%------------------------------------------------------------------------------
% File     : ITP010^7 : 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    : one.ax [Gau19]
%          : HL4010^7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   33 (  12 unt;  16 typ;   0 def)
%            Number of atoms       :   19 (   7 equ;   1 cnn)
%            Maximal formula atoms :    2 (   0 avg)
%            Number of connectives :   53 (   1   ~;   1   |;   1   &;  40   @)
%                                         (   8 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg;  40 nst)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   3 con; 0-4 aty)
%            Number of variables   :   46 (   3   ^  32   !;   3   ?;  46   :)
%                                         (   8  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: $tType > $tType > $tType ).

thf(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: $tType ).

thf(c_2Ebool_2E_21,type,
    c_2Ebool_2E_21: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Ebool_2E_2F_5C,type,
    c_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: 
      !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).

thf(c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(c_2Ebool_2E_3F,type,
    c_2Ebool_2E_3F: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Ebool_2E_3F_21,type,
    c_2Ebool_2E_3F_21: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Emin_2E_40,type,
    c_2Emin_2E_40: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).

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

thf(c_2Ebool_2ETYPE__DEFINITION,type,
    c_2Ebool_2ETYPE__DEFINITION: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > A_27a ) > $o ) ).

thf(c_2Ebool_2E_5C_2F,type,
    c_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(c_2Eone_2Eone,type,
    c_2Eone_2Eone: tyop_2Eone_2Eone ).

thf(c_2Eone_2Eone__CASE,type,
    c_2Eone_2Eone__CASE: 
      !>[A_27a: $tType] : ( tyop_2Eone_2Eone > A_27a > A_27a ) ).

thf(c_2Ebool_2E_7E,type,
    c_2Ebool_2E_7E: $o > $o ).

thf(logicdef_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(logicdef_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(logicdef_2E_7E,axiom,
    ! [V0: $o] :
      ( ( c_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(logicdef_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
      ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
    <=> ( V0 = V1 ) ) ).

thf(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
    <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
    <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(thm_2Eone_2Eone__TY__DEF,axiom,
    ? [V0rep: tyop_2Eone_2Eone > $o] :
      ( c_2Ebool_2ETYPE__DEFINITION @ $o @ tyop_2Eone_2Eone
      @ ^ [V1b: $o] : V1b
      @ V0rep ) ).

thf(thm_2Eone_2Eone__DEF,axiom,
    ( c_2Eone_2Eone
    = ( c_2Emin_2E_40 @ tyop_2Eone_2Eone
      @ ^ [V0x: tyop_2Eone_2Eone] : c_2Ebool_2ET ) ) ).

thf(thm_2Eone_2Eone__case__def,axiom,
    ! [A_27a: $tType,V0u: tyop_2Eone_2Eone,V1x: A_27a] :
      ( ( c_2Eone_2Eone__CASE @ A_27a @ V0u @ V1x )
      = V1x ) ).

thf(thm_2Eone_2Eone__axiom,axiom,
    ! [A_27a: $tType,V0f: A_27a > tyop_2Eone_2Eone,V1g: A_27a > tyop_2Eone_2Eone] : ( V0f = V1g ) ).

thf(thm_2Eone_2Eone,axiom,
    ! [V0v: tyop_2Eone_2Eone] : ( V0v = c_2Eone_2Eone ) ).

thf(thm_2Eone_2Eone__Axiom,axiom,
    ! [A_27a: $tType,V0e: A_27a] :
      ( c_2Ebool_2E_3F_21 @ ( tyop_2Eone_2Eone > A_27a )
      @ ^ [V1fn: tyop_2Eone_2Eone > A_27a] : ( c_2Emin_2E_3D @ A_27a @ ( V1fn @ c_2Eone_2Eone ) @ V0e ) ) ).

thf(thm_2Eone_2Eone__prim__rec,axiom,
    ! [A_27a: $tType,V0e: A_27a] :
    ? [V1fn: tyop_2Eone_2Eone > A_27a] :
      ( ( V1fn @ c_2Eone_2Eone )
      = V0e ) ).

thf(thm_2Eone_2Eone__induction,axiom,
    ! [V0P: tyop_2Eone_2Eone > $o] :
      ( ( V0P @ c_2Eone_2Eone )
     => ! [V1x: tyop_2Eone_2Eone] : ( V0P @ V1x ) ) ).

thf(thm_2Eone_2EFORALL__ONE,axiom,
    ! [V0P: tyop_2Eone_2Eone > $o] :
      ( ! [V1x: tyop_2Eone_2Eone] : ( V0P @ V1x )
    <=> ( V0P @ c_2Eone_2Eone ) ) ).

thf(thm_2Eone_2Eone__case__thm,axiom,
    ! [A_27a: $tType,V0x: A_27a] :
      ( ( c_2Eone_2Eone__CASE @ A_27a @ c_2Eone_2Eone @ V0x )
      = V0x ) ).

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