TSTP Solution File: ITP011_1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP011_1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 22:21:32 EDT 2024

% Result   : Theorem 56.01s 23.31s
% Output   : Refutation 56.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :  122
% Syntax   : Number of formulae    :  252 (  86 unt;  68 typ;   0 def)
%            Number of atoms       :  620 ( 314 equ;   0 cnn)
%            Maximal formula atoms :   33 (   3 avg)
%            Number of connectives : 6557 ( 166   ~; 121   |; 157   &;5969   @)
%                                         (  36 <=>; 108  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :   42 (  42   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   65 (  62 usr;  36 con; 0-3 aty)
%            Number of variables   :  429 (   0   ^ 415   !;  14   ?; 429   :)

% Comments : 
%------------------------------------------------------------------------------
thf(u_type,type,
    u: $tType ).

thf(d_type,type,
    d: $tType ).

thf(du_type,type,
    du: $tType ).

thf(mono_2Etyop_2Emin_2Ebool_type,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(tyop_2Emin_2Ebool_type,type,
    tyop_2Emin_2Ebool: d ).

thf(tyop_2Emin_2Efun_type,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(tyop_2Eoption_2Eoption_type,type,
    tyop_2Eoption_2Eoption: d > d ).

thf(s_type,type,
    s: d > u > du ).

thf(app_2E2_type,type,
    app_2E2: du > du > u ).

thf(p_type,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

thf(combin_i_2E0_type,type,
    combin_i_2E0: u ).

thf(combin_k_2E0_type,type,
    combin_k_2E0: u ).

thf(combin_s_2E0_type,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0_type,type,
    c_2Ebool_2E_21_2E0: u ).

thf(c_2Ebool_2E_21_2E1_type,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(c_2Emin_2E_3D_2E0_type,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E2_type,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Ebool_2E_3F_2E0_type,type,
    c_2Ebool_2E_3F_2E0: u ).

thf(c_2Ebool_2E_3F_2E1_type,type,
    c_2Ebool_2E_3F_2E1: du > u ).

thf(c_2Eoption_2EIS__NONE_2E0_type,type,
    c_2Eoption_2EIS__NONE_2E0: u ).

thf(c_2Eoption_2EIS__NONE_2E1_type,type,
    c_2Eoption_2EIS__NONE_2E1: du > u ).

thf(c_2Eoption_2EIS__SOME_2E0_type,type,
    c_2Eoption_2EIS__SOME_2E0: u ).

thf(c_2Eoption_2EIS__SOME_2E1_type,type,
    c_2Eoption_2EIS__SOME_2E1: du > u ).

thf(c_2Eoption_2ENONE_2E0_type,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(c_2Eoption_2EOPTION__JOIN_2E0_type,type,
    c_2Eoption_2EOPTION__JOIN_2E0: u ).

thf(c_2Eoption_2EOPTION__JOIN_2E1_type,type,
    c_2Eoption_2EOPTION__JOIN_2E1: du > u ).

thf(c_2Eoption_2EOPTION__MAP_2E0_type,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

thf(c_2Eoption_2EOPTION__MAP_2E2_type,type,
    c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).

thf(c_2Eoption_2EOPTREL_2E0_type,type,
    c_2Eoption_2EOPTREL_2E0: u ).

thf(c_2Eoption_2EOPTREL_2E3_type,type,
    c_2Eoption_2EOPTREL_2E3: du > du > du > u ).

thf(c_2Eoption_2ESOME_2E0_type,type,
    c_2Eoption_2ESOME_2E0: u ).

thf(c_2Eoption_2ESOME_2E1_type,type,
    c_2Eoption_2ESOME_2E1: du > u ).

thf(c_2Eoption_2ETHE_2E0_type,type,
    c_2Eoption_2ETHE_2E0: u ).

thf(c_2Eoption_2ETHE_2E1_type,type,
    c_2Eoption_2ETHE_2E1: du > u ).

thf(c_2Eoption_2Eoption__CASE_2E0_type,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

thf(c_2Eoption_2Eoption__CASE_2E3_type,type,
    c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_type,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

thf(mono_2Ec_2Ebool_2E_2F_5C_2E0_type,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Ebool_2E_2F_5C_2E2_type,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E0_type,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E2_type,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Ebool_2EF_2E0_type,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Ebool_2ET_2E0_type,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Ebool_2E_5C_2F_2E0_type,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Ebool_2E_5C_2F_2E2_type,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Ebool_2E_7E_2E0_type,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

thf(mono_2Ec_2Ebool_2E_7E_2E1_type,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(i_mono_2Etyop_2Emin_2Ebool_type,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).

