ITP001 Axioms: ITP020^7.ax
%------------------------------------------------------------------------------
% File : ITP020^7 : TPTP v8.2.0. 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 : basicSize.ax [Gau19]
% : HL4020^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 39 ( 8 unt; 27 typ; 0 def)
% Number of atoms : 16 ( 8 equ; 1 cnn)
% Maximal formula atoms : 2 ( 0 avg)
% Number of connectives : 86 ( 1 ~; 1 |; 3 &; 73 @)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg; 73 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 2 con; 0-5 aty)
% Number of variables : 53 ( 2 ^ 33 !; 1 ?; 53 :)
% ( 17 !>; 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_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
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_2Esum_2EINL,type,
c_2Esum_2EINL:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ).
thf(c_2Esum_2EINR,type,
c_2Esum_2EINR:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ).
thf(c_2Eoption_2ENONE,type,
c_2Eoption_2ENONE:
!>[A_27a: $tType] : ( tyop_2Eoption_2Eoption @ A_27a ) ).
thf(c_2Eoption_2ESOME,type,
c_2Eoption_2ESOME:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epair_2EUNCURRY,type,
c_2Epair_2EUNCURRY:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a > A_27b > A_27c ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27c ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2EbasicSize_2Ebool__size,type,
c_2EbasicSize_2Ebool__size: $o > tyop_2Enum_2Enum ).
thf(c_2EbasicSize_2Eone__size,type,
c_2EbasicSize_2Eone__size: tyop_2Eone_2Eone > tyop_2Enum_2Enum ).
thf(c_2EbasicSize_2Eoption__size,type,
c_2EbasicSize_2Eoption__size:
!>[A_27a: $tType] : ( ( A_27a > tyop_2Enum_2Enum ) > ( tyop_2Eoption_2Eoption @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2EbasicSize_2Epair__size,type,
c_2EbasicSize_2Epair__size:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > tyop_2Enum_2Enum ) > ( A_27b > tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > tyop_2Enum_2Enum ) ).
thf(c_2EbasicSize_2Esum__size,type,
c_2EbasicSize_2Esum__size:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > tyop_2Enum_2Enum ) > ( A_27b > tyop_2Enum_2Enum ) > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > tyop_2Enum_2Enum ) ).
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_2EbasicSize_2Ebool__size__def,axiom,
! [V0b: $o] :
( ( c_2EbasicSize_2Ebool__size @ V0b )
= c_2Enum_2E0 ) ).
thf(thm_2EbasicSize_2Epair__size__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > tyop_2Enum_2Enum,V1g: A_27b > tyop_2Enum_2Enum] :
( ( c_2EbasicSize_2Epair__size @ A_27a @ A_27b @ V0f @ V1g )
= ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ tyop_2Enum_2Enum
@ ^ [V2x: A_27a,V3y: A_27b] : ( c_2Earithmetic_2E_2B @ ( V0f @ V2x ) @ ( V1g @ V3y ) ) ) ) ).
thf(thm_2EbasicSize_2Eone__size__def,axiom,
! [V0x: tyop_2Eone_2Eone] :
( ( c_2EbasicSize_2Eone__size @ V0x )
= c_2Enum_2E0 ) ).
thf(thm_2EbasicSize_2Esum__size__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f: A_27a > tyop_2Enum_2Enum,V1g: A_27b > tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2EbasicSize_2Esum__size @ A_27a @ A_27b @ V0f @ V1g @ ( c_2Esum_2EINL @ A_27a @ A_27b @ V2x ) )
= ( V0f @ V2x ) )
& ! [V3f: A_27a > tyop_2Enum_2Enum,V4g: A_27b > tyop_2Enum_2Enum,V5y: A_27b] :
( ( c_2EbasicSize_2Esum__size @ A_27a @ A_27b @ V3f @ V4g @ ( c_2Esum_2EINR @ A_27a @ A_27b @ V5y ) )
= ( V4g @ V5y ) ) ) ).
thf(thm_2EbasicSize_2Eoption__size__def,axiom,
! [A_27a: $tType] :
( ! [V0f: A_27a > tyop_2Enum_2Enum] :
( ( c_2EbasicSize_2Eoption__size @ A_27a @ V0f @ ( c_2Eoption_2ENONE @ A_27a ) )
= c_2Enum_2E0 )
& ! [V1f: A_27a > tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2EbasicSize_2Eoption__size @ A_27a @ V1f @ ( c_2Eoption_2ESOME @ A_27a @ V2x ) )
= ( c_2Enum_2ESUC @ ( V1f @ V2x ) ) ) ) ).
%------------------------------------------------------------------------------