ~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
        ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
      <=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
          & ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(55,plain,
    ~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
        ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
         => ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
            & ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) )
        & ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
            & ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) )
         => ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(51,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( p @ C )
      <=> ( B = A ) )
    <=> ( ( ( p @ C )
          | ( p @ B )
          | ( p @ A ) )
        & ( ( p @ C )
          | ~ ( p @ A )
          | ~ ( p @ B ) )
        & ( ( p @ B )
          | ~ ( p @ A )
          | ~ ( p @ C ) )
        & ( ( p @ A )
          | ~ ( p @ B )
          | ~ ( p @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).

thf(401,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( ( ( p @ C )
           => ( B = A ) )
          & ( ( B = A )
           => ( p @ C ) ) )
       => ( ( ( p @ C )
            | ( p @ B )
            | ( p @ A ) )
          & ( ( p @ C )
            | ~ ( p @ A )
            | ~ ( p @ B ) )
          & ( ( p @ B )
            | ~ ( p @ A )
            | ~ ( p @ C ) )
          & ( ( p @ A )
            | ~ ( p @ B )
            | ~ ( p @ C ) ) ) )
      & ( ( ( ( p @ C )
            | ( p @ B )
            | ( p @ A ) )
          & ( ( p @ C )
            | ~ ( p @ A )
            | ~ ( p @ B ) )
          & ( ( p @ B )
            | ~ ( p @ A )
            | ~ ( p @ C ) )
          & ( ( p @ A )
            | ~ ( p @ B )
            | ~ ( p @ C ) ) )
       => ( ( ( p @ C )
           => ( B = A ) )
          & ( ( B = A )
           => ( p @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(46,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
    <=> ( ( p @ A )
        | ( p @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).

thf(378,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
       => ( ( p @ A )
          | ( p @ B ) ) )
      & ( ( ( p @ A )
          | ( p @ B ) )
       => ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(37,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
    <=> ~ ( p @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_7E) ).

thf(272,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
       => ~ ( p @ A ) )
      & ( ~ ( p @ A )
       => ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(43,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ B )
      <=> ~ ( p @ A ) )
    <=> ( ( ( p @ B )
          | ( p @ A ) )
        & ( ~ ( p @ A )
          | ~ ( p @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__neg) ).

thf(346,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ( ( p @ B )
           => ~ ( p @ A ) )
          & ( ~ ( p @ A )
           => ( p @ B ) ) )
       => ( ( ( p @ B )
            | ( p @ A ) )
          & ( ~ ( p @ A )
            | ~ ( p @ B ) ) ) )
      & ( ( ( ( p @ B )
            | ( p @ A ) )
          & ( ~ ( p @ A )
            | ~ ( p @ B ) ) )
       => ( ( ( p @ B )
           => ~ ( p @ A ) )
          & ( ~ ( p @ A )
           => ( p @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(9,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( app_2E2 @ TA @ TB @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) @ ( combin_k_2E0 @ TB @ TA ) @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).

thf(82,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( app_2E2 @ TA @ TB @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) @ ( combin_k_2E0 @ TB @ TA ) @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(8,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ),B: tyop_2Emin_2Efun @ TC @ TB,C: TC] :
      ( ( app_2E2 @ TC @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) @ ( combin_s_2E0 @ TC @ TB @ TA ) @ A ) @ B ) @ C )
      = ( app_2E2 @ TB @ TA @ ( app_2E2 @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ C ) @ ( app_2E2 @ TC @ TB @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).

thf(79,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ),B: tyop_2Emin_2Efun @ TC @ TB,C: TC] :
      ( ( app_2E2 @ TC @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) @ ( combin_s_2E0 @ TC @ TB @ TA ) @ A ) @ B ) @ C )
      = ( app_2E2 @ TB @ TA @ ( app_2E2 @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ C ) @ ( app_2E2 @ TC @ TB @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(13,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
        & ( p @ B ) )
    <=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).

thf(94,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
          & ( p @ B ) )
       => ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) )
      & ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) )
       => ( ( p @ A )
          & ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(39,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( p @ C )
      <=> ( ( p @ B )
          & ( p @ A ) ) )
    <=> ( ( ( p @ C )
          | ~ ( p @ B )
          | ~ ( p @ A ) )
        & ( ( p @ B )
          | ~ ( p @ C ) )
        & ( ( p @ A )
          | ~ ( p @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__conj) ).

thf(283,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
      ( ( ( ( ( p @ C )
           => ( ( p @ B )
              & ( p @ A ) ) )
          & ( ( ( p @ B )
              & ( p @ A ) )
           => ( p @ C ) ) )
       => ( ( ( p @ C )
            | ~ ( p @ B )
            | ~ ( p @ A ) )
          & ( ( p @ B )
            | ~ ( p @ C ) )
          & ( ( p @ A )
            | ~ ( p @ C ) ) ) )
      & ( ( ( ( p @ C )
            | ~ ( p @ B )
            | ~ ( p @ A ) )
          & ( ( p @ B )
            | ~ ( p @ C ) )
          & ( ( p @ A )
            | ~ ( p @ C ) ) )
       => ( ( ( p @ C )
           => ( ( p @ B )
              & ( p @ A ) ) )
          & ( ( ( p @ B )
              & ( p @ A ) )
           => ( p @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(19,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( p @ A )
      | ~ ( p @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXCLUDED__MIDDLE) ).