thf(j_mono_2Etyop_2Emin_2Ebool_type,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(sk1_type,type,
    sk1: d ).

thf(sk2_type,type,
    sk2: u ).

thf(sk3_type,type,
    sk3: d ).

thf(sk4_type,type,
    sk4: u ).

thf(sk5_type,type,
    sk5: u ).

thf(sk6_type,type,
    sk6: d ).

thf(sk7_type,type,
    sk7: u ).

thf(sk8_type,type,
    sk8: u ).

thf(sk9_type,type,
    sk9: d ).

thf(sk10_type,type,
    sk10: u ).

thf(sk11_type,type,
    sk11: u ).

thf(sk12_type,type,
    sk12: u ).

thf(1,conjecture,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2ET_2E0 )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2EF_2E0 )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
        = mono_2Ec_2Ebool_2EF_2E0 )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
        = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def) ).

thf(2,negated_conjecture,
    ~ ! [A: d,B: u,C: u,D: u] :
        ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET_2E0 )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2EF_2E0 )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
          = mono_2Ec_2Ebool_2EF_2E0 )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(56,plain,
    ~ ! [A: d,B: u,C: u,D: u] :
        ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET_2E0 )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2EF_2E0 )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
          = mono_2Ec_2Ebool_2EF_2E0 )
        & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
    <=> ( ( p @ A )
       => ( p @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).

thf(74,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
       => ( ( p @ A )
         => ( p @ B ) ) )
      & ( ( ( p @ A )
         => ( p @ B ) )
       => ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(75,plain,
    ( ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
        ( ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
       => ( ( p @ A )
         => ( p @ B ) ) )
    & ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
        ( ( ( p @ A )
         => ( p @ B ) )
       => ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[74]) ).

thf(78,plain,
    ! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
      | ~ ( p @ A )
      | ( p @ B ) ),
    inference(cnf,[status(esa)],[75]) ).

thf(51,axiom,
    ! [A: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).

thf(386,plain,
    ! [A: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(387,plain,
    ! [A: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ A ) ),
    inference(cnf,[status(esa)],[386]) ).

thf(388,plain,
    ! [A: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ A ) ),
    inference(lifteq,[status(thm)],[387]) ).

thf(26,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).

thf(246,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(247,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
      = A ),
    inference(cnf,[status(esa)],[246]) ).

thf(248,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
      = A ),
    inference(lifteq,[status(thm)],[247]) ).

thf(57,plain,
    ~ ( ! [A: d,B: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [A: d,B: u,C: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2EF_2E0 )
      & ! [A: d,B: u,C: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
          = mono_2Ec_2Ebool_2EF_2E0 )
      & ! [A: d,B: u,C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[56]) ).

thf(58,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2ET_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) ) )
     != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[57]) ).

thf(59,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2ET_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) ) )
     != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[58]) ).

thf(408,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2ET_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) )
     != ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ) ),
    inference(simp,[status(thm)],[59]) ).

thf(426,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A != mono_2Ec_2Ebool_2ET_2E0 )
      | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
       != mono_2Ec_2Ebool_2EF_2E0 )
      | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
       != mono_2Ec_2Ebool_2EF_2E0 )
      | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) )
       != ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) )
      | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
       != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[248,408]) ).

thf(452,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
     != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ) ),
    inference(simp,[status(thm)],[426]) ).

thf(460,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
     != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ) ),
    inference(simp,[status(thm)],[452]) ).

thf(496,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A != mono_2Ec_2Ebool_2EF_2E0 )
      | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
       != mono_2Ec_2Ebool_2EF_2E0 )
      | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
       != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
      | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
       != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) )
      | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
       != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[248,460]) ).

thf(502,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) )
     != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
    inference(simp,[status(thm)],[496]) ).

thf(513,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) )
     != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
    inference(simp,[status(thm)],[502]) ).

thf(695,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A != mono_2Ec_2Ebool_2EF_2E0 )
      | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
       != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
      | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
       != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
      | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) )
       != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) )
      | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
       != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[248,513]) ).

thf(702,plain,
    ( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
    | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) )
     != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
    inference(simp,[status(thm)],[695]) ).

