ITP001 Axioms: ITP020^5.ax
%------------------------------------------------------------------------------
% File : ITP020^5 : TPTP v8.2.0. 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 : 17 ( 2 unt; 6 typ; 0 def)
% Number of atoms : 124 ( 8 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 192 ( 0 ~; 0 |; 2 &; 178 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg; 178 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 30 usr; 26 con; 0-2 aty)
% Number of variables : 26 ( 2 ^ 24 !; 0 ?; 26 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EbasicSize_2Ebool__size,type,
c_2EbasicSize_2Ebool__size: $i ).
thf(mem_c_2EbasicSize_2Ebool__size,axiom,
mem @ c_2EbasicSize_2Ebool__size @ ( arr @ bool @ ty_2Enum_2Enum ) ).
thf(tp_c_2EbasicSize_2Eone__size,type,
c_2EbasicSize_2Eone__size: $i ).
thf(mem_c_2EbasicSize_2Eone__size,axiom,
mem @ c_2EbasicSize_2Eone__size @ ( arr @ ty_2Eone_2Eone @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2EbasicSize_2Eone__size,type,
fo__c_2EbasicSize_2Eone__size: tp__ty_2Eone_2Eone > tp__ty_2Enum_2Enum ).
thf(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 ) ) ) ).
thf(tp_c_2EbasicSize_2Eoption__size,type,
c_2EbasicSize_2Eoption__size: del > $i ).
thf(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 ) ) ) ).
thf(tp_c_2EbasicSize_2Epair__size,type,
c_2EbasicSize_2Epair__size: del > del > $i ).
thf(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 ) ) ) ) ).
thf(tp_c_2EbasicSize_2Esum__size,type,
c_2EbasicSize_2Esum__size: del > del > $i ).
thf(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 ) ) ) ) ).
thf(ax_thm_2EbasicSize_2Ebool__size__def,axiom,
! [V0b: $i] :
( ( mem @ V0b @ bool )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EbasicSize_2Ebool__size @ V0b ) )
= fo__c_2Enum_2E0 ) ) ).
thf(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 )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( lam @ A_27b
@ ^ [V3y: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V2x ) ) @ ( ap @ V1g @ V3y ) ) ) ) ) ) ) ) ).
thf(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 ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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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