ITP001 Axioms: ITP007_4.ax


%------------------------------------------------------------------------------
% File     : ITP007_4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : sat.ax [Gau19]
%          : HL4007_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  116 (  21 unt;  56 typ;   0 def)
%            Number of atoms       :  189 (  30 equ)
%            Maximal formula atoms :   16 (   1 avg)
%            Number of connectives :  183 (  54   ~;  41   |;  21   &)
%                                         (  31 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    8 (   7 usr)
%            Number of type conns  :   45 (  28   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   48 (  48 usr;  21 con; 0-3 aty)
%            Number of variables   :  117 ( 116   !;   1   ?; 117   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(u,type,
    u: $tType ).

tff(d,type,
    d: $tType ).

tff(du,type,
    du: $tType ).

tff(mono_2Etyop_2Emin_2Ebool,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( d * d ) > d ).

tff(s,type,
    s: ( d * u ) > du ).

tff(app_2E2,type,
    app_2E2: ( du * du ) > u ).

tff(p,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,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 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,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 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,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 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,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 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,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 ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,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 ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,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 ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 > u ).

tff(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,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 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,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 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 ).

tff(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) )
     => ( s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ) ).

tff(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(reserved_2Eho_2Etruth,axiom,
    p(mono_2Ec_2Ebool_2ET_2E0) ).

tff(reserved_2Eho_2Enotfalse,axiom,
    ~ p(mono_2Ec_2Ebool_2EF_2E0) ).

tff(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

tff(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a: d,V0x_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ) ).

tff(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ) ).

tff(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] : ( s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ) ).

tff(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))
    <=> ( s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ) ).

tff(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
    <=> ! [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).

tff(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
    <=> ? [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,V0_2E0)))) = s(tyop_2Emin_2Ebool,V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: 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),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: 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)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),V0_2E0) ) ).

tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: 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(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: 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(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> 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,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))))) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> 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,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(X0_2E0,X1_2E0,X2_2E0) = 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_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> 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,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: 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(V0_2E0,V1_2E0))) = 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(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( 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(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool,V2_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V2_2E0)))) ) ).

tff(thm_2Esat_2EAND__IMP,axiom,
    ! [V0A_2E0: mono_2Etyop_2Emin_2Ebool,V1B_2E0: mono_2Etyop_2Emin_2Ebool,V2C_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p(V0A_2E0)
          & p(V1B_2E0) )
       => p(V2C_2E0) )
    <=> ( p(V0A_2E0)
       => ( p(V1B_2E0)
         => p(V2C_2E0) ) ) ) ).

tff(thm_2Esat_2ENOT__NOT,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ~ p(V0t_2E0)
    <=> p(V0t_2E0) ) ).

tff(thm_2Esat_2EAND__INV,axiom,
    ! [V0A_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ p(V0A_2E0)
        & p(V0A_2E0) )
    <=> p(mono_2Ec_2Ebool_2EF_2E0) ) ).

tff(thm_2Esat_2EAND__INV__IMP,axiom,
    ! [V0A_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(V0A_2E0)
     => ( ~ p(V0A_2E0)
       => p(mono_2Ec_2Ebool_2EF_2E0) ) ) ).

tff(thm_2Esat_2EOR__DUAL,axiom,
    ! [V0B_2E0: mono_2Etyop_2Emin_2Ebool,V1A_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ ( p(V1A_2E0)
            | p(V0B_2E0) )
       => p(mono_2Ec_2Ebool_2EF_2E0) )
    <=> ( ~ p(V1A_2E0)
       => ( ~ p(V0B_2E0)
         => p(mono_2Ec_2Ebool_2EF_2E0) ) ) ) ).

tff(thm_2Esat_2EOR__DUAL2,axiom,
    ! [V0B_2E0: mono_2Etyop_2Emin_2Ebool,V1A_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ ( p(V1A_2E0)
            | p(V0B_2E0) )
       => p(mono_2Ec_2Ebool_2EF_2E0) )
    <=> ( ( p(V1A_2E0)
         => p(mono_2Ec_2Ebool_2EF_2E0) )
       => ( ~ p(V0B_2E0)
         => p(mono_2Ec_2Ebool_2EF_2E0) ) ) ) ).

tff(thm_2Esat_2EOR__DUAL3,axiom,
    ! [V0B_2E0: mono_2Etyop_2Emin_2Ebool,V1A_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ ( ~ p(V1A_2E0)
            | p(V0B_2E0) )
       => p(mono_2Ec_2Ebool_2EF_2E0) )
    <=> ( p(V1A_2E0)
       => ( ~ p(V0B_2E0)
         => p(mono_2Ec_2Ebool_2EF_2E0) ) ) ) ).

tff(thm_2Esat_2EAND__INV2,axiom,
    ! [V0A_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ p(V0A_2E0)
       => p(mono_2Ec_2Ebool_2EF_2E0) )
     => ( ( p(V0A_2E0)
         => p(mono_2Ec_2Ebool_2EF_2E0) )
       => p(mono_2Ec_2Ebool_2EF_2E0) ) ) ).