thf(709,plain,
    ( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
    | ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) )
     != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
    inference(simp,[status(thm)],[702]) ).

thf(983,plain,
    ( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
    | ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
    inference(simp,[status(thm)],[709]) ).

thf(984,plain,
    ( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
    inference(simp,[status(thm)],[983]) ).

thf(16,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ! [F: u,G: u] :
          ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) )
        <=> ( ( s @ A @ F )
            = ( s @ A @ G ) ) )
      & ! [F: u] :
          ( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
          = ( s @ A @ F ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
         != ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
         != ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) ) )
          = mono_2Ec_2Ebool_2ET_2E0 )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2EF_2E0 )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ! [F: u] :
          ( ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
        <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
            = ( s @ B @ E ) ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
      & ! [F: u,G: u] :
          ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) ) )
          = ( s @ B @ F ) )
      & ! [F: u,G: u,H: u] :
          ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) @ ( s @ A @ F ) ) ) )
      & ! [F: u,G: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES) ).

thf(134,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ! [F: u,G: u] :
          ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) )
           => ( ( s @ A @ F )
              = ( s @ A @ G ) ) )
          & ( ( ( s @ A @ F )
              = ( s @ A @ G ) )
           => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) ) ) )
      & ! [F: u] :
          ( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
          = ( s @ A @ F ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
         != ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
         != ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) ) )
          = mono_2Ec_2Ebool_2ET_2E0 )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2EF_2E0 )
      & ! [F: u] :
          ( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
           => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
          & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
           => ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
      & ! [F: u] :
          ( ( ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
           => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
          & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
           => ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
            = ( s @ B @ E ) ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
      & ! [F: u] :
          ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
      & ! [F: u,G: u] :
          ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) ) )
          = ( s @ B @ F ) )
      & ! [F: u,G: u,H: u] :
          ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) @ ( s @ A @ F ) ) ) )
      & ! [F: u,G: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) )
      & ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [F: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(135,plain,
    ( ! [A: d,B: u,C: u] :
        ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) )
       => ( ( s @ A @ B )
          = ( s @ A @ C ) ) )
    & ! [A: d,B: u,C: u] :
        ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) ) )
    & ! [A: d,B: u] :
        ( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
        = ( s @ A @ B ) )
    & ~ ? [A: d,B: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) )
    & ~ ? [A: d,B: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
    & ! [A: d,B: u] :
        ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
        = mono_2Ec_2Ebool_2ET_2E0 )
    & ! [A: d] :
        ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2EF_2E0 )
    & ! [A: d,B: u] :
        ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
       => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
    & ! [A: d,B: u] :
        ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
       => ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ) )
    & ! [A: d,B: u] :
        ( ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
       => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
    & ! [A: d,B: u] :
        ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
       => ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ) )
    & ! [A: d,B: u] :
        ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
       => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
    & ! [A: d,B: u] :
        ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) )
    & ! [A: d,B: u] :
        ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) )
    & ! [A: d,B: d,C: u,D: u,E: u] :
        ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) ) ) ) )
       => ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
          = ( s @ B @ D ) ) )
    & ! [A: d,B: d,C: u,D: u,E: u] :
        ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) ) ) ) )
       => ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) ) ) ) ) ) )
    & ! [A: d,B: u,C: u] :
        ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) ) )
       => ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) )
    & ! [A: d,B: d,C: u,D: u] :
        ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ B @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) )
        = ( s @ B @ C ) )
    & ! [A: d,B: d,C: u,D: u,E: u] :
        ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) )
        = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ C ) ) ) )
    & ! [A: d,B: d,C: u,D: u] :
        ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ D ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
    & ! [A: d,B: d,C: u] :
        ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) )
    & ! [A: d] :
        ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
    & ! [A: d,B: u] :
        ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ),
    inference(miniscope,[status(thm)],[134]) ).

thf(148,plain,
    ! [A: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      = mono_2Ec_2Ebool_2EF_2E0 ),
    inference(cnf,[status(esa)],[135]) ).

thf(185,plain,
    ! [A: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      = mono_2Ec_2Ebool_2EF_2E0 ),
    inference(lifteq,[status(thm)],[148]) ).

thf(186,plain,
    ! [A: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
      = mono_2Ec_2Ebool_2EF_2E0 ),
    inference(simp,[status(thm)],[185]) ).

thf(39,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) ).

thf(333,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(27,axiom,
    ! [A: d,B: u] :
      ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
    <=> ? [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).

