ITP001 Axioms: ITP020_5.ax


%------------------------------------------------------------------------------
% File     : ITP020_5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : basicSize_2.ax [Gau20]
%          : HL4020_5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   23 (   9 unt;   9 typ;   0 def)
%            Number of atoms       :  142 (  11 equ)
%            Maximal formula atoms :    8 (   6 avg)
%            Number of connectives :   18 (   0   ~;   0   |;   2   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :  110 ( 110 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   16 (   7   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   26 (  25 usr;  10 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-5 aty)
%            Number of variables   :   36 (  36   !;   0   ?;  36   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2EbasicSize_2Ebool__size,type,
    c_2EbasicSize_2Ebool__size: $i ).

tff(mem_c_2EbasicSize_2Ebool__size,axiom,
    mem(c_2EbasicSize_2Ebool__size,arr(bool,ty_2Enum_2Enum)) ).

tff(stp_fo_c_2EbasicSize_2Ebool__size,type,
    fo__c_2EbasicSize_2Ebool__size: tp__o > tp__ty_2Enum_2Enum ).

tff(stp_eq_fo_c_2EbasicSize_2Ebool__size,axiom,
    ! [X0: tp__o] : ( inj__ty_2Enum_2Enum(fo__c_2EbasicSize_2Ebool__size(X0)) = ap(c_2EbasicSize_2Ebool__size,inj__o(X0)) ) ).

tff(tp_c_2EbasicSize_2Eone__size,type,
    c_2EbasicSize_2Eone__size: $i ).

tff(mem_c_2EbasicSize_2Eone__size,axiom,
    mem(c_2EbasicSize_2Eone__size,arr(ty_2Eone_2Eone,ty_2Enum_2Enum)) ).

tff(stp_fo_c_2EbasicSize_2Eone__size,type,
    fo__c_2EbasicSize_2Eone__size: tp__ty_2Eone_2Eone > tp__ty_2Enum_2Enum ).

tff(stp_eq_fo_c_2EbasicSize_2Eone__size,axiom,
    ! [X0: tp__ty_2Eone_2Eone] : ( inj__ty_2Enum_2Enum(fo__c_2EbasicSize_2Eone__size(X0)) = ap(c_2EbasicSize_2Eone__size,inj__ty_2Eone_2Eone(X0)) ) ).

tff(tp_c_2EbasicSize_2Eoption__size,type,
    c_2EbasicSize_2Eoption__size: del > $i ).

tff(mem_c_2EbasicSize_2Eoption__size,axiom,
    ! [A_27a: del] : mem(c_2EbasicSize_2Eoption__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Eoption_2Eoption(A_27a),ty_2Enum_2Enum))) ).

tff(tp_c_2EbasicSize_2Epair__size,type,
    c_2EbasicSize_2Epair__size: ( del * del ) > $i ).

tff(mem_c_2EbasicSize_2Epair__size,axiom,
    ! [A_27a: del,A_27b: del] : mem(c_2EbasicSize_2Epair__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum)))) ).

tff(tp_c_2EbasicSize_2Esum__size,type,
    c_2EbasicSize_2Esum__size: ( del * del ) > $i ).

tff(mem_c_2EbasicSize_2Esum__size,axiom,
    ! [A_27a: del,A_27b: del] : mem(c_2EbasicSize_2Esum__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Esum_2Esum(A_27a,A_27b),ty_2Enum_2Enum)))) ).

tff(ax_thm_2EbasicSize_2Ebool__size__def,axiom,
    ! [V0b: tp__o] : ( surj__ty_2Enum_2Enum(ap(c_2EbasicSize_2Ebool__size,inj__o(V0b))) = fo__c_2Enum_2E0 ) ).

tff(lamtp_f226,type,
    f226: ( del * del * $i * $i * $i ) > $i ).

tff(lameq_f226,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
     => ! [V2x: $i] :
          ( mem(V2x,A_27a)
         => ! [V1g: $i] :
              ( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
             => ! [V3y: $i] : ( ap(f226(A_27a,A_27b,V0f,V2x,V1g),V3y) = ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V2x)),ap(V1g,V3y)) ) ) ) ) ).

tff(lamtp_f227,type,
    f227: ( del * del * $i * $i ) > $i ).

tff(lameq_f227,axiom,
    ! [A_27b: del,A_27a: del,V0f: $i] :
      ( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
     => ! [V1g: $i] :
          ( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
         => ! [V2x: $i] : ( ap(f227(A_27b,A_27a,V0f,V1g),V2x) = f226(A_27a,A_27b,V0f,V2x,V1g) ) ) ) ).

tff(ax_thm_2EbasicSize_2Epair__size__def,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
     => ! [V1g: $i] :
          ( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
         => ( ap(ap(c_2EbasicSize_2Epair__size(A_27a,A_27b),V0f),V1g) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Enum_2Enum),f227(A_27b,A_27a,V0f,V1g)) ) ) ) ).

tff(ax_thm_2EbasicSize_2Eone__size__def,axiom,
    ! [V0x: tp__ty_2Eone_2Eone] : ( surj__ty_2Enum_2Enum(ap(c_2EbasicSize_2Eone__size,inj__ty_2Eone_2Eone(V0x))) = fo__c_2Enum_2E0 ) ).

tff(ax_thm_2EbasicSize_2Esum__size__def,axiom,
    ! [A_27a: del,A_27b: del] :
      ( ! [V0f: $i] :
          ( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
         => ! [V1g: $i] :
              ( mem(V1g,arr(A_27b,ty_2Enum_2Enum))
             => ! [V2x: $i] :
                  ( mem(V2x,A_27a)
                 => ( surj__ty_2Enum_2Enum(ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V0f),V1g),ap(c_2Esum_2EINL(A_27a,A_27b),V2x))) = surj__ty_2Enum_2Enum(ap(V0f,V2x)) ) ) ) )
      & ! [V3f: $i] :
          ( mem(V3f,arr(A_27a,ty_2Enum_2Enum))
         => ! [V4g: $i] :
              ( mem(V4g,arr(A_27b,ty_2Enum_2Enum))
             => ! [V5y: $i] :
                  ( mem(V5y,A_27b)
                 => ( surj__ty_2Enum_2Enum(ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V3f),V4g),ap(c_2Esum_2EINR(A_27a,A_27b),V5y))) = surj__ty_2Enum_2Enum(ap(V4g,V5y)) ) ) ) ) ) ).

tff(ax_thm_2EbasicSize_2Eoption__size__def,axiom,
    ! [A_27a: del] :
      ( ! [V0f: $i] :
          ( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
         => ( surj__ty_2Enum_2Enum(ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V0f),c_2Eoption_2ENONE(A_27a))) = fo__c_2Enum_2E0 ) )
      & ! [V1f: $i] :
          ( mem(V1f,arr(A_27a,ty_2Enum_2Enum))
         => ! [V2x: $i] :
              ( mem(V2x,A_27a)
             => ( surj__ty_2Enum_2Enum(ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V1f),ap(c_2Eoption_2ESOME(A_27a),V2x))) = surj__ty_2Enum_2Enum(ap(c_2Enum_2ESUC,ap(V1f,V2x))) ) ) ) ) ).

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