thf(131,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(3,axiom,
    ! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
      ( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ C )
      = ( app_2E2 @ TA @ TA @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) ) @ ( c_2Ebool_2ECOND_2E0 @ TA ) @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).

thf(62,plain,
    ! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
      ( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ C )
      = ( app_2E2 @ TA @ TA @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) ) @ ( c_2Ebool_2ECOND_2E0 @ TA ) @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(28,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
    <=> ( ( p @ A )
       => ( p @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).

thf(178,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
       => ( ( p @ A )
         => ( p @ B ) ) )
      & ( ( ( p @ A )
         => ( p @ B ) )
       => ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(38,axiom,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( p @ A )
       => ( p @ B ) )
    <=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).

thf(277,plain,
    ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
         => ( p @ B ) )
       => ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) )
      & ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) )
       => ( ( p @ A )
         => ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(699,plain,
    $false,
    inference(cvc4,[status(thm)],[385,185,106,65,188,471,264,313,76,112,146,138,101,88,372,196,157,448,261,397,132,396,85,366,160,70,73,266,205,398,128,343,345,91,155,175,446,143,231,104,55,401,378,272,346,82,79,94,283,131,62,178,277]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP021_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n009.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sat May 18 16:20:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.86/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/1.00  % [INFO] 	 Parsing done (149ms). 
% 1.18/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.88/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.88/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.88/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ... 
% 2.17/1.33  % [INFO] 	 Axiom selection finished. Selected 52 axioms (removed 1 axioms). 
% 2.43/1.40  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.43/1.42  % [INFO] 	 Type checking passed. 
% 2.43/1.42  % [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 ... 
% 2.91/1.58  % [INFO] 	 [Domain constraints] Detected constraint on tyop_2Emin_2Ebool 
% 2.91/1.58  % [INFO] 	 [Domain constraints] dom(tyop_2Emin_2Ebool) ⊆ {c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0} 
% 9.95/3.85  % External prover 'cvc4' found a proof!
% 9.95/3.85  % [INFO] 	 Killing All external provers ... 
% 9.95/3.85  % Time passed: 3332ms (effective reasoning time: 2836ms)
% 9.95/3.85  % 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)>
% 9.95/3.85  % Axioms used in derivation (52): thm_2Ebool_2EDISJ__SYM, thm_2Eextra_2Dho_2Eboolext, thm_2Esat_2Edc__conj, arityeq2_2Ec_2Eextreal_2Eextreal__max_2E2, thm_2Ebool_2EFALSITY, thm_2Eextra_2Dho_2Ek__thm, thm_2Ebool_2ECOND__CLAUSES, thm_2Ebool_2EF__IMP, logicdef_2E_3D_3D_3E, thm_2Esat_2ENOT__NOT, thm_2Eextra_2Dho_2Etruth, thm_2Eextreal_2Ele__total, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, thm_2Eextreal_2Eextreal__max__def, logicdef_2E_7E, quantdef_2E_3F, thm_2Eextra_2Dho_2Eeq__ext, thm_2Ebool_2ENOT__CLAUSES, thm_2Esat_2EAND__INV__IMP, thm_2Esat_2EOR__DUAL3, logicdef_2E_3D, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EIMP__ANTISYM__AX, thm_2Eextra_2Dho_2Ei__thm, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, thm_2Eextra_2Dho_2Ebool__cases__ax, thm_2Esat_2Edc__eq, thm_2Ebool_2EIMP__F, thm_2Esat_2Edc__imp, logicdef_2E_5C_2F, thm_2Eextreal_2Ele__trans, thm_2Eextra_2Dho_2Enotfalse, thm_2Esat_2Edc__neg, quantdef_2E_21, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal, arityeq2_2Ec_2Eextreal_2Eextreal__le_2E2, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, thm_2Ebool_2EEXCLUDED__MIDDLE, thm_2Ebool_2EDE__MORGAN__THM, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, thm_2Esat_2EAND__INV2, thm_2Ebool_2EDISJ__ASSOC, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Esat_2EOR__DUAL2, logicdef_2E_2F_5C, thm_2Eextra_2Dho_2Es__thm, thm_2Esat_2Edc__disj
% 9.95/3.85  % No. of inferences in proof: 108
% 9.95/3.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3332 ms resp. 2836 ms w/o parsing
% 9.95/3.89  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.95/3.89  % [INFO] 	 Killing All external provers ... 
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