thf(249,plain,
    ! [A: d,B: u] :
      ( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
       => ? [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) )
      & ( ? [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
       => ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(34,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( mono_2Ec_2Ebool_2ET_2E0 = A )
      <=> ( p @ A ) )
      & ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
      <=> ( p @ A ) )
      & ( ( mono_2Ec_2Ebool_2EF_2E0 = A )
      <=> ~ ( p @ A ) )
      & ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
      <=> ~ ( p @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).

thf(276,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( mono_2Ec_2Ebool_2ET_2E0 = A )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( mono_2Ec_2Ebool_2ET_2E0 = A ) )
      & ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( A = mono_2Ec_2Ebool_2ET_2E0 ) )
      & ( ( mono_2Ec_2Ebool_2EF_2E0 = A )
       => ~ ( p @ A ) )
      & ( ~ ( p @ A )
       => ( mono_2Ec_2Ebool_2EF_2E0 = A ) )
      & ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
       => ~ ( p @ A ) )
      & ( ~ ( p @ A )
       => ( A = mono_2Ec_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(12,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ A )
        & ( p @ B ) )
    <=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).

thf(120,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
          & ( p @ B ) )
       => ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) )
      & ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) )
       => ( ( p @ A )
          & ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(48,axiom,
    p @ mono_2Ec_2Ebool_2ET_2E0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).

thf(379,plain,
    p @ mono_2Ec_2Ebool_2ET_2E0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(495,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
    inference(simp,[status(thm)],[460]) ).

thf(511,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
    inference(simp,[status(thm)],[495]) ).

thf(29,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
    <=> ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).

thf(257,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) ) )
      & ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) )
       => ( ( s @ A @ B )
          = ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(52,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) ).

thf(389,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(21,axiom,
    ! [A: d,B: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ B ) )
    <=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).

thf(230,plain,
    p @ mono_2Ec_2Ebool_2ET_2E0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(6,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
    <=> ~ ( p @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).

thf(81,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
       => ~ ( p @ A ) )
      & ( ~ ( p @ A )
       => ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(82,plain,
    ( ! [A: mono_2Etyop_2Emin_2Ebool] :
        ( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
       => ~ ( p @ A ) )
    & ! [A: mono_2Etyop_2Emin_2Ebool] :
        ( ~ ( p @ A )
       => ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) ) ) ),
    inference(miniscope,[status(thm)],[81]) ).

thf(84,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
      | ~ ( p @ A ) ),
    inference(cnf,[status(esa)],[82]) ).

thf(465,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
      | ( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
       != ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[230,84]) ).

thf(475,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
      | ( ( mono_2Ec_2Ebool_2E_7E_2E1 @ A )
       != mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(simp,[status(thm)],[465]) ).

thf(23,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(238,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(25,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).

thf(243,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(32,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(270,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(3,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
    <=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).

thf(60,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ ( p @ A )
       => ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) )
      & ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
       => ~ ( p @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(49,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a) ).

thf(380,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(35,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
          | ( p @ A ) )
      <=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
      & ( ( ( p @ A )
          | ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
      <=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
      & ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
          | ( p @ A ) )
      <=> ( p @ A ) )
      & ( ( ( p @ A )
          | ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
      <=> ( p @ A ) )
      & ( ( ( p @ A )
          | ( p @ A ) )
      <=> ( p @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).

thf(302,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
          | ( p @ A ) )
       => ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
      & ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
       => ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
          | ( p @ A ) ) )
      & ( ( ( p @ A )
          | ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
       => ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
      & ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
       => ( ( p @ A )
          | ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) )
      & ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
          | ( p @ A ) )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
          | ( p @ A ) ) )
      & ( ( ( p @ A )
          | ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( ( p @ A )
          | ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(53,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).

thf(392,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(4,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ A )
      <=> ( p @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).

thf(65,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
         => ( p @ B ) )
        & ( ( p @ B )
         => ( p @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(66,plain,
    ! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ B )
      | ~ ( p @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[65]) ).

thf(70,plain,
    ! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = B )
      | ~ ( p @ B )
      | ~ ( p @ A ) ),
    inference(lifteq,[status(thm)],[66]) ).

thf(8,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ ( mono_2Ec_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
    <=> ( ( p @ A )
        | ( p @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).