tff(thm_2Esat_2ENOT__ELIM2,axiom,
    ! [V0A_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ p(V0A_2E0)
       => p(mono_2Ec_2Ebool_2EF_2E0) )
    <=> p(V0A_2E0) ) ).

tff(thm_2Esat_2EEQT__Imp1,axiom,
    ! [V0b_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(V0b_2E0)
     => ( V0b_2E0 = mono_2Ec_2Ebool_2ET_2E0 ) ) ).

tff(thm_2Esat_2EEQF__Imp1,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(V0t_2E0)
     => ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Esat_2Edc__eq,axiom,
    ! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( V1q_2E0 = V0r_2E0 ) )
    <=> ( ( p(V2p_2E0)
          | p(V1q_2E0)
          | p(V0r_2E0) )
        & ( p(V2p_2E0)
          | ~ p(V0r_2E0)
          | ~ p(V1q_2E0) )
        & ( p(V1q_2E0)
          | ~ p(V0r_2E0)
          | ~ p(V2p_2E0) )
        & ( p(V0r_2E0)
          | ~ p(V1q_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__conj,axiom,
    ! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( p(V1q_2E0)
          & p(V0r_2E0) ) )
    <=> ( ( p(V2p_2E0)
          | ~ p(V1q_2E0)
          | ~ p(V0r_2E0) )
        & ( p(V1q_2E0)
          | ~ p(V2p_2E0) )
        & ( p(V0r_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__disj,axiom,
    ! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( p(V1q_2E0)
          | p(V0r_2E0) ) )
    <=> ( ( p(V2p_2E0)
          | ~ p(V1q_2E0) )
        & ( p(V2p_2E0)
          | ~ p(V0r_2E0) )
        & ( p(V1q_2E0)
          | p(V0r_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__imp,axiom,
    ! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V2p_2E0)
      <=> ( p(V1q_2E0)
         => p(V0r_2E0) ) )
    <=> ( ( p(V2p_2E0)
          | p(V1q_2E0) )
        & ( p(V2p_2E0)
          | ~ p(V0r_2E0) )
        & ( ~ p(V1q_2E0)
          | p(V0r_2E0)
          | ~ p(V2p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__neg,axiom,
    ! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V1p_2E0)
      <=> ~ p(V0q_2E0) )
    <=> ( ( p(V1p_2E0)
          | p(V0q_2E0) )
        & ( ~ p(V0q_2E0)
          | ~ p(V1p_2E0) ) ) ) ).

tff(thm_2Esat_2Edc__cond,axiom,
    ! [V0s_2E0: mono_2Etyop_2Emin_2Ebool,V1r_2E0: mono_2Etyop_2Emin_2Ebool,V2q_2E0: mono_2Etyop_2Emin_2Ebool,V3p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V3p_2E0 = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool(V2q_2E0,V1r_2E0,V0s_2E0) )
    <=> ( ( p(V3p_2E0)
          | p(V2q_2E0)
          | ~ p(V0s_2E0) )
        & ( p(V3p_2E0)
          | ~ p(V1r_2E0)
          | ~ p(V2q_2E0) )
        & ( p(V3p_2E0)
          | ~ p(V1r_2E0)
          | ~ p(V0s_2E0) )
        & ( ~ p(V2q_2E0)
          | p(V1r_2E0)
          | ~ p(V3p_2E0) )
        & ( p(V2q_2E0)
          | p(V0s_2E0)
          | ~ p(V3p_2E0) ) ) ) ).

tff(thm_2Esat_2Epth__ni1,axiom,
    ! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p(V1p_2E0)
         => p(V0q_2E0) )
     => p(V1p_2E0) ) ).

tff(thm_2Esat_2Epth__ni2,axiom,
    ! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p(V1p_2E0)
         => p(V0q_2E0) )
     => ~ p(V0q_2E0) ) ).

tff(thm_2Esat_2Epth__no1,axiom,
    ! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p(V1p_2E0)
          | p(V0q_2E0) )
     => ~ p(V1p_2E0) ) ).

tff(thm_2Esat_2Epth__no2,axiom,
    ! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( p(V1p_2E0)
          | p(V0q_2E0) )
     => ~ p(V0q_2E0) ) ).

tff(thm_2Esat_2Epth__an1,axiom,
    ! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V1p_2E0)
        & p(V0q_2E0) )
     => p(V1p_2E0) ) ).

tff(thm_2Esat_2Epth__an2,axiom,
    ! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V1p_2E0)
        & p(V0q_2E0) )
     => p(V0q_2E0) ) ).

tff(thm_2Esat_2Epth__nn,axiom,
    ! [V0p_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ~ p(V0p_2E0)
     => p(V0p_2E0) ) ).

%------------------------------------------------------------------------------