thf(92,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ ( mono_2Ec_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
       => ( ( p @ A )
          | ( p @ B ) ) )
      & ( ( ( p @ A )
          | ( p @ B ) )
       => ( p @ ( mono_2Ec_2Ebool_2E_5C_2F_2E2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(36,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).

thf(324,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(19,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
      | ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).

thf(224,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
      | ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(28,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).

thf(254,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(255,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
      = A ),
    inference(cnf,[status(esa)],[254]) ).

thf(256,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
      = A ),
    inference(lifteq,[status(thm)],[255]) ).

thf(41,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__NONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) ).

thf(339,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__NONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(61,plain,
    ( ! [A: mono_2Etyop_2Emin_2Ebool] :
        ( ~ ( p @ A )
       => ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) )
    & ! [A: mono_2Etyop_2Emin_2Ebool] :
        ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
       => ~ ( p @ A ) ) ),
    inference(miniscope,[status(thm)],[60]) ).

thf(62,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
      | ~ ( p @ A ) ),
    inference(cnf,[status(esa)],[61]) ).

thf(64,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
      | ~ ( p @ A ) ),
    inference(simp,[status(thm)],[62]) ).

thf(518,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
      | ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
       != ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[230,64]) ).

thf(526,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ A )
      | ( ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A )
       != mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(simp,[status(thm)],[518]) ).

thf(69,plain,
    ! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ A )
      | ( p @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[65]) ).

thf(73,plain,
    ! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = B )
      | ( p @ A )
      | ( p @ B ) ),
    inference(lifteq,[status(thm)],[69]) ).

thf(14,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ A @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) ).

thf(128,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ A @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(10,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ ( mono_2Ec_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
    <=> ( ( p @ A )
        & ( p @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).

thf(105,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ ( mono_2Ec_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
       => ( ( p @ A )
          & ( p @ B ) ) )
      & ( ( ( p @ A )
          & ( p @ B ) )
       => ( p @ ( mono_2Ec_2Ebool_2E_2F_5C_2E2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(55,axiom,
    ! [A: d,B: u] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).

thf(398,plain,
    ! [A: d,B: u] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(30,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a) ).

thf(264,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(24,axiom,
    ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).

thf(241,plain,
    ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(242,plain,
    ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ),
    inference(polarity_switch,[status(thm)],[241]) ).

thf(401,plain,
    ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
   != ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[230,242]) ).

thf(402,plain,
    mono_2Ec_2Ebool_2ET_2E0 != mono_2Ec_2Ebool_2EF_2E0,
    inference(simp,[status(thm)],[401]) ).

thf(17,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) ).

thf(204,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(225,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
      | ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(cnf,[status(esa)],[224]) ).

thf(226,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
      | ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
    inference(lifteq,[status(thm)],[225]) ).

thf(519,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
      | ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
       != ( p @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[230,64]) ).

thf(520,plain,
    ~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( mono_2Ec_2Ebool_2ET_2E0 ))]]) ).

thf(530,plain,
    ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ) )
   != ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[230,520]) ).

thf(533,plain,
    ( ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 )
   != mono_2Ec_2Ebool_2ET_2E0 ),
    inference(simp,[status(thm)],[530]) ).

thf(610,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
      | ( A
       != ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[226,533]) ).

thf(611,plain,
    ( ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 )
    = mono_2Ec_2Ebool_2EF_2E0 ),
    inference(pattern_uni,[status(thm)],[610:[bind(A,$thf( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ))]]) ).

thf(7,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ A )
        | ( p @ B ) )
    <=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).

thf(86,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
          | ( p @ B ) )
       => ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) )
      & ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) )
       => ( ( p @ A )
          | ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(244,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    inference(cnf,[status(esa)],[243]) ).

thf(245,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    inference(lifteq,[status(thm)],[244]) ).

thf(466,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
      | ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
       != ( p @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[230,84]) ).

thf(467,plain,
    ~ ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(pattern_uni,[status(thm)],[466:[bind(A,$thf( mono_2Ec_2Ebool_2ET_2E0 ))]]) ).

thf(477,plain,
    ( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ) )
   != ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[230,467]) ).

thf(479,plain,
    ( ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 )
   != mono_2Ec_2Ebool_2ET_2E0 ),
    inference(simp,[status(thm)],[477]) ).

thf(598,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
      | ( A
       != ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
    inference(paramod_ordered,[status(thm)],[226,479]) ).

thf(599,plain,
    ( ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 )
    = mono_2Ec_2Ebool_2EF_2E0 ),
    inference(pattern_uni,[status(thm)],[598:[bind(A,$thf( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ))]]) ).

thf(38,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) ).

thf(330,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(1260,plain,
    ! [B: u,A: d] :
      ( ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
        = ( s @ tyop_2Emin_2Ebool @ B ) )
      | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
       != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[186,388]) ).

thf(1261,plain,
    ! [A: d] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1260:[bind(A,$thf( F )),bind(B,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ F ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).

thf(1820,plain,
    ! [A: d] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
    inference(simp,[status(thm)],[1261]) ).

thf(43,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
          & ( p @ A ) )
      <=> ( p @ A ) )
      & ( ( ( p @ A )
          & ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
      <=> ( p @ A ) )
      & ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
          & ( p @ A ) )
      <=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
      & ( ( ( p @ A )
          & ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
      <=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
      & ( ( ( p @ A )
          & ( p @ A ) )
      <=> ( p @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).

thf(345,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
          & ( p @ A ) )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
          & ( p @ A ) ) )
      & ( ( ( p @ A )
          & ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
       => ( p @ A ) )
      & ( ( p @ A )
       => ( ( p @ A )
          & ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) )
      & ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
          & ( p @ A ) )
       => ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
      & ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
       => ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
          & ( p @ A ) ) )
      & ( ( ( p @ A )
          & ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
       => ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
      & ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
       => ( ( p @ A )
          & ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(44,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).

thf(367,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(31,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).

thf(267,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(47,axiom,
    ! [A: d,B: u] :
      ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
    <=> ! [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).

thf(374,plain,
    ! [A: d,B: u] :
      ( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
       => ! [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) )
      & ( ! [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
       => ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(42,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(342,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(63,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ A )
      | ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) ),
    inference(cnf,[status(esa)],[61]) ).

thf(694,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
    inference(simp,[status(thm)],[513]) ).

thf(707,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
    inference(simp,[status(thm)],[694]) ).

thf(37,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a) ).

thf(327,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(45,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).

thf(370,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(13,axiom,
    ! [A: d,B: mono_2Etyop_2Emin_2Ebool] :
      ( ? [C: u] : ( p @ B )
    <=> ( p @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__SIMP) ).

thf(127,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(40,axiom,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ A ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) ).

thf(336,plain,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ A ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(22,axiom,
    ! [A: d,B: u,C: u] :
      ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) )
    <=> ( ( s @ A @ B )
        = ( s @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).

thf(231,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) )
       => ( ( s @ A @ B )
          = ( s @ A @ C ) ) )
      & ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(9,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ A )
       => ( p @ B ) )
    <=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).

thf(99,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( p @ A )
         => ( p @ B ) )
       => ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) )
      & ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) )
       => ( ( p @ A )
         => ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(18,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ) )
    <=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
            = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
          & ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
            = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) ) )
        | ? [F: u,G: u] :
            ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
              = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ G ) ) ) )
            & ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def) ).

thf(207,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ) )
       => ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
              = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) ) )
          | ? [F: u,G: u] :
              ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
                = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
              & ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
                = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ G ) ) ) )
              & ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ) ) ) ) )
      & ( ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
              = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
            & ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
              = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) ) )
          | ? [F: u,G: u] :
              ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
                = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
              & ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
                = ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ G ) ) ) )
              & ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ) ) ) )
       => ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(50,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).

thf(383,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(33,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).

thf(273,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(46,axiom,
    p @ mono_2Ec_2Ebool_2ET_2E0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).

thf(373,plain,
    p @ mono_2Ec_2Ebool_2ET_2E0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(76,plain,
    ! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ A )
      | ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[75]) ).

thf(79,plain,
    ! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ A )
      | ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ),
    inference(simp,[status(thm)],[76]) ).

thf(143,plain,
    ! [B: u,A: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
      = mono_2Ec_2Ebool_2ET_2E0 ),
    inference(cnf,[status(esa)],[135]) ).

thf(194,plain,
    ! [B: u,A: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
      = mono_2Ec_2Ebool_2ET_2E0 ),
    inference(lifteq,[status(thm)],[143]) ).

thf(195,plain,
    ! [B: u,A: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
      = mono_2Ec_2Ebool_2ET_2E0 ),
    inference(simp,[status(thm)],[194]) ).

thf(409,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2ET_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[408]) ).

thf(415,plain,
    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2ET_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
     != mono_2Ec_2Ebool_2EF_2E0 )
    | ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
     != ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
    inference(simp,[status(thm)],[409]) ).

thf(54,axiom,
    ( ! [A: mono_2Etyop_2Emin_2Ebool] :
        ( ~ ~ ( p @ A )
      <=> ( p @ A ) )
    & ( ~ ( p @ mono_2Ec_2Ebool_2ET_2E0 )
    <=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
    & ( ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 )
    <=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).

thf(395,plain,
    ( ( ~ ( p @ mono_2Ec_2Ebool_2ET_2E0 )
     => ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
    & ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
     => ~ ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
    & ( ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 )
     => ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
    & ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
     => ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(15,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).

thf(131,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(11,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_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(111,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p @ A )
       => ( p @ B ) )
     => ( ( ( p @ B )
         => ( p @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(20,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
     => ( p @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).

thf(227,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
     => ( p @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(32704,plain,
    $false,
    inference(cvc4,[status(thm)],[56,78,388,984,186,333,249,408,276,120,379,511,709,257,389,460,475,238,84,243,74,248,270,60,380,302,392,70,92,65,324,224,256,339,526,134,73,128,105,398,513,264,64,402,59,204,611,86,81,230,245,599,330,1820,345,367,226,267,241,374,342,63,707,327,370,127,336,386,231,99,246,207,383,273,373,242,79,195,415,395,131,111,254,227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : ITP011_1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.15/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.39  % Computer : n019.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit : 300
% 0.17/0.39  % WCLimit  : 300
% 0.17/0.39  % DateTime : Sat May 18 18:18:24 EDT 2024
% 0.17/0.39  % CPUTime  : 
% 0.95/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.61/1.07  % [INFO] 	 Parsing done (167ms). 
% 1.61/1.08  % [INFO] 	 Running in sequential loop mode. 
% 2.02/1.32  % [INFO] 	 eprover registered as external prover. 
% 2.02/1.32  % [INFO] 	 cvc4 registered as external prover. 
% 2.02/1.32  % [INFO] 	 Scanning for conjecture ... 
% 2.39/1.45  % [INFO] 	 Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ... 
% 2.54/1.52  % [INFO] 	 Axiom selection finished. Selected 53 axioms (removed 0 axioms). 
% 3.01/1.63  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.01/1.64  % [INFO] 	 Type checking passed. 
% 3.01/1.64  % [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 ... 
% 5.02/2.18  % [INFO] 	 [Domain constraints] Detected constraint on mono_2Etyop_2Emin_2Ebool 
% 5.02/2.18  % [INFO] 	 [Domain constraints] dom(mono_2Etyop_2Emin_2Ebool) ⊆ {mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2EF_2E0} 
% 56.01/23.31  % External prover 'cvc4' found a proof!
% 56.01/23.31  % [INFO] 	 Killing All external provers ... 
% 56.01/23.31  % Time passed: 22758ms (effective reasoning time: 22225ms)
% 56.01/23.31  % 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)>
% 56.01/23.31  % Axioms used in derivation (53): arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a, thm_2Ebool_2ENOT__CLAUSES, reserved_2Eho_2Enotfalse, thm_2Ebool_2EREFL__CLAUSE, arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b, thm_2Eoption_2Eoption__CLAUSES, arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b, arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29, reserved_2Eho_2Ebool__cases__ax, thm_2Ebool_2EOR__CLAUSES, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a, ji_2Emono_2Etyop_2Emin_2Ebool, reserved_2Equant_2E_21, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EIMP__ANTISYM__AX, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b, reserved_2Equant_2E_3F, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, thm_2Eoption_2EOPTREL__def, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, thm_2Ebool_2EFALSITY, reserved_2Elogic_2E_3D, arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ebool_2ETRUTH, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, reserved_2Elogic_2E_7E, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, reserved_2Eho_2Eboolext, arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a, reserved_2Eho_2Eeq__ext, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Ebool_2EEXISTS__SIMP, arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a, arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b, ij_2Emono_2Etyop_2Emin_2Ebool, thm_2Ebool_2EAND__CLAUSES, reserved_2Elogic_2E_5C_2F, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 56.01/23.31  % No. of inferences in proof: 184
% 56.01/23.31  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22758 ms resp. 22225 ms w/o parsing
% 56.36/23.43  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 56.36/23